
==== Front
Commun Earth Environ
Commun Earth Environ
Communications Earth & Environment
2662-4435
Nature Publishing Group UK London

1653
10.1038/s43247-024-01653-8
Article
Strong bottom currents in large, deep Lake Geneva generated by higher vertical-mode Poincaré waves
http://orcid.org/0000-0002-5000-6799
Reiss Rafael Sebastian rr704@cam.ac.uk

12
Lemmin Ulrich 1
http://orcid.org/0009-0008-4315-4137
Monin Claire 13
http://orcid.org/0000-0002-8621-0425
Barry David Andrew andrew.barry@epfl.ch

1
1 https://ror.org/02s376052 grid.5333.6 0000 0001 2183 9049 Ecological Engineering Laboratory (ECOL), Institute of Environmental Engineering (IIE), Faculty of Architecture, Civil and Environmental Engineering (ENAC), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
2 https://ror.org/013meh722 grid.5335.0 0000 0001 2188 5934 Present Address: Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ UK
3 https://ror.org/03nh7d505 grid.16068.39 0000 0001 2203 9289 Present Address: Research Laboratory in Hydrodynamics, Energetics and Atmospheric Environment (LHEEA), Ecole Centrale de Nantes, UMR CNRS 6598, 44321 Nantes, France
3 9 2024
3 9 2024
2024
5 1 48024 11 2023
27 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by/4.0/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Although internal seiches are ubiquitous in large, deep lakes, little is known about the effect of higher vertical-mode seiches on deepwater dynamics. Here, by combining entire summer season current and temperature observations and 3D numerical modeling, we demonstrate that previously undetected vertical mode-two and mode-three Poincaré waves in 309-meter deep Lake Geneva (Switzerland/France) generate bottom-boundary layer currents up to 4 cm s−1. Poincaré wave amphidromic patterns revealed three strong cells excited simultaneously. Weak hypolimnetic stratification (N2 ≈ 10−6 s−2), typical of deep lakes, significantly modified the wave structure by shifting the lower vertical node in the lake’s center from ~75-meter depth (without stratification) to ~150-meter depth (with stratification). This shift induces shear in the middle of the hypolimnion and strengthens bottom currents, with important implications for hypolimnetic mixing and sediment-water exchange. Our findings demonstrate that classical concepts based on constant temperature layers cannot correctly characterize higher vertical-mode Poincaré seiches in deep lakes.

Higher vertical-mode Poincaré waves in Lake Geneva generate strong bottom boundary layer currents which have significant implications for sediment dynamics and oxygen consumption, according to analysis of summer observations and 3D numerical modelling.

Subject terms

Limnology
Physical oceanography
https://doi.org/10.13039/501100001711 Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (Swiss National Science Foundation) 159422 217960 159422 Reiss Rafael Sebastian Barry David Andrew The Bois Chamblard Foundation (https://bois-chamblard-fondation.ch/)issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

Standing internal (gravity) waves, also called internal seiches, are ubiquitous in stratified lakes. They generate shear-driven thermocline mixing1–3, enhance mixing in the bottom boundary layer2,4,5, and modulate sediment-water exchange6–8. Mortimer9 introduced a conceptual model for studying basin-scale internal seiche modes in lakes by approximating water column stratification as distinct constant-temperature (density) layers to distinguish different vertical seiche modes. Depending on stratification and basin morphology, different vertical seiche modes (Vn) can occur in lakes, where n nodes separate layers with currents (and isotherms) oscillating in- or out-of-phase9,10. The most often observed vertical mode-one (V1) seiche is characterized by two layers, typically the epilimnion and hypolimnion, with opposing currents11. Vertical mode-two (V2) seiches have a three-layer structure due to: (i) a wide thermocline9,12–14 or (ii) chemical gradients producing a chemocline below the thermocline15. Reports of higher vertical modes (n > 2) are rare16. Comprehensive treatises on the theory of internal gravity waves are provided by Hutter et al.17 and Sutherland18.

In large lakes, where the Coriolis force can modify the internal wave field, Coriolis force effects become important when Burger number S = c/(Lf) < 1, where f denotes the latitude-dependent Coriolis parameter, c the non-rotating phase speed and L a characteristic length scale. In large lakes, due to Coriolis force, longitudinal seiches transform into shore-hugging Kelvin waves. Transversal seiches become super-inertial Poincaré waves with horizontal water motions describing clockwise-rotating (Northern Hemisphere) ellipses in the lake interior19 which converge to near-inertial circles as the Burger number approaches zero. Like non-rotational seiches, “standing” Kelvin/Poincaré waves are formed by the superposition of two oppositely-propagating Poincaré/Kelvin waves and rotate around the respective amphidromic points. Therefore, the term “quasi-standing” is often used in this context (for details, see Hutter et al.17). In many large lakes, V1 Kelvin and Poincaré waves have been documented (for example, ref. 20–26). Reports of higher vertical-mode Kelvin or Poincaré waves, on the other hand, are scarce5,22,27–30. It has been suggested that this could be due to a lack of adequate observations rather than the nonexistence of these wave modes8,17.

In deep large lakes, internal seiches drive hypolimnetic and near-bottom mixing5,31,32. However, few studies have been carried out in a lake as deep as Lake Geneva (309-m depth; Switzerland/France; Fig. 1a). In the mid-latitude climate belt, where Lake Geneva and many other deep lakes are located, lake stratification during summer still has a noticeable gradient down to 100-m depth. Below that depth, the stratification gradient becomes much smaller and is often ignored. In the present study, lakes that have more than 100-m depth are considered deep. It appears that field studies that have focused on deep hypolimnion hydrodynamics in such deep lakes are rare8,33. Therefore, the contribution of internal seiches to deep hypolimnion hydrodynamics of deep lakes remains poorly quantified.Fig. 1 Study site, wind, and field observations of higher vertical-mode Poincaré waves.

a Topographic and bathymetric map of the Lake Geneva area. Bise and Vent: The two dominant winds that blow over most of the lake surface. White dot: mooring location. White cross: CIPEL monitoring station SHL251,73. b, c Measured (black, yellow) and modeled (realistic simulations; red) rotary current spectra at the mooring location (depth-averaged over the lowest ~20 m) from 1 June to 1 September 2021 and 2022, respectively (CCW: counterclockwise; CW: clockwise). Black dashed line: V2/V3 Poincaré period of 14 h (b) and 14.5 h (c). Black dotted line: Inertial period (Ti = 16.5 h). Black dash-dotted line: V1 Poincaré period (TV1 = 10.5 h23). The 95% confidence interval is given in b. d Wind direction and (e) wind stress (black) and wind speed (red) from the MeteoSwiss COSMO-1 model averaged over the main basin. For clarity, wind vectors are colored by direction. Green: Bise wind; purple: Vent wind; yellow: cross-basin winds. f, g Measured raw and bandpass-filtered east velocities, depth-averaged over the lowest ~20 m. Black: bandpass-filtered 13–15 h; red: bandpass-filtered 9.3–11.3 h. h, i Bandpass-filtered (13–15 h) progressive vector diagrams around 7 and 19 June, respectively; indicated by red crosses in g. Black circles are marked every 14 h. Red crosses in g–i: start of the progressive vector diagrams; red diamonds: end. j Temperature profile measured by CIPEL (black) near the mooring location in August 2021. For comparison, the “realistic” temperature profile, Tr, used in the numerical modeling is also shown (red). Horizontal black dashed lines: limits of the thermocline layer. Dates in d–j refer to 2021. Close-ups of b, c around the near-inertial band are given in Supplementary Fig. 1.

The deep hypolimnion in such large, deep lakes is an important part of the lake system. In Lake Geneva, for example, the volume below 100-m depth is ~48% of the total lake volume and the sediment surface below 100-m depth is ~60% of the total sediment surface. Thus, processes occurring in the deep hypolimnion significantly contribute to the biogeochemical development of the whole lake system. Unlike Kelvin waves that act in the nearshore zone, Poincaré waves in the lake interior can contribute to these deepwater dynamics.

In Lake Michigan (maximum depth 281 m; USA), strong V1 Poincaré wave activity was observed at a 150-m deep midlake location during the entire stratification period34. The strongest currents associated with these waves occurred near the surface and could be linked to enhanced lateral dispersion in these layers35,36. In contrast, the bottom boundary layers were only weakly affected by V1 Poincaré waves, and no evidence of higher vertical modes was found (see also Ahmed et al.21).

In Lake Constance (maximum depth 250 m; Austria, Germany, Switzerland), higher mode longitudinal seiches with wave periods >100 h were studied in a shallow side basin (depth ~100 m) under strong wind forcing12,37, and V2 Poincaré waves were documented in the upper 60 m in shallow lateral zones27. No V2 Poincaré waves in the deep hypolimnion layers were reported. In Lake Iseo (256-m depth; Italy), V2 Poincaré waves were observed, but only investigated in the thermocline and the upper hypolimnion based on temperature measurements38. In their analysis of current measurements in the bottom boundary layer in the deepest part of Lake Iseo, Simoncelli et al.5 found that V1 Poincaré waves contributed to bottom boundary mixing in the deep hypolimnion. In the deepest layers of Lake Garda (maximum depth 346 m; Italy), high rates of turbulence dissipation have been associated with turbulent convection under propagating high-frequency internal waves, which can be triggered by basin-scale internal seiches39,40. In Lake Geneva, Lemmin41 documented ever-present inertial currents near the lake’s deepest point (~300-m depth), which contribute to hypolimnetic mixing and sediment-water exchange. Note, however, to our knowledge, vertical mode-three (V3) Poincaré waves have not yet been reported in any of the aforementioned lakes or in any other large, deep lake.

