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Quantifying the effect of wind on internal wave resonance in Lake Villarrica, Chile

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Abstract

Lake Villarrica, located in south central Chile, has a maximum depth of 167 m and a maximum fetch of about 20 km. The lake is monomictic, with a seasonal thermocline located at a depth of approximately 20 m. Field data show the presence of basin-scale internal waves that are forced by daily winds and affected by Coriolis acceleration. A modal linear and non-linear analysis of internal waves has been used, assuming a two-layer system. The numerical simulations show good agreement with the internal wave field observations. The obtained modes were used to study the energy dissipation within the system, which is necessary to control the amplitude growth. Field data and numerical simulations identify (1) the occurrence of a horizontal mode 1 Kelvin wave, with a period of about a day that coincides with the frequency of daily winds, suggesting that this mode of the Kelvin waves is in a resonant state (subject to damping and controlled by frictional effects in the field) and (2) the presence of higher-frequency internal waves, which are excited by non-linear interactions between basin-scale internal waves. The non-linear simulation indicates that only 10 % of the dissipation rate of the Kelvin wave is because of bottom friction, while the rest 90 % represents the energy that is radiated from the Kelvin wave to other modes. Also, this study shows that modes with periods between 5 and 8 h are excited by non-linear interactions between the fundamental Kelvin wave and horizontal Poincaré-type waves. A laboratory study of the resonant interaction between a periodic forcing and the internal wave field response has also been performed, confirming the resonance for the horizontal mode 1 Kelvin wave.

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References

  1. Antenucci JP, Imberger J (2001) Energetics of long internal gravity waves in large lakes. Limnol Oceanogr 46:1760–1773

    Article  Google Scholar 

  2. Antenucci JP, Imberger J (2003) The seasonal evolution of wind/internal wave resonance in Lake Kinneret. Limnol Oceanogr 48:2055–2061

    Article  Google Scholar 

  3. Boegman L, Ivey GN (2012) The dynamics of internal wave resonance in periodically forced narrow basins. J Geophys Res 117:C11002. doi:10.1029/2012JC008134

    Article  Google Scholar 

  4. Boegman L, Imberger J, Ivey GN, Antenucci JP (2003) High-frequency internal waves in large stratified lakes. Limnol Oceanogr 48:895–919

    Article  Google Scholar 

  5. Boegman L, Ivey GN, Imberger J (2005a) The energetics of large-scale internal wave degeneration in lakes. J Fluid Mech 531:159–180

    Article  Google Scholar 

  6. Boegman L, Ivey GN, Imberger J (2005b) The degeneration of internal waves in lakes with sloping topography. Limnol Oceanogr 50:1620–1637

    Article  Google Scholar 

  7. Cushman-Roisin B (1994) Introduction to geophysical fluid dynamics. Prentice Hall, New York

    Google Scholar 

  8. de la Fuente A, Shimizu K, Imberger J, Niño Y (2008) The evolution of internal waves in a rotating, stratified, circular basin and the influence of weakly nonlinear and nonhydrostatic accelerations. Limnol Oceanogr 53(6):2738–2748

    Article  Google Scholar 

  9. de la Fuente A, Shimizu K, Niño Y, Imberger J (2010) Nonlinear and weakly nonhydrostatic inviscid evolution of internal gravitational basin-scale waves in a large, deep lake: Lake Constance. J Geophys Res 115:C12045. doi:10.1029/2009JC005839

    Article  Google Scholar 

  10. Fischer H, List E, Koh R, Imberger J, Brooks N (1979) Mixing in inland and coastal waters. Academic Press, New York

    Google Scholar 

  11. Garvine RW (1987) Estuary plumes and fronts in shelf waters: a layer model. J Phys Oceanogr 11:1877–1895

    Article  Google Scholar 

  12. Gill AE (1982) Atmosphere–ocean dynamics. Academic Press, London

    Google Scholar 

  13. Helfrich K, Melville W (2006) Long nonlinear internal waves. Annu Rev Fluid Mech 38:395–425

    Article  Google Scholar 

  14. Hodges BR, Imberger J, Saggio A, Winters KB (2000) Modeling basin-scale internal waves in a stratified lake. Limnol Oceanogr 45:1603–1620

    Article  Google Scholar 

  15. Horn D, Imberger J, Ivey GN (2001) The degradation of long-scale interfacial gravity waves in lakes. J Fluid Mech 434:181–207

    Article  Google Scholar 

  16. Imberger J (1998) Flux paths in a stratified lake: a review. In Imberger J (ed) Physical processes in lakes and oceans, coastal and estuarine studies, vol 54. American Geophysical Union, Washington, pp 1–17

  17. Imberger J, Hamblin PF (1982) Dynamics of lakes, reservoirs and cooling ponds. Annu Rev Fluid Mech 14:153–187

    Article  Google Scholar 

  18. Linden PF, van Heijst GJF (1984) Two-layer spin-up and frontogenesis. J Fluid Mech 143:69–94

    Article  Google Scholar 

  19. Meruane C, Niño Y, Garreaud R (2005) Simulation of phytoplankton response to strong wind events in Lake Villarrica, Chile. In: Proceedings of the XXXI IAHR congress. Seoul, Korea

