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Physical mechanisms of internal seiche attenuation for non-ideal stratification and basin topography

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Abstract

The dynamics of vertical mixing and the occurrence of basin-scale internal waves (internal seiches) in lakes and reservoirs are often classified and described based on the force balance of wind shear and horizontal pressure gradients resulting from wind-generated currents (the Wedderburn number). The classification schemes consider specific time scales that are derived based on a simplified vertical density distribution, a rectangular basin shape, and a constant water depth. Using field measurements and numerical simulations with a validated hydrodynamic model, we analyzed the transfer of energy from wind to the internal seiche field in a small reservoir. Our results demonstrate that the basin shape has a strong influence on the energy dissipation and on the transfer of energy to propagating high-frequency internal waves, thereby attenuating the generation of basin-scale internal seiches. Most of the energy loss of the internal seiche occurs at the sloping boundary, where the internal seiche is susceptible to shoaling and breaking. These findings suggest that the Wedderburn number can be used to predict the occurrence of internal seiche activity in continuously stratified systems. As the Wedderburn number and derived mixing classifications are widely applied also for the interpretation of observed ecological and biogeochemical processes, its application to basins with sloping bathymetry and complex shape should be critically scrutinized, and deviations from predicted dynamics, including the presence of hotspots of turbulent mixing, should be considered.

Key points

  • The interaction of internal seiches with a sloping bottom is the primary mechanism in inhibiting the generation of internal seiches by promoting strong vertical mixing near the lakeshore

  • Lake shape and its influence on the mean flow acts as a secondary mechanism to inhibit the generation of internal seiches by promoting the formation of high-frequency internal waves

  • Sloping bottom and vertically distributed density gradients promote the generation of internal seiches of higher vertical modes

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Acknowledgements

This study was financially supported by the Coordenação de Aperfeiçoamento de Pessoas de Nivel Superior—Brasil (CAPES)—Finance Code 001, and by the German Federal Ministry of Education and Research (BMBF) as part of the MuDak-WRM project (grant numbers 02WGR1431 B and 02WGR1431 F). RCB thanks CAPES for the scholarships. TB acknowledges the productivity stipend from the National Council for Scientific and Technological Development – CNPq, Grant no. 312211/2020-1, call 09/2020. All input data to support the findings presented here are available at https://github.com/buenorc/wepaper.git (https://doi.org/10.5281/zenodo.5708040).

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Authors and Affiliations

  1. Graduate Program On Environmental Engineering, Federal University of Paraná, Curitiba, Brazil

    Rafael de Carvalho Bueno

  2. Department of Environmental Engineering, Federal University of Paraná, Curitiba, Brazil

    Tobias Bleninger

  3. Department of Lake Research, Helmholtz-Centre for Environmental Research, Magdeburg, Germany

    Bertram Boehrer

  4. Institute for Environmental Sciences, University of Kaiserslautern-Landau, Landau, Germany

    Andreas Lorke

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The authors confirm their contribution to the paper as follows: study conception and design: RCB, TB, and AL; three-dimensional numerical simulations: RCB and TB; Field measurements: TB, and AL; Analysis and interpretation of results: RCB, TB, BB and AL; draft manuscript preparation: RCB, TB, BB and AL. All authors read and approved the final manuscript.

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de Carvalho Bueno, R., Bleninger, T., Boehrer, B. et al. Physical mechanisms of internal seiche attenuation for non-ideal stratification and basin topography. Environ Fluid Mech 23, 689–710 (2023). https://doi.org/10.1007/s10652-023-09928-y

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