Full-depth current and temperature profiles that allow investigation of details of higher mode Poincaré wave dynamics in the deepest layers of large deep lakes over a full season have thus far not been documented in the literature. In the present study, we therefore combine temperature and current mooring observations covering the full depth range near the deepest point (~300-m depth) in Lake Geneva over two summers with detailed 3D numerical modeling and show that V2 and V3 Poincaré waves are frequently excited over many consecutive wave cycles in the deep hypolimnion. We are then able to explain how these waves dominate the lake’s deepwater dynamics during summer and generate currents of up to 4 cm s−1 at ~300-m depth. In the deep hypolimnion, the integrated kinetic energy of the V2 and V3 Poincaré wave modes is significantly (~2–2.5 times) higher than that of the V1 Poincaré mode.

Using 3D numerical simulations, we reveal that weak hypolimnetic stratification (N2 ≈ 10−6 s−2; N is the buoyancy frequency), typical of deep lakes, but often ignored, fundamentally changes the vertical structure of higher vertical-mode seiches, inducing shear in the middle of the hypolimnion and strengthening near-bottom currents. We demonstrate that after a short wind impulse of only 4 h duration, V2 and V3 Poincaré waves can persist for more than one week, with integrated kinetic energy progressively shifting towards the inertial period, which explains previously observed near-inertial currents in the deepest layers41. Our findings provide ample evidence that higher vertical-mode Poincaré waves make an important contribution to deep-water hydrodynamics, and that they are highly likely to be more widespread in large, deep lakes than the current sparse literature suggests.

Results and discussion

Field evidence of Poincaré waves

The current and temperature data collected at a midlake mooring (Fig. 1a) covered two entire stratified summer seasons in 2021 and 2022 (see Methods section). A strong thermocline developed between ~7 and ~35-m depth (Fig. 1j). Rotary spectra of the measured near-bottom currents in the lake’s center have a prominent, broad peak in the clockwise-rotating component, which is centered at ~14 h (2021; Fig. 1b) and ~14.5 h (2022; Fig. 1c), and is near the inertial period (~16.5 h). In that frequency range, the spectral power of the counterclockwise rotating component is relatively low compared to the clockwise component, indicating that water mass movement is clockwise. Progressive vector diagrams confirm that horizontal deepwater motions in this frequency range describe clockwise-rotating ellipses (Fig. 1h, i and Supplementary Fig. 2d, e), thus suggesting that this is an internal wave motion affected by the Coriolis force. However, wave modes within the ~14–15 h period range have not been previously detected in Lake Geneva, raising the question of what causes this dominant current signal.

Bandpass-filtered (13–15 h) velocities show bursts of consecutive oscillations, up to 4 cm s−1, in the deepest layers that occur throughout the observation period (Fig. 1g). Combined with background currents, the total near-bottom velocity frequently exceeds 5 cm s−1 in short bursts (Fig. 1f). There is no apparent link between current strength and wind speed or direction (Fig. 1d, e, g). The role of the wind is addressed below in the section, Role of wind forcing. Oscillating velocities within the ~14–15 h period range are seen throughout the water column, for example, in late June and early July 2022 (Fig. 2f, g). At certain instances, a few days apart, profiles of the horizontal velocities reveal a three- (Fig. 2a) or four-layer (Fig. 2b) current structure. The three-layer current structure resembles a vertical mode-two (V2) internal seiche with two nodes at ~8 and 150–200 m depth which separate layers of opposing currents that reverse direction every half period (compare curves in Fig. 2a, f, g). The four-layer current structure, on the other hand, resembles a vertical mode-three (V3) internal seiche with three nodes at ~13, 25 and 150–200 m depth (see phase differences between adjacent layers in Fig. 2b, f, g).Fig. 2 Measured vertical current structure.

a–c Measured east velocity profiles of V1, V2 and V3 Poincaré waves at selected times (see legends), bandpass-filtered between 13.5 and 15.5 h (a, b; V2, V3), and 9.3 and 11.3 h (c; V1). Red and black diamonds: depths of the curves in d–g. The thermocline is located between the horizontal black dashed lines. d–g Corresponding measured time series at selected depths (see legend), bandpass-filtered between 9.3–11.3 h (d, e) and 13.5–15.5 h (f, g). Vertical blue lines in d, e: time of profiles in c. Vertical red dash-dotted and blue lines in f, g: time of profiles in b and a, respectively. Measurements were taken at the mooring location in 2022 (for location, see Fig. 1a).

Bandpass-filtered hypolimnetic temperature measurements show regular periodic isotherm upwelling and downwelling with the same ~14–15 h period occurring continuously and are in phase with the current pattern (Fig. 3). Spectra of temperature have the strongest peak within the ~14–15 h period range coinciding with the peak in current velocities (see Supplementary Fig. 2c). The observed three- and four-layer current structures, the matching temperature and current fluctuations, and the clockwise rotating currents are features that suggest that the dominant ~14–15 h signals measured near the lake’s bottom are caused by V2 and V3 Poincaré waves.Fig. 3 Temperature observations.

a Temperature contours 0–50 m above the lakebed (309-m depth). Black arrows on the top of the panel are given every 14 h. b, c Raw and bandpass-filtered (13–15 h) east velocities, depth-averaged over the lowest ~20 m (black) and temperatures (temperature variations, δT, in panel c) 15 m above the lakebed (red). Measurements were taken at the mooring location in 2021 (for location, see Fig. 1a).

Using an analytically-based dispersion relation33 for an elliptic basin similar to Lake Geneva’s deep main basin (Fig. 1a), V2 and V3 Poincaré wave periods of ~14.7 h and 15.7 h, respectively, are obtained for the mean summer 2022 stratification (Supplementary Text 1) in good agreement with our observations, corroborating that these signals are likely due to V2 and V3 Poincaré waves.

Peaks in the clockwise rotating component at periods of ~10–11 h in the measured and modeled spectra (Fig. 1b, c) indicate the presence of V1 Poincaré waves that were previously observed in Lake Geneva23,42. However, V1 Poincaré spectral peaks are an order of magnitude smaller than the peak in the ~14–15 h period range. The two-layer current structure of V1 Poincaré waves is confirmed by full-depth current measurements (Fig. 2c). Comparing the observed V1 and V2/V3 wave current profiles, it can be seen that in the upper layer, the velocities of these modes are of the same order of magnitude, as reported in the literature43. However, in the deep hypolimnion, close to the bed, V2 and V3 currents are significantly stronger than V1 currents.

This major difference between V1 and V2/V3 current amplitudes is even more pronounced in the full-season time series (Fig. 1g), suggesting that V1 wave-generated currents do not contribute significantly to deep hypolimnion dynamics. The strong increase in V2 and V3 currents when approaching the bed indicates that they can contribute to sediment-water exchange dynamics. The regular and continuous change in V2 and V3 Poincaré current strength and direction (Fig. 1g–i) produces shear that contributes to mixing in the bottom boundary layer. The reason for this V2 and V3 Poincaré wave current increase towards the lakebed is discussed below in the section, Hypolimnetic stratification impacts vertical wave structure and bottom current strength. Note that the observed regular, continuous excitation of V2 and V3 Poincaré waves and the dominance of the associated spectral peak over the V1 peak (Fig. 1b, c) are different than those reported in the literature where V2 Poincaré waves are excited after V1 Poincaré waves and occur only in short bursts43.

More details of the current structure are difficult to determine from these observations because: (i) no measurements are available in the topmost 6 m due to surface reflections of the Acoustic Doppler Current Profiler signal, and (ii) low acoustic backscatter at mid-depth (insufficient particles in the water column) produces a noisy signal between ~100 and 200-m depth. Furthermore, in large lakes, different horizontal Poincaré modes with similar periods are often excited simultaneously24. Since these different horizontal Poincaré modes cannot be disentangled spectrally due to their similar periods21,23,44, modal decomposition methods are often employed (for example, refs. 12,29,45–47). Here, using a calibrated 3D hydrodynamic model42, we carried out realistic simulations (see Methods) that reproduced the clockwise rotating 14–15 h oscillations during the summers of 2021 and 2022 (Fig. 1b, c). Based on the thus validated model, idealized simulations were performed and are analyzed below for V2 and V3 Poincaré wave features.

V1, V2 and V3 Poincaré wave features revealed by idealized simulations

The idealized simulations (for details, see Methods) were forced with a Bise wind impulse (Fig. 1a; from the northeast) and initialized with the realistic initial temperature profile, Tr, which was obtained by averaging the model results of the 2022 realistic simulation near station SHL2 (Fig. 1a). It agrees well with the measured temperature profile (Fig. 1j). All near-bottom currents obtained from the idealized simulations show a strong peak in the clockwise rotary spectra within the ~14–15 h period range and a smaller peak at ~9.5 h (Fig. 4a), similar to rotary spectra of the measured currents and those produced by realistic simulations (Fig. 1b, c). Due to the short duration of the time series, the limited frequency resolution of the model rotary spectra cannot resolve the two neighboring peaks associated with V2 and V3 Poincaré waves. Instead, the respective wave periods were obtained by manually changing the center period of a 0.5-h narrow bandpass-filter in increments of 0.1 h to maximize the thus filtered near-bottom velocities. The following wave periods were determined: V1: ~9.3 h, V2: ~14.3 h, and V3: ~15.0 h. In the sections below, the bandpass-filtered model results are analyzed with narrow filter bands of 9.05–9.55 h (V1), 14.05–14.55 h (V2), and 14.75–15.25 h (V3). Note that no signals of vertical Poincaré modes higher than V3 were found in the observations or model results, suggesting that they do not play an important role in Lake Geneva.Fig. 4 Idealized simulations of V2 and V3 Poincaré waves at the mooring location.

a Clockwise rotary spectra of the near-bottom currents for different initial temperature profiles (TX) and wind conditions (Bise or Vent). Vertical lines: 16.5 h (inertial period; dotted), 14.5 h (V2/V3 Poincaré; dashed), 9.5 h (V1 Poincaré; dashed-dotted). The 95% confidence interval is given. Compare with spectra in Fig. 1b, c for field measurements and realistic simulations. b, c East velocities at selected depths (see legends). Vertical blue lines: time of the profiles in d. Grey shaded area: 4-h wind impulse. d East velocity profiles at selected times (see legend). Red and black diamonds: depths of the curves in b, c. Horizontal dashed lines: thermocline layer. Modeling results in b–d are 14.05–14.55 h bandpass-filtered (V2 Poincaré). e Initial temperature profiles. Tr: from the realistic simulations. Tcg: same as Tr but with constant hypolimnetic stratification. Tct: same as Tr but with constant hypolimnetic temperatures. Horizontal dashed lines: depths of the vertical nodes in d, h (10, 15, 25, 150, 160 m). The corresponding density and buoyancy frequency profiles are given in Supplementary Fig. 3. f–h Same as b–d but bandpass-filtered between 14.75–15.25 h (V3 Poincaré). Simulations were forced with a 4-h Bise wind impulse and initialized with temperature profile Tr (see panel e).