  20. Miles JW (1984) Resonantly forced surface waves in a circular cylinder. J Fluid Mech 149:15–31

    Article  Google Scholar 

  21. Monismith SG (1986) An experimental study of the upwelling response of stratified reservoirs to surface shear stress. J Fluid Mech 171:407–439

    Article  Google Scholar 

  22. Mortimer CH (1974) Lake hydrodynamics. Mitt Int Ver Limnol 20:124–197

    Google Scholar 

  23. Münnich M, Wüest A, Imboden DM (1992) Observations of the second vertical mode of the internal seiche in an alpine lake. Limnol Oceanogr 37:1705–1719

    Article  Google Scholar 

  24. Munro RJ, Davies PA (2006) The flow generated in a continuously stratified rotating fluid by the differential rotation of a plane horizontal disc. Fluid Dyn Res 38:522–538

    Article  Google Scholar 

  25. Nurser AJG, Lee M-M (2004) Isopycnal averaging at constant height. Part I: the formulation and a case study. J Phys Oceanogr 34:2721–2739

    Article  Google Scholar 

  26. Preusse M, Peeters F, Lorke A (2010) Internal waves and the generation of turbulence in the thermocline of a large lake. Limnol Oceanogr 55(2010):2353–2365

    Article  Google Scholar 

  27. Saggio A, Imberger J (1998) Internal wave weather in a stratified lake. Limnol Oceanogr 43:1780–1795

    Google Scholar 

  28. Shimizu K, Imberger J (2008) Energetics and damping of basin-scale waves in a strongly stratified lake. Limnol Oceanogr 53:1574–1588

    Article  Google Scholar 

  29. Shimizu K, Imberger J (2009) Damping mechanisms of internal waves in continuously stratified rotating basins. J Fluid Mech 637:137–172

    Article  Google Scholar 

  30. Shimizu K, Imberger J (2010) Seasonal differences in the evolution of damped basin-scale waves in a shallow stratified lake. Limnol Oceanogr 55(3):1449–1462

    Article  Google Scholar 

  31. Shimizu K, Imberger J, Kumagai M (2007) Horizontal structure and excitation of primary motions in a strongly stratified lake. Limnol Oceanogr 52:2641–2655

    Article  Google Scholar 

  32. Shintani T, de la Fuente A, Niño Y, Imberger J (2010) Generalizations of the Wedderburn number: parameterizing upwelling in stratified lakes. Limnol Oceanogr 55(3):1377–1389

    Article  Google Scholar 

  33. Thompson R, Imberger J (1980) Response of a numerical model of a stratified lake to wind stress. In: Proceedings of 2nd international symposium on stratified flows, vol 2, pp 562–570, Trondheim, Norway

  34. Thorpe SA (1974) Near-resonant forcing in a shallow two-layer fluid: a model for the internal surge in Loch Ness. J Fluid Mech 63:509–527

    Article  Google Scholar 

  35. Ulloa H, de la Fuente A, Niño Y, Rozas C, García CM (2011) Experimental study of the free evolution of the internal gravitational waves affected by Coriolis in a stratified flow. In: 7th international symposium on stratified flows, Rome, Italy

  36. Valle-Levinson A (2008) Density-driven exchange flow in terms of the Kelvin and Ekman numbers. J Geophys Res 113:C04001

    Google Scholar 

  37. Van Heijst GJF, Davies PA, Davis RG (1990) Spin-up in a rectangular container. Phys Fluids A 2(2):150–159

    Article  Google Scholar 

  38. Wake GW, Hopfinger EJ, Ivey GN (2007) Experimental study on resonantly forced interfacial waves in a stratified circular cylindrical basin. J Fluid Mech 582:203–222

    Article  Google Scholar 

  39. Wang Y, Hutter K, Baüerle E (2000) Wind-induced baroclinic response of Lake Constance. Ann Geophys 18:1488–1501

    Article  Google Scholar 

  40. Wüest A, Lorke A (2003) Small-scale hydrodynamics in lakes. Annu Rev Fluid Mech 35:373–412

    Article  Google Scholar 

Download references

Acknowledgments

The authors acknowledge support of the Civil Engineering Department, Universidad de Chile, FONDECYT Project 1080617 and the Civil Engineering Department, University of Dundee. The first author acknowledges financial support from Department of Graduate and Postgraduate Degree, Universidad de Chile. Finally, the authors would also like to thank to the anonymous reviewers of this article who provided helpful, interesting and constructive comments.

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Authors and Affiliations

  1. Departamento de Ingeniería Civil, Universidad de Chile, Santiago, Chile

    Carlos Rozas, Alberto de la Fuente & Hugo Ulloa

  2. Department of Civil Engineering, University of Dundee, Dundee, UK

    Peter Davies

  3. Departamento de Ingeniería Civil and Advanced Mining Technology Center, Universidad de Chile, Santiago, Chile

    Yarko Niño

Authors
  1. Carlos Rozas
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  2. Alberto de la Fuente
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  3. Hugo Ulloa
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  4. Peter Davies
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  5. Yarko Niño
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Correspondence to Carlos Rozas.

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Rozas, C., de la Fuente, A., Ulloa, H. et al. Quantifying the effect of wind on internal wave resonance in Lake Villarrica, Chile. Environ Fluid Mech 