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Three-dimensional numerical simulation of basin-scale internal waves in a long narrow lake

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Abstract

The three-dimensional MITgcm (MIT general circulation model) was applied to simulate wind-induced baroclinic oscillations in Cayuga Lake, to obtain an understanding of the internal seiche/surge dynamics and associated mixing in long narrow lakes. The MITgcm has not been rigorously validated for closed basins against field observations. Thus, qualitative and quantitative methods were used to validate the model and study the sensitivity to different model parameters against observed temperature data. The linear equation of state (EoS) yielded poor results, in comparison to the polynomial EoS formulations where the density gradient was large. The vertical density stratification was strongly sensitive to the background vertical viscosity and diffusivity (when > 10–5 m2s−1), because the prescribed background values control mixing in the KPP scheme, except on the surface and bottom boundary layers. After calibration, the model correctly simulated the vertical stratification, upwelling, basin-scale seiche (with a horizontal mode-one period T1 = 80 h) and surge formation with a basin-wide root-mean-square-error 1.9 °C. Flow visualization indicated that internal surges evolved due to (i) a wind-induced locally downwelled thermocline (wind duration < T1/4), (ii) a basin-scale wind-induced upwelled thermocline (wind duration > T1/4) and (iii) internal hydraulic jumps.

Article Highlights

  • The MITgcm was extensively validated against field data in simulation of Cayuga Lake

  • A polynomial equation-of-state and space–time variable turbulence closure scheme were applied

  • Three distinct processes were found to generate internal surges

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Acknowledgements

The authors thank Todd Cowen for providing the field observations. Thanks also to Kevin Lamb, Damien Bouffard and Jody Klymak for helpful discussions. This research was funded by the NSERC Discovery Grants to LB and AP. AD was also supported by Queen’s University and the Huntly Macdonald Sinclair Tuition Fellowship. Computing facilities were provided by the High-Performance Computing Virtual Laboratory (HPCVL), Queen’s University. The model setup files used in this research are archived in the Department of Civil Engineering at Queen’s University and will be made available upon manuscript acceptance at https://dataverse.scholarsportal.info/dataverse/queens

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Authors and Affiliations

  1. Environmental Fluid Dynamics Laboratory, Department of Civil Engineering, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Abbas Dorostkar & Leon Boegman

  2. School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, USA

    Seth A. Schweitzer

  3. Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Andrew Pollard

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  1. Abbas Dorostkar
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Correspondence to Leon Boegman.

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Dorostkar, A., Boegman, L., Schweitzer, S.A. et al. Three-dimensional numerical simulation of basin-scale internal waves in a long narrow lake. Environ Fluid Mech 23, 1167–1192 (2023). https://doi.org/10.1007/s10652-022-09868-z

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