Horizontal velocity profiles bandpass-filtered around 9.3 h have a two-layer pattern with a current reversal just below the thermocline (Fig. 8a). This pattern, also seen in the field observations (Fig. 2c), is typical of V1 Poincaré modes, as discussed for Lake Geneva by Lemmin et al.23

Horizontal velocity profiles bandpass-filtered around 14.3 h have a three-layer structure with two nodes: one within the thermocline at ~15-m depth and one in the middle of the hypolimnion at ~150-m depth (Fig. 4d). Moreover, currents in adjacent layers are 180° out-of-phase (Fig. 4b, c). Profiles of vertical isotherm displacements show one node in the center of the thermocline, with isotherms in the epilimnion and upper thermocline moving vertically in opposite directions compared to deeper layers (Fig. 5e). Isotherm excursions are largest in the weakly stratified hypolimnion. Such a three-layer current structure with periodic compression and expansion of the middle layer is characteristic of V2 seiches14,17,48.Fig. 5 Horizontal and vertical structure of higher vertical-mode Poincaré waves.

Left column: Vertical mode-two (V2). Right column: Vertical mode-three (V3). a, b Timelines of vertical isotherm displacement (diso) at ~35-m depth (grey lines) and depth-averaged (V2: 20–25 m, and V3: 15–20 m) current speeds. The diso timelines show the crest arrival time during one wave period (1-h intervals). Black dot: mooring location. Red line: location of the transversal transect in c, d. c, d Current velocities into (red) and out of (blue) the plane along the transect shown in a, b. Distance is measured from the northern shore. e, f Vertical isotherm displacements, relative to the initial temperature profile, Tr, at a ~ 200-m depth location north of the mooring location. Horizontal dashed lines: thermocline layer. The model was forced with a 4-h Bise wind impulse and initialized with temperature profile Tr (Fig. 4e). Modeling results are bandpass-filtered (V2: 14.05–14.55 h, and V3: 14.75–15.25 h).

Horizontal velocity profiles bandpass-filtered around 15.0 h, on the other hand, have three nodes at ~10, 25, and 160-m depth (Fig. 4h) that separate four layers with currents in adjacent layers 180° out-of-phase (Fig. 4f, g). Typical of V3 internal seiches, profiles of vertical isotherm displacement show two nodes, one at the center of the thermocline and one at its lower end (Fig. 5f). Here, hypolimnetic waters move vertically in phase with the epilimnion and upper thermocline layers, and out-of-phase with the lower thermocline layers.

The clockwise-rotating currents (Fig. 1h, i) and the multi-layer structures in the profiles of isotherm displacement and horizontal currents (Figs. 5e, f and 4d, h) confirm that the dominant ~14-15 h signals are caused by V2 and V3 Poincaré waves. The observations and model results at the mooring location suggest that modes V2 and V3 are comparably strong, with very similar shapes in the hypolimnion; significant differences only appear above ~50-m depth (Fig. 4d, h). The three-dimensional structure of these wave modes and their relative strength compared to the V1 Poincaré mode will be discussed in the following two sections.

Horizontal and vertical structure of V2 and V3 Poincaré waves

In large lakes, Poincaré waves are horizontally characterized by one (horizontal mode-one) or several (higher horizontal modes) circular cells with maximum velocities at the cell centers and maximum isotherm displacements at the boundaries. Each cell rotates around an amphidromic point where vertical velocities and thus isotherm displacements vanish21,23. For both modes V2 and V3, vertical isotherm displacement timelines at 35-m depth suggest several large cells in the main basin, with the amphidromic points approximately located along the lake’s central axis (Fig. 5a, grey lines). In addition to these large cells, several smaller cells are found near the shores (see, for example, at 20-km East and 18-km North in Fig. 5a). These results show that V2 and V3 Poincaré waves of higher horizontal modes in along- and cross-basin directions (see, e.g., ref. 24) are simultaneously excited by a wind event over most of the main lake basin. As is typical for Poincaré waves, isotherm displacements are strongest near the shores (Supplementary Figs 4, 5).

Similar to the isotherm displacements, several larger cells appear along the lake’s central axis in the depth-averaged (V2: 20–25 m, and V3: 15–20 m) horizontal current velocity maps, with currents strongest near the center, diminishing shoreward (Fig. 5a, b). Furthermore, smaller, significantly weaker cells are found near the shores, in agreement with the isotherm displacement patterns. The discussed amphidromic patterns characterized by several larger cells centered along the lake’s longitudinal axis and smaller cells near the shores are similar to the amphidromic patterns of V1 waves23, which were confirmed by field measurements. However, in contrast to V1 Poincaré waves23, V2 and V3 Poincaré waves are limited to Lake Geneva’s deep central basin (Fig. 5a, b).

Currents along a vertical transect through the ~300-m deep mooring location (red line in Fig. 5a, b) confirm the three- (V2) and four-layer (V3 Poincaré wave) structures in the previously discussed velocity profiles (Fig. 4d, h). The depths of the lower nodal lines and thus the thickness of the current layers in the hypolimnion vary significantly along the transect, with the maximum nodal depth of ~150 m found in the deepest regions of the lake (Fig. 5c, d). Similar shoreward shoaling of the lower nodal lines occurs at other transects throughout the lake (e.g., Supplementary Fig. 6c, d). Furthermore, at shallower transects, the lower nodal line is generally found at shallower depths. For example, in the cell near the lake’s center (~300-m depth), the maximum nodal depth is ~150 m, whereas it is only ~75 m at the strong westernmost cell (~150-m depth; Supplementary Fig. 6c, d). The time evolution of the currents at different transects is shown in Supplementary Movie 1.

The vertical current transects demonstrate that the currents induced by V2 and V3 Poincaré waves exhibit a strong spatial heterogeneity, with the vertical current structure in the hypolimnion significantly impacted by sloping topography and local depth. The great depth of the lower nodal lines and the horizontal and vertical heterogeneities produce shear that can contribute to mixing in the deep hypolimnion.

The amphidromic points do not always coincide with the strongest currents (Fig. 5a, b). This mismatch is likely due to the superposition of different horizontal modes that cannot be distinguished spectrally. The dispersion relation for Poincaré waves in a rectangular basin is given as TPW−2=Ti−2+1+r2Tnr−2, where TPW denotes the Poincaré wave period, Ti the inertial period, r the basin aspect ratio, and Tnr the nonrotational cross-basin wave period24,49. Thus, TPW is typically close to Ti, but does not exceed it. For very large lakes, such as the Laurentian Great Lakes (Canada, USA), TPW approaches Ti and different horizontal-mode Poincaré waves have nearly identical periods21,44,50. For Lake Geneva, it was demonstrated that different horizontal-mode V1 Poincaré waves have similar periods that cannot be distinguished spectrally23. Our results suggest this also holds for higher vertical-mode Poincaré waves. Note that in very large lakes, where all Poincaré modes converge to the inertial frequency, Ti, narrow bandpass-filtering, as employed here for Lake Geneva, cannot effectively separate different vertical modes. In that case, the contribution of different vertical modes can be estimated by decomposing the observed or modeled baroclinic currents into a linear combination of the theoretical vertical modal shapes obtained by solving the Taylor-Goldstein equation25.

The cell-like isotherm displacement and current patterns, and the three- and four-layer current structures obtained from the idealized simulations, again corroborate that the ~14–15 h signals observed and modeled in the lake’s deepest layers during summers 2021 and 2022 are due to previously unknown V2 and V3 Poincaré waves of higher horizontal order. Disentangling the complex horizontal structure of these V2 and V3 Poincaré waves in Lake Geneva is beyond the scope of this study.

Relative strength of V1, V2, and V3 Poincaré waves

The full-season observations and realistic simulations for summers 2021 and 2022 suggest that the currents produced by Poincaré modes V2 and V3 are significantly stronger in the bottom layers than those of mode V1 (Fig. 1). This is confirmed by the basin-wide integrated kinetic energy associated with the different modes obtained from the bandpass-filtered idealized model results. When considering the entire depth range, V1 Poincaré mode energy is twice as high as that of V2 and V3 modes during the first ~2 d after the wind impulse (Fig. 6a). However, when considering only the layers below 100-m depth, V1 energy is as high as V2 energy only during the first ~1.5 d. Thereafter, V1 mode energy quickly dies down, whereas V2 and V3 mode energies get stronger for 2-3 d, peaking at ~4 d (V2) and ~5 d (V3) after the simulation started (Fig. 6b). This temporal lag between V1 and V2/V3 modes is similar to the observations of Wiegand and Chamberlain43.Fig. 6 Strength of V1, V2 and V3 Poincaré waves, and their interaction.

Kinetic energy (KE) of the different modes integrated over the entire lake (a) over the full depth range and (b) below 100-m depth. KE was computed based on the bandpass-filtered east and north velocity components. c Near-bottom velocities at the mooring location obtained with narrow bandpass filters (legend in a). d Same as c but filtered with a wider bandpass filter (13.5–15.5 h) that includes both the V2 and V3 wave periods. The magenta vertical lines in c, d mark times of positive (+) and negative (−) interference between modes V2 and V3, causing beat pulsation (compare panels c, d). The simulation was forced with a 4-h Bise wind impulse (grey shaded area) and initialized with temperature profile Tr (Fig. 4e). Results in a–c are filtered with a 0.5-h narrow passband (V1: 9.05–9.55 h, V2: 14.05–14.55 h, and V3: 14.75–15.25 h). Idealized simulation for 2022.

The maximum hypolimnion-integrated kinetic energy of the V2 and V3 mode is ~40% (V2) and 20% (V3) higher than that of the V1 mode. More striking is that the time-integrated hypolimnetic kinetic energy of the higher vertical modes during the first week of the simulation is 2.3 (V2) and 2.1 (V3) times higher than that of the first vertical mode. This analysis confirms that V2 and V3 Poincaré waves play an important, but as yet overlooked role in the deepwater dynamics of Lake Geneva, whereas V1 Poincaré waves are more relevant in the upper layers. The V3 mode becomes stronger than the V2 mode in the hypolimnion after ~4-5 d, as is reflected in a shift of the dominant oscillation period towards longer periods in the bottom layers during the first week of the simulation (Supplementary Fig. 7). Thus, after an initial short wind impulse, the oscillation period gradually approaches the inertial period, which can explain previously observed near-inertial currents in the deepest layers of Lake Geneva41.

Beat pulsation by superposition of V2 and V3 Poincaré waves

The superposition of two oscillations with similar strength and periods can lead to so-called beat pulsation, a well-known phenomenon in acoustics. Both the V2 and V3 Poincaré modes are initiated simultaneously by the 4-h wind impulse (Fig. 6c). However, as the waves evolve, the relative phase difference continuously changes due to the small difference in the wave periods. This causes alternating positive and negative interference between the two modes (see + and − signs in Fig. 6c, d) and manifests itself as a typical beat pattern in the combined signal (Fig. 6d). Mortimer24 showed that beat pulsation due to different horizontal-mode Poincaré waves is a common phenomenon in Lake Ontario and Lake Michigan. Our results demonstrate that beat pulsation also occurs due to superposition of different vertical-mode Poincaré waves in Lake Geneva. In addition to time-varying wind forcing, such beat pulsations can be one explanation for the pulsating current patterns seen in the full-season observations (Fig. 1g).

Hypolimnetic stratification impacts vertical wave structure and bottom current strength

Twice a month monitoring by the Commission Internationale pour la Protection des Eaux du Léman (CIPEL51) over several decades shows that a weak mean stratification, N2, of O(10−6 s−2)51 is always present during summer in Lake Geneva’s deep hypolimnion. This was also confirmed by the present long-term timeseries data where slight depth variations of this mean gradient were observed41. To investigate the effect of deep hypolimnion stratification on the vertical structure of V2 and V3 Poincaré waves, idealized simulations were carried out with different stratification profiles in the deep hypolimnion below 100-m depth.

For the simulation initialized with the realistic temperature profile Tr, the lower node of the V2 and V3 modes in the lake’s ~300-m deep center is located well within the hypolimnion at a maximum depth of ~150 m (Fig. 7a–d). Below that depth, only a weak temperature gradient exists, which changes slightly at ~200-m depth (see profile Tr in Fig. 4e). When the model is initialized with a temperature profile that is identical to Tr above 100-m depth, but has a constant weak temperature gradient (N2 ≈ 10−6 s−2; N2 profile in Supplementary Fig. 3) below 100-m depth (profile Tcg in Fig. 4e), the results for both the V2 and V3 modes are nearly identical to those obtained for the simulation initialized with Tr (velocity profiles in Fig. 7a, b and rotary spectra in Fig. 4a).Fig. 7 Effect of hypolimnetic stratification on vertical wave structure.

Left column: Vertical mode-two (V2). Right column: Vertical mode-three (V3). a, b East velocity profiles at the mooring location (see Fig. 5a), ~1.5 d after the simulation started with initial temperature profiles Tr (black), Tcg (red), and Tct (green) (for profiles, see Fig. 4e). The inset shows the corresponding time series depth-averaged over the lowest ~30 m (vertical blue dashed line: time of the profiles in a, b). c–f Current velocities into (red) and out of (blue) the plane along a transversal transect through the mooring location from the simulation initialized with temperature profiles Tr (c, d) and Tct (e, f). Green lines: zero-isotachs marking the nodal lines. Distance is measured from the northern shore. Note the stronger lower hypolimnion currents and deeper nodal lines for the case of Tr.. Data are bandpass-filtered (V2: 14.05–14.55 h, and V3: 14.75–15.25 h). Idealized simulation for 2022.

However, when hypolimnetic stratification is entirely removed (constant temperatures below 100-m depth; profile Tct in Fig. 4e), the vertical current structure changes significantly. In particular, the lower node in the lake’s center, which was located at a maximum depth of ~150 m with stratification, moved up to ~75-m depth (Fig. 7; transects at other locations in Supplementary Figs 6 and 8), that is, to the depth range where the thermocline transitions into the now unstratified hypolimnion. Moreover, without hypolimnetic stratification, the three- (V2) and four-layer (V3) current structures closely followed the stratification, as expected from the literature52. However, the resulting lower layer currents were considerably weaker than when weak hypolimnetic stratification was present. Without hypolimnetic stratification, V2 and V3 near-bottom currents at the mooring location weakened by a factor of up to 2.4 (V2) and 3.4 (V3) (Fig. 7a, b; also see rotary spectra in Fig. 4a). Note that without hypolimnetic stratification, no vertical gradients of velocity exist in the hypolimnion, except in the frictional bottom boundary layer (Fig. 7a, b).

The Taylor-Goldstein equation can be used to determine the profile shape of different vertical modes for different stratification profiles53. Good agreement is found between the bandpass-filtered profiles of the horizontal velocities from the 3D numerical simulations discussed above (Fig. 8, left column) and the theoretical modal shapes of the V1, V2, and V3 modes obtained by solving the Taylor-Goldstein equation for the three different stratification profiles (Fig. 8, right column). Furthermore, the shapes of the eigenfunctions of the vertical velocity for both V2 and V3 agree well with the profiles of the bandpass-filtered modeled vertical isotherm displacements (Fig. 5e, f and Supplementary Fig. 9). This confirms that the newly discovered ~14–15 h oscillations in Lake Geneva are V2 and V3 internal seiches and corroborates the important impact that weak hypolimnetic stratification has on the modal shape of higher vertical-mode seiches in deep lakes. Different from V2 and V3 modes, the shape of the V1 mode is not significantly affected by weak hypolimnion stratification (Fig. 8a, b).Fig. 8 Vertical structure of V1, V2, and V3 modes.

Left column (a, c, e): Bandpass-filtered (V1: 9.05–9.55 h, V2: 14.05–14.55 h, and V3: 14.75–15.25 h) east velocity profiles at the mooring location for different initial temperature profiles (see legend and Fig. 4e), normalized to the maximum velocity in the thermocline layer. Right column (b, d, f): Corresponding theoretical horizontal velocity eigenfunctions for different initial temperature profiles, normalized to the maximum value in the thermocline layer. The eigenfunctions were obtained by solving the Taylor-Goldstein equation without background current (for details, see Methods section).

Our results make evident that this ever-present weak hypolimnetic stratification, typical for deep lakes, significantly modifies the structure of higher vertical-mode seiches. In Lake Geneva, hypolimnetic stratification caused the greater depth of the lower V2 and V3 Poincaré wave nodes and strengthened near-bottom currents. The deep node within the weakly stratified hypolimnion induces shear in the water column that can contribute to hypolimnetic mixing in the intermediate layers. Furthermore, enhanced near-bottom currents strengthen hypolimnetic mixing in the bottom boundary layer4,5 and affect sediment-water exchange processes that modulate dissolved oxygen consumption7,54. The above findings are particularly important since higher vertical-mode seiches are often studied with simplified models based on multiple layers of constant density52,55,56; this in turn, produces unrealistic hypolimnion current patterns.

Role of wind forcing

Previous observations have reported that internal waves are initiated in the upper layers of the lake after a strong wind impulse12,27,43. Changing the 4-h wind impulse from a Bise wind (from the northeast; Supplementary Fig. 10a, b, e) to a similarly strong Vent wind (from the southwest; Supplementary Fig. 10c, d, f) did not significantly change the V2 and V3 Poincaré wave structure or strength (Fig. 4a). This suggests that wind direction has no effect on their generation, in agreement with the measurements (Fig. 1). However, winds lasting longer than ~8 h (half the inertial period) are less efficient in generating Poincaré waves, as previously suggested57. Thus, wind field fluctuations of O(4–8 h) would excite V2 and V3 Poincaré waves more efficiently23.

Conclusions and implications

Combining field observations and 3D numerical modeling, we discovered vertical mode-two (V2) and vertical mode-three (V3) Poincaré waves in large, 309-meter deep Lake Geneva and demonstrated how they dominate the dynamics in the deepest layers during summer stratification, generating currents of up to 4 cm s-1 at ~300-m depth. Furthermore, we revealed that weak hypolimnetic stratification (N2 ≈ 10−6 s−2), characteristic of deep lakes, fundamentally changes the vertical structure of higher vertical-mode seiches compared to a hypolimnion without stratification. Although relatively weak, hypolimnetic stratification is important because it induces shear in the middle of the hypolimnion and strengthens near-bottom currents. This has significant implications for hypolimnetic mixing, sediment-water exchange and biogeochemical lake system development, since in deep lakes, the hypolimnion below 100-m depth may contain a large volume and sediment surface; in Lake Geneva this amounts to ~48% of the total volume and ~60% of the sediment surface. Our analysis has made evident that classical concepts such as those based on multiple constant-temperature (density) layers cannot correctly characterize higher vertical-mode seiche dynamics in deep lakes with weak hypolimnetic stratification. Although mixing and transport processes directly driven by wind barely reach below 100-m depth in large deep lakes during summer stratification, internal seiches generated by the same wind, in particular V2 and V3 Poincaré waves, can produce significant deepwater movements even down to the deepest layers, as we have demonstrated here.

The findings of the present study will become even more pertinent in the future since persistent global warming will further extend the stratification period58,59 and thus the period when Poincaré waves can be generated. On the other hand, a longer stratification period will shorten the winter period during which convective cooling can contribute to deepwater renewal. This shift will lead to a different annual deepwater cycle in the future. Therefore, improving the understanding of deepwater dynamics in deep lakes is becoming increasingly important, in particular, since the role of higher vertical-mode (Poincaré) seiches in generating strong deepwater currents apparently has not been investigated in any deep (>100-m depth) lake prior to this study. The higher mode Poincaré waves that we detected can also be expected to occur in similar large, deep lakes.

Methods

Study site and observations

Lake Geneva (local name: Lac Léman; Switzerland/France) is a ~14-km wide, ~73-km long and ~309-m deep oligomictic lake. The mountainous topography channels two large-scale winds from the southwest (Vent) and northeast (Bise) (Fig. 1a), which drive most of the lake’s circulation60–67 and induce V1 Poincaré and Kelvin waves2,23.

A mooring was deployed in the lake’s center at ~305-m depth (Fig. 1a) during the summer from 1 June to 1 September in 2021 and 2022. In 2021, one downward-looking Acoustic Doppler Current Profiler (ADCP) at ~280-m depth measured currents in the lowest ~20 m of the water column. Temperatures were recorded in the lowest 50 m. In 2022, two upward-looking ADCPs at ~290 and ~55-m depth provided full-column measurements (mooring details in Supplementary Table 1). Full-depth temperature profiles were taken twice a month at monitoring station SHL2 (for location, see Fig. 1a) by CIPEL51.

Hydrodynamic model

The 3D numerical model (MITgcm68) employed here has been validated for Lake Geneva42. Following Reiss et al.66,67, the model employed a uniform horizontal Cartesian grid with a resolution of 113 m and 100 size-varying z-layers (30 cm at the surface and 4.8 m at the lake’s deepest point). Density as a function of temperature and pressure was computed with a 25-term equation-of-state69 with salinity kept constant at 0.03 psu; salinity plays a minor role in determining water density in Lake Geneva. The wind stress vector, τ, was computed as τ=CDρaΔU10ΔU10, with ρa being the density of air, ΔU10=U10−U0 being the difference between the wind velocity vector at 10 m above the lake surface, U10, and the surface current vector, U0, and CD being the wind speed-dependent drag coefficient as described by Large and Yeager70.

Two types of simulations were performed: (i) Two realistic simulations in 2021 and 2022, with several months of spin-up and realistic external forcing, and (ii) four different idealized simulations that were initialized from rest with horizontally homogeneous temperatures, forced at the beginning with a 4-h wind impulse and run for ~20 d.

The realistic simulations were initialized from rest on 20 August 2020 at 11:00 CET (2021 model run) and 15 September 2021 at 12:00 (2022 model run) with horizontally homogeneous temperatures derived from the temperature profiles taken at CIPEL monitoring station SHL2 (for location, see Fig. 1a) and forced with hourly output from the COSMO-1 numerical weather model (resolution 1.1 km) provided by MeteoSwiss.

The idealized simulations were initialized from rest with horizontally homogeneous temperatures derived from the 2022 realistic simulation by time-averaging the modeled temperature profile at station SHL2 (for location, see Fig. 1a) from 17 to 19 August 2022 (referred to as profile Tr ; see Figs. 1j and 4e). To study how hypolimnetic stratification impacts the structure of vertical mode-two (V2) and vertical mode-three (V3) Poincaré waves, two additional idealized simulations were run with the initial temperature profile above 100-m depth identical to profile Tr. However, below that depth, in one simulation, the temperature gradient was kept constant (profile Tcg) and in the other one, temperatures were kept constant (profile Tct) (Fig. 4e).

To efficiently excite near-inertial Poincaré waves while keeping other basin-scale motions comparably low, the idealized simulations were forced only at the beginning with a realistic, strong (~10 m s−1) 4-h wind impulse derived from the COSMO-1 wind field during either Bise (from the northeast; three simulations, initialized with profiles Tr, Tcg, and Tct) or Vent (from the southwest; one simulation, initialized with profile Tr) wind conditions (Supplementary Fig. 10; also see Fig. 1a).

The realistic simulations served to validate the model. The idealized simulations, on the other hand, allowed exploring details of the internal waves, including the effect of different hypolimnetic stratifications and wind forcing.

Analysis methods

Multitaper rotary current spectra and wavelet transforms were computed using the MATLAB package of Lilly71. Furthermore, to analyze internal wave characteristics, such as the vertical and horizontal wave structures, model results and field observations were bandpass-filtered with a phase-preserving Butterworth filter centered around the corresponding wave period/frequency (V1 Poincaré wave: ~9.3 h, V2 Poincaré wave: ~14.3 h, and V3 Poincaré wave: ~15.0 h).

Vertical mode structure

The theoretical shape of the first three vertical modes for a given initial temperature profile was estimated by solving the Taylor-Goldstein equation531 ∂2ϕz∂z2+N2zŪz−c2−∂2Ū/∂z2Ūz−c−k2ϕ=0

where ϕ(z) denotes the vertical structure or streamfunction, Ū the background horizontal current, c the phase speed, and k the horizontal wavenumber. N2(z)=−gρ0−1∂ρ/∂z is the squared buoyancy frequency and ρ0 a reference density. At the lake bottom and surface, ϕz=0=ϕz=−D=0.

Equation (1) was solved for the three different initial temperature (stratification) profiles (Fig. 4e and Supplementary Fig. 3) using the MATLAB code provided by Smyth72, with Ū=0 (no background current). The horizontal wavenumber, km, corresponding to the horizontal mode m, was set to km=mπ/L, where L is the basin length17. As previously reported12, the solutions of Eq. (1) are not sensitive to the choice of the horizontal order or to using basin width instead of basin length as a characteristic dimension. Note that Eq. (1) does not consider rotational effects, which is justified25 because f~ω≪Nmax, where f is the latitude-dependent Coriolis-parameter and ω is the angular wave frequency, both O (10−4 s−1).

Supplementary information

Transparent Peer Review file

Supplementary Information

Description of Additional Supplementary Files

Supplementary Movie 1

Supplementary information

The online version contains supplementary material available at 10.1038/s43247-024-01653-8.

Acknowledgements

This work was supported by the Swiss National Science Foundation (Grant numbers 159422 and 217960) and the Bois Chamblard Foundation. We thank Htet Kyi Wynn and Valentin Kindschi for fieldwork assistance.

Author contributions

All authors contributed substantially to the study’s conception. R.S. Reiss was responsible for data acquisition, modeling, data analysis, and drafting/revising the manuscript. U. Lemmin was involved in the design of the field campaign, data interpretation, discussion, and drafting/revising the manuscript. C. Monin contributed to data analysis and discussion. D.A. Barry contributed to data interpretation, discussion, and revising the manuscript.

Peer review

Peer review information

Communications Earth & Environment thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editors: Jennifer Veitch, Alireza Bahadori and Clare Davis. A peer review file is available.

Data availability

The in situ data and model results supporting the findings of this study are available online at 10.5281/zenodo.13143847.

Code availability

The main MITgcm model configuration files are available online at 10.5281/zenodo.13144189.

Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
==== Refs
References

1. Bouffard D Boegman L Ackerman JD Valipour R Rao YR Near-inertial wave driven dissolved oxygen transfer through the thermocline of a large lake J. Gt. Lakes Res. 2014 40 300 307 10.1016/j.jglr.2014.03.014
Bouffard, D., Boegman, L., Ackerman, J. D., Valipour, R. & Rao, Y. R. Near-inertial wave driven dissolved oxygen transfer through the thermocline of a large lake. J. Gt. Lakes Res. 40, 300–307 (2014).10.1016/j.jglr.2014.03.014
2. Bouffard D Lemmin U Kelvin waves in Lake Geneva J. Gt. Lakes Res. 2013 39 637 645 10.1016/j.jglr.2013.09.005
Bouffard, D. & Lemmin, U. Kelvin waves in Lake Geneva. J. Gt. Lakes Res. 39, 637–645 (2013).10.1016/j.jglr.2013.09.005
3. Preusse M Peeters F Lorke A Internal waves and the generation of turbulence in the thermocline of a large lake Limnol. Oceanogr. 2010 55 2353 2365 10.4319/lo.2010.55.6.2353
Preusse, M., Peeters, F. & Lorke, A. Internal waves and the generation of turbulence in the thermocline of a large lake. Limnol. Oceanogr. 55, 2353–2365 (2010).10.4319/lo.2010.55.6.2353
4. Lemckert C Antenucci J Saggio A Imberger J Physical properties of turbulent benthic boundary layers generated by internal waves J. Hydraulic Eng. 2004 130 58 69 10.1061/(ASCE)0733-9429(2004)130:1(58)
Lemckert, C., Antenucci, J., Saggio, A. & Imberger, J. Physical properties of turbulent benthic boundary layers generated by internal waves. J. Hydraulic Eng. 130, 58–69 (2004).10.1061/(ASCE)0733-9429(2004)130:1(58)
5. Simoncelli S Sources and scales of near-bottom turbulent mixing in large meromictic Lake Iseo J. Gt. Lakes Res. 2020 46 1581 1594 10.1016/j.jglr.2020.09.013
Simoncelli, S. et al. Sources and scales of near-bottom turbulent mixing in large meromictic Lake Iseo. J. Gt. Lakes Res. 46, 1581–1594 (2020).10.1016/j.jglr.2020.09.013
6. Bryant LD Variable sediment oxygen uptake in response to dynamic forcing Limnol. Oceanogr. 2010 55 950 964 10.4319/lo.2010.55.2.0950
Bryant, L. D. et al. Variable sediment oxygen uptake in response to dynamic forcing. Limnol. Oceanogr. 55, 950–964 (2010).10.4319/lo.2010.55.2.0950
7. Lorke A Müller B Maerki M Wüest A Breathing sediments: The control of diffusive transport across the sediment—water interface by periodic boundary-layer turbulence Limnol. Oceanogr. 2003 48 2077 2085 10.4319/lo.2003.48.6.2077
Lorke, A., Müller, B., Maerki, M. & Wüest, A. Breathing sediments: The control of diffusive transport across the sediment—water interface by periodic boundary-layer turbulence. Limnol. Oceanogr. 48, 2077–2085 (2003).10.4319/lo.2003.48.6.2077
8. Valerio G Pilotti M Lau MP Hupfer M Oxycline oscillations induced by internal waves in deep Lake Iseo Hydrol. Earth Syst. Sci. 2019 23 1763 1777 10.5194/hess-23-1763-2019
Valerio, G., Pilotti, M., Lau, M. P. & Hupfer, M. Oxycline oscillations induced by internal waves in deep Lake Iseo. Hydrol. Earth Syst. Sci. 23, 1763–1777 (2019).10.5194/hess-23-1763-2019
9. Mortimer CH Water movements in lakes during summer stratification; evidence from the distribution of temperature in Windermere Philos. Trans. R. Soc. Lond. Ser. B, Biol. Sci. 1952 236 355 404
Mortimer, C. H. Water movements in lakes during summer stratification; evidence from the distribution of temperature in Windermere. Philos. Trans. R. Soc. Lond. Ser. B, Biol. Sci. 236, 355–404 (1952).
10. Boegman, L. Currents in stratified water bodies 2: Internal waves. in Encyclopedia of Inland Waters (ed. Likens, G. E.) 539–558 (Academic Press, Oxford, 2009).
11. Mortimer CH The resonant response of stratified lakes to wind Schweizerische Z. f. ür. Hydrologie 1953 15 94 151
Mortimer, C. H. The resonant response of stratified lakes to wind. Schweizerische Z. f. ür. Hydrologie 15, 94–151 (1953).
12. Boehrer B Modal response of a deep stratified lake: Western Lake Constance J. Geophys. Res.: Oceans 2000 105 28837 28845 10.1029/2000JC900125
Boehrer, B. Modal response of a deep stratified lake: Western Lake Constance. J. Geophys. Res.: Oceans 105, 28837–28845 (2000).10.1029/2000JC900125
13. LaZerte BD The dominating higher order vertical modes of the internal seiche in a small lake Limnol. Oceanogr. 1980 25 846 854 10.4319/lo.1980.25.5.0846
LaZerte, B. D. The dominating higher order vertical modes of the internal seiche in a small lake. Limnol. Oceanogr. 25, 846–854 (1980).10.4319/lo.1980.25.5.0846
14. Lemmin U The structure and dynamics of internal waves in Baldeggersee Limnol. Oceanogr. 1987 32 43 61 10.4319/lo.1987.32.1.0043
Lemmin, U. The structure and dynamics of internal waves in Baldeggersee. Limnol. Oceanogr. 32, 43–61 (1987).10.4319/lo.1987.32.1.0043
15. Salvadè G Stocker K Trösch J Zamboni F Hydrodynamics of Lake Lugano Aquat. Sci. 1992 54 187 204 10.1007/BF00878136
Salvadè, G., Stocker, K., Trösch, J. & Zamboni, F. Hydrodynamics of Lake Lugano. Aquat. Sci. 54, 187–204 (1992).10.1007/BF00878136
16. Vidal J Rueda FJ Casamitjana X The seasonal evolution of high vertical-mode internal waves in a deep reservoir Limnol. Oceanogr. 2007 52 2656 2667 10.4319/lo.2007.52.6.2656
Vidal, J., Rueda, F. J. & Casamitjana, X. The seasonal evolution of high vertical-mode internal waves in a deep reservoir. Limnol. Oceanogr. 52, 2656–2667 (2007).10.4319/lo.2007.52.6.2656
17. Hutter K Wang Y Chubarenko IP Physics of Lakes Volume 2 2011 Berlin, Heidelberg Springer Berlin Heidelberg
Hutter, K., Wang, Y. & Chubarenko, I. P. Physics of Lakes Volume 2 2 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2011).
18. Sutherland BR Internal Gravity Waves 2010 Cambridge Cambridge University Press
Sutherland, B. R. Internal Gravity Waves. (Cambridge University Press, Cambridge, 2010).
19. Mortimer CH Lake Michigan in Motion: Responses of an Inland Sea to Weather, Earth-Spin, and Human Activities 2004 Madison University of Wisconsin Press
Mortimer, C. H. Lake Michigan in Motion: Responses of an Inland Sea to Weather, Earth-Spin, and Human Activities. (University of Wisconsin Press, Madison, 2004).
20. Abarca J Ulloa HN Niño Y Basin-scale hydrodynamics and physical connectivity in a great Patagonian lake J. Gt. Lakes Res. 2023 49 172 189 10.1016/j.jglr.2022.12.008
Abarca, J., Ulloa, H. N. & Niño, Y. Basin-scale hydrodynamics and physical connectivity in a great Patagonian lake. J. Gt. Lakes Res. 49, 172–189 (2023).10.1016/j.jglr.2022.12.008
21. Ahmed S Troy CD Hawley N Spatial structure of internal Poincaré waves in Lake Michigan Environ. Fluid Mech. 2014 14 1229 1249 10.1007/s10652-013-9294-3
Ahmed, S., Troy, C. D. & Hawley, N. Spatial structure of internal Poincaré waves in Lake Michigan. Environ. Fluid Mech. 14, 1229–1249 (2014).10.1007/s10652-013-9294-3
22. Antenucci JP Imberger J Saggio A Seasonal evolution of the basin-scale internal wave field in a large stratified lake Limnol. Oceanogr. 2000 45 1621 1638 10.4319/lo.2000.45.7.1621
Antenucci, J. P., Imberger, J. & Saggio, A. Seasonal evolution of the basin-scale internal wave field in a large stratified lake. Limnol. Oceanogr. 45, 1621–1638 (2000).10.4319/lo.2000.45.7.1621
23. Lemmin U Mortimer CH Bäuerle E Internal seiche dynamics in Lake Geneva Limnol. Oceanogr. 2005 50 207 216 10.4319/lo.2005.50.1.0207
Lemmin, U., Mortimer, C. H. & Bäuerle, E. Internal seiche dynamics in Lake Geneva. Limnol. Oceanogr. 50, 207–216 (2005).10.4319/lo.2005.50.1.0207
24. Mortimer CH Inertial oscillations and related internal beat pulsations and surges in Lakes Michigan and Ontario Limnol. Oceanogr. 2006 51 1941 1955 10.4319/lo.2006.51.5.1941
Mortimer, C. H. Inertial oscillations and related internal beat pulsations and surges in Lakes Michigan and Ontario. Limnol. Oceanogr. 51, 1941–1955 (2006).10.4319/lo.2006.51.5.1941
25. Valipour R Bouffard D Boegman L Rao YR Near-inertial waves in Lake Erie Limnol. Oceanogr. 2015 60 1522 1535 10.1002/lno.10114
Valipour, R., Bouffard, D., Boegman, L. & Rao, Y. R. Near-inertial waves in Lake Erie. Limnol. Oceanogr. 60, 1522–1535 (2015).10.1002/lno.10114
26. Wang Y Hutter K Bäuerle E Wind-induced baroclinic response of Lake Constance Annales Geophysicae 2000 18 1488 1501 10.1007/s00585-000-1488-6
Wang, Y., Hutter, K. & Bäuerle, E. Wind-induced baroclinic response of Lake Constance. Annales Geophysicae 18, 1488–1501 (2000).10.1007/s00585-000-1488-6
27. Appt J Imberger J Kobus H Basin-scale motion in stratified Upper Lake Constance Limnol. Oceanogr. 2004 49 919 933 10.4319/lo.2004.49.4.0919
Appt, J., Imberger, J. & Kobus, H. Basin-scale motion in stratified Upper Lake Constance. Limnol. Oceanogr. 49, 919–933 (2004).10.4319/lo.2004.49.4.0919
28. MacIntyre S Flynn KM Jellison R Romero JR Boundary mixing and nutrient fluxes in Mono Lake, California Limnol. Oceanogr. 1999 44 512 529 10.4319/lo.1999.44.3.0512
MacIntyre, S., Flynn, K. M., Jellison, R. & Romero, J. R. Boundary mixing and nutrient fluxes in Mono Lake, California. Limnol. Oceanogr. 44, 512–529 (1999).10.4319/lo.1999.44.3.0512
29. Saggio A Imberger J Internal wave weather in a stratified lake Limnol. Oceanogr. 1998 43 1780 1795 10.4319/lo.1998.43.8.1780
Saggio, A. & Imberger, J. Internal wave weather in a stratified lake. Limnol. Oceanogr. 43, 1780–1795 (1998).10.4319/lo.1998.43.8.1780
30. Hodges BR Imberger J Saggio A Winters KB Modeling basin-scale internal waves in a stratified lake Limnol. Oceanogr. 2000 45 1603 1620 10.4319/lo.2000.45.7.1603
Hodges, B. R., Imberger, J., Saggio, A. & Winters, K. B. Modeling basin-scale internal waves in a stratified lake. Limnol. Oceanogr. 45, 1603–1620 (2000).10.4319/lo.2000.45.7.1603
31. Cannon DJ Troy C Bootsma H Liao Q MacLellan-Hurd R-A Characterizing the seasonal variability of hypolimnetic mixing in a large, deep lake J. Geophys. Res.: Oceans 2021 126 e2021JC017533 10.1029/2021JC017533
Cannon, D. J., Troy, C., Bootsma, H., Liao, Q. & MacLellan-Hurd, R.-A. Characterizing the seasonal variability of hypolimnetic mixing in a large, deep lake. J. Geophys. Res.: Oceans 126, e2021JC017533 (2021).10.1029/2021JC017533
32. Troy C Cannon D Liao Q Bootsma H Logarithmic velocity structure in the deep hypolimnetic waters of Lake Michigan J. Geophys. Res.: Oceans 2016 121 949 965 10.1002/2014JC010506
Troy, C., Cannon, D., Liao, Q. & Bootsma, H. Logarithmic velocity structure in the deep hypolimnetic waters of Lake Michigan. J. Geophys. Res.: Oceans 121, 949–965 (2016).10.1002/2014JC010506
33. Antenucci JP Imberger J Energetics of long internal gravity waves in large lakes Limnol. Oceanogr. 2001 46 1760 1773 10.4319/lo.2001.46.7.1760
Antenucci, J. P. & Imberger, J. Energetics of long internal gravity waves in large lakes. Limnol. Oceanogr. 46, 1760–1773 (2001).10.4319/lo.2001.46.7.1760
34. Choi J Troy CD Hsieh T-C Hawley N McCormick MJ A year of internal Poincaré waves in southern Lake Michigan J. Geophys. Res.: Oceans 2012 117 C07014 10.1029/2012JC007984
Choi, J., Troy, C. D., Hsieh, T.-C., Hawley, N. & McCormick, M. J. A year of internal Poincaré waves in southern Lake Michigan. J. Geophys. Res.: Oceans 117, C07014 (2012).10.1029/2012JC007984
35. Choi JM Troy CD Hawley N Shear dispersion from near-inertial internal Poincaré waves in large lakes: Shear dispersion in stratified large lakes Limnol. Oceanogr. 2015 60 2222 2235 10.1002/lno.10163
Choi, J. M., Troy, C. D. & Hawley, N. Shear dispersion from near-inertial internal Poincaré waves in large lakes: Shear dispersion in stratified large lakes. Limnol. Oceanogr. 60, 2222–2235 (2015).10.1002/lno.10163
36. Choi J Troy C Hawley N McCormick M Wells M Lateral dispersion of dye and drifters in the center of a very large lake Limnol. Oceanogr. 2020 65 336 348 10.1002/lno.11302
Choi, J., Troy, C., Hawley, N., McCormick, M. & Wells, M. Lateral dispersion of dye and drifters in the center of a very large lake. Limnol. Oceanogr. 65, 336–348 (2020).10.1002/lno.11302
37. Boehrer B Imberger J Münnich KO Vertical structure of currents in western Lake Constance J. Geophys. Res.: Oceans 2000 105 28823 28835 10.1029/2000JC900139
Boehrer, B., Imberger, J. & Münnich, K. O. Vertical structure of currents in western Lake Constance. J. Geophys. Res.: Oceans 105, 28823–28835 (2000).10.1029/2000JC900139
38. Valerio G Pilotti M Marti CL Imberger J The structure of basin-scale internal waves in a stratified lake in response to lake bathymetry and wind spatial and temporal distribution: Lake Iseo, Italy Limnol. Oceanogr. 2012 57 772 786 10.4319/lo.2012.57.3.0772
Valerio, G., Pilotti, M., Marti, C. L. & Imberger, J. The structure of basin-scale internal waves in a stratified lake in response to lake bathymetry and wind spatial and temporal distribution: Lake Iseo, Italy. Limnol. Oceanogr. 57, 772–786 (2012).10.4319/lo.2012.57.3.0772
39. van Haren, H., Piccolroaz, S., Amadori, M., Toffolon, M. & Dijkstra, H. A. Moored observations of turbulent mixing events in deep Lake Garda, Italy. J. Limnol. 80, (2020).
40. van Haren H Dijkstra HA Convection under internal waves in an alpine lake Environ. Fluid Mech. 2021 21 305 316 10.1007/s10652-020-09774-2
van Haren, H. & Dijkstra, H. A. Convection under internal waves in an alpine lake. Environ. Fluid Mech. 21, 305–316 (2021).10.1007/s10652-020-09774-2
41. Lemmin U Insights into the dynamics of the deep hypolimnion of Lake Geneva as revealed by long-term temperature, oxygen, and current measurements Limnol. Oceanogr. 2020 65 2092 2107 10.1002/lno.11441
Lemmin, U. Insights into the dynamics of the deep hypolimnion of Lake Geneva as revealed by long-term temperature, oxygen, and current measurements. Limnol. Oceanogr. 65, 2092–2107 (2020).10.1002/lno.11441
42. Cimatoribus AA Lemmin U Bouffard D Barry DA Nonlinear dynamics of the nearshore boundary layer of a large lake (Lake Geneva) J. Geophys. Res.: Oceans 2018 123 1016 1031 10.1002/2017JC013531
Cimatoribus, A. A., Lemmin, U., Bouffard, D. & Barry, D. A. Nonlinear dynamics of the nearshore boundary layer of a large lake (Lake Geneva). J. Geophys. Res.: Oceans 123, 1016–1031 (2018).10.1002/2017JC013531
43. Wiegand RC Chamberlain V Internal waves of the second vertical mode in a stratified lake Limnol. Oceanogr. 1987 32 29 42 10.4319/lo.1987.32.1.0029
Wiegand, R. C. & Chamberlain, V. Internal waves of the second vertical mode in a stratified lake. Limnol. Oceanogr. 32, 29–42 (1987).10.4319/lo.1987.32.1.0029
44. Csanady GT Transverse internal seiches in large oblong lakes and marginal seas J. Phys. Oceanogr. 1973 3 439 447 10.1175/1520-0485(1973)003<0439:TISILO>2.0.CO;2
Csanady, G. T. Transverse internal seiches in large oblong lakes and marginal seas. J. Phys. Oceanogr. 3, 439–447 (1973).10.1175/1520-0485(1973)003<0439:TISILO>2.0.CO;2
45. Shimizu K Imberger J Kumagai M Horizontal structure and excitation of primary motions in a strongly stratified lake Limnol. Oceanogr. 2007 52 2641 2655 10.4319/lo.2007.52.6.2641
Shimizu, K., Imberger, J. & Kumagai, M. Horizontal structure and excitation of primary motions in a strongly stratified lake. Limnol. Oceanogr. 52, 2641–2655 (2007).10.4319/lo.2007.52.6.2641
46. Shimizu K Imberger J Energetics and damping of basin-scale internal waves in a strongly stratified lake Limnol. Oceanogr. 2008 53 1574 1588 10.4319/lo.2008.53.4.1574
Shimizu, K. & Imberger, J. Energetics and damping of basin-scale internal waves in a strongly stratified lake. Limnol. Oceanogr. 53, 1574–1588 (2008).10.4319/lo.2008.53.4.1574
47. Shimizu K Imberger J Seasonal differences in the evolution of damped basin-scale internal waves in a shallow stratified lake Limnol. Oceanogr. 2010 55 1449 1462 10.4319/lo.2010.55.3.1449
Shimizu, K. & Imberger, J. Seasonal differences in the evolution of damped basin-scale internal waves in a shallow stratified lake. Limnol. Oceanogr. 55, 1449–1462 (2010).10.4319/lo.2010.55.3.1449
48. Ulloa HN Horizontal transport under wind-induced resonance in stratified waterbodies Phys. Rev. Fluids 2020 5 054503 10.1103/PhysRevFluids.5.054503
Ulloa, H. N. et al. Horizontal transport under wind-induced resonance in stratified waterbodies. Phys. Rev. Fluids 5, 054503 (2020).10.1103/PhysRevFluids.5.054503
49. Bouffard, D. & Boegman, L. Basin-Scale Internal Waves. In Encyclopedia of Lakes and Reservoirs (eds. Bengtsson, L., Herschy, R. W. & Fairbridge, R. W.) 102–107 (Springer Netherlands, Dordrecht, 2012).
50. Schwab DJ Internal free oscillations in Lake Ontario Limnol. Oceanogr. 1977 22 700 708 10.4319/lo.1977.22.4.0700
Schwab, D. J. Internal free oscillations in Lake Ontario. Limnol. Oceanogr. 22, 700–708 (1977).10.4319/lo.1977.22.4.0700
51. CIPEL. Rapports Sur Les Études et Recherches Entreprises Dans Le Bassin Lémanique, Campagne 2021. Commission internationale pour la protection des eaux du Léman (CIPEL), Nyon, Switzerland. Retrieved from https://www.cipel.org/wp-content/uploads/2022/11/rapport-scientifique-2021-2022-low.pdf, last accessed 1 August 2024. (2022).
52. Hutter, K., Wang, Y. & Chubarenko, I. P. Higher-Order Baroclinicity (II): Interpretation of Lake Data with Rotating and Non-rotating Models. In Physics of Lakes: Volume 2: Lakes as Oscillators (eds. Hutter, K., Wang, Y. & Chubarenko, I. P.) 251–286 (Springer, Berlin, Heidelberg, 2011).
53. Cushman-Roisin, B. & Beckers, J.-M. Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects. vol. 101 (Academic Press, 2011).
54. Schwefel R Hondzo M Wüest A Bouffard D Scaling oxygen microprofiles at the sediment interface of deep stratified waters Geophys. Res. Lett. 2017 44 1340 1349 10.1002/2016GL072079
Schwefel, R., Hondzo, M., Wüest, A. & Bouffard, D. Scaling oxygen microprofiles at the sediment interface of deep stratified waters. Geophys. Res. Lett. 44, 1340–1349 (2017).10.1002/2016GL072079
55. Heaps NS Seiches in a narrow lake, uniformly stratified in three layers Geophys. J. Int. 1961 5 134 156 10.1111/j.1365-246X.1961.tb00418.x
Heaps, N. S. Seiches in a narrow lake, uniformly stratified in three layers. Geophys. J. Int. 5, 134–156 (1961).10.1111/j.1365-246X.1961.tb00418.x
56. Longuet-Higgins MS Water movements in lakes during summer stratification; Evidence from the distribution of temperature in Windermere: Appendix: Oscillations in a three-layered stratified basin Philos. Trans. R. Soc. Lond. Ser. B, Biol. Sci. 1952 236 399 404
Longuet-Higgins, M. S. Water movements in lakes during summer stratification; Evidence from the distribution of temperature in Windermere: Appendix: Oscillations in a three-layered stratified basin. Philos. Trans. R. Soc. Lond. Ser. B, Biol. Sci. 236, 399–404 (1952).
57. Boyce FM Donelan MA Hamblin PF Murthy CR Simons TJ Thermal structure and circulation in the Great Lakes Atmosphere-Ocean 1989 27 607 642 10.1080/07055900.1989.9649358
Boyce, F. M., Donelan, M. A., Hamblin, P. F., Murthy, C. R. & Simons, T. J. Thermal structure and circulation in the Great Lakes. Atmosphere-Ocean 27, 607–642 (1989).10.1080/07055900.1989.9649358
58. Mesman JP The role of internal feedbacks in shifting deep lake mixing regimes under a warming climate Freshw. Biol. 2021 66 1021 1035 10.1111/fwb.13704
Mesman, J. P. et al. The role of internal feedbacks in shifting deep lake mixing regimes under a warming climate. Freshw. Biol. 66, 1021–1035 (2021).10.1111/fwb.13704
59. Woolway RI Phenological shifts in lake stratification under climate change Nat. Commun. 2021 12 2318 10.1038/s41467-021-22657-4 33875656
Woolway, R. I. et al. Phenological shifts in lake stratification under climate change. Nat. Commun. 12, 2318 (2021).33875656 10.1038/s41467-021-22657-4
60. Foroughan M Hamze-Ziabari SM Lemmin U Barry DA A persistent submesoscale frontal slick: A novel marker of the mesoscale flow field in a large lake (Lake Geneva) Geophys. Res. Lett. 2022 49 e2022GL100262 10.1029/2022GL100262
Foroughan, M., Hamze-Ziabari, S. M., Lemmin, U. & Barry, D. A. A persistent submesoscale frontal slick: A novel marker of the mesoscale flow field in a large lake (Lake Geneva). Geophys. Res. Lett. 49, e2022GL100262 (2022).10.1029/2022GL100262
61. Hamze-Ziabari SM Razmi AM Lemmin U Barry DA Detecting submesoscale cold filaments in a basin-scale gyre in large, deep Lake Geneva (Switzerland/France) Geophys. Res. Lett. 2022 49 e2021GL096185 10.1029/2021GL096185
Hamze-Ziabari, S. M., Razmi, A. M., Lemmin, U. & Barry, D. A. Detecting submesoscale cold filaments in a basin-scale gyre in large, deep Lake Geneva (Switzerland/France). Geophys. Res. Lett. 49, e2021GL096185 (2022).10.1029/2021GL096185
62. Hamze-Ziabari SM Lemmin U Soulignac F Foroughan M Barry DA Basin-scale gyres and mesoscale eddies in large lakes: A novel procedure for their detection and characterization, assessed in Lake Geneva Geoscientific Model Dev. 2022 15 8785 8807 10.5194/gmd-15-8785-2022
Hamze-Ziabari, S. M., Lemmin, U., Soulignac, F., Foroughan, M. & Barry, D. A. Basin-scale gyres and mesoscale eddies in large lakes: A novel procedure for their detection and characterization, assessed in Lake Geneva. Geoscientific Model Dev. 15, 8785–8807 (2022).10.5194/gmd-15-8785-2022
63. Hamze-Ziabari SM Foroughan M Lemmin U Barry DA Monitoring mesoscale to submesoscale processes in large lakes with Sentinel-1 SAR imagery: The case of Lake Geneva Remote Sens. 2022 14 4967 10.3390/rs14194967
Hamze-Ziabari, S. M., Foroughan, M., Lemmin, U. & Barry, D. A. Monitoring mesoscale to submesoscale processes in large lakes with Sentinel-1 SAR imagery: The case of Lake Geneva. Remote Sens. 14, 4967 (2022).10.3390/rs14194967
64. Hamze-Ziabari SM Lemmin U Foroughan M Reiss RS Barry DA Chimney-like intense pelagic upwelling in the center of basin-scale cyclonic gyres in large Lake Geneva J. Geophys. Res.: Oceans 2023 128 e2022JC019592 10.1029/2022JC019592
Hamze-Ziabari, S. M., Lemmin, U., Foroughan, M., Reiss, R. S. & Barry, D. A. Chimney-like intense pelagic upwelling in the center of basin-scale cyclonic gyres in large Lake Geneva. J. Geophys. Res.: Oceans 128, e2022JC019592 (2023).10.1029/2022JC019592
65. Reiss, R. S., Lemmin, U., Cimatoribus, A. A. & Barry, D. A. Wintertime coastal upwelling in Lake Geneva: An efficient transport process for deepwater renewal in a large, deep lake. J. Geophys. Res.: Oceans 125, e2020JC016095 (2020).
66. Reiss RS Lemmin U Barry DA Wind-induced hypolimnetic upwelling between the multi-depth basins of Lake Geneva during winter: An overlooked deepwater renewal mechanism? J. Geophys. Res.: Oceans 2022 127 e2021JC018023 10.1029/2021JC018023
Reiss, R. S., Lemmin, U. & Barry, D. A. Wind-induced hypolimnetic upwelling between the multi-depth basins of Lake Geneva during winter: An overlooked deepwater renewal mechanism? J. Geophys. Res.: Oceans 127, e2021JC018023 (2022).10.1029/2021JC018023
67. Reiss RS Lemmin U Barry DA What role does stratification play during winter in wind-induced exchange between the multi-depth basins of a large lake (Lake Geneva)? J. Gt. Lakes Res. 2023 49 406 421 10.1016/j.jglr.2023.02.005
Reiss, R. S., Lemmin, U. & Barry, D. A. What role does stratification play during winter in wind-induced exchange between the multi-depth basins of a large lake (Lake Geneva)? J. Gt. Lakes Res. 49, 406–421 (2023).10.1016/j.jglr.2023.02.005
68. Marshall J Adcroft A Hill C Perelman L Heisey C A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers J. Geophys. Res.: Oceans 1997 102 5753 5766 10.1029/96JC02775
Marshall, J., Adcroft, A., Hill, C., Perelman, L. & Heisey, C. A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res.: Oceans 102, 5753–5766 (1997).10.1029/96JC02775
69. McDougall TJ Jackett DR Wright DG Feistel R Accurate and computationally efficient algorithms for potential temperature and density of seawater J. Atmos. Ocean. Technol. 2003 20 730 741 10.1175/1520-0426(2003)20<730:AACEAF>2.0.CO;2
McDougall, T. J., Jackett, D. R., Wright, D. G. & Feistel, R. Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmos. Ocean. Technol. 20, 730–741 (2003).10.1175/1520-0426(2003)20<730:AACEAF>2.0.CO;2
70. Large, G. & Yeager, S. Diurnal to decadal global forcing for ocean and sea-ice models: The data sets and flux climatologies (No. NCAR/TN-460 + STR). University Corporation for Atmospheric Research. 10.5065/D6KK98Q6 (2004).
71. Lilly, J. jLab: A data analysis package for Matlab, v.1.7.1. Zenodo 10.5281/ZENODO.4547006 (2021).
72. Smyth WD Moum JN Nash JD Narrowband oscillations in the Upper Equatorial Ocean. Part II: Properties of shear instabilities J. Phys. Oceanogr. 2011 41 412 428 10.1175/2010JPO4451.1
Smyth, W. D., Moum, J. N. & Nash, J. D. Narrowband oscillations in the Upper Equatorial Ocean. Part II: Properties of shear instabilities. J. Phys. Oceanogr. 41, 412–428 (2011).10.1175/2010JPO4451.1
73. Rimet, F. et al. The Observatory on LAkes (OLA) database: Sixty years of environmental data accessible to the public: The Observatory on LAkes (OLA) database. J. Limnol. 79, (2020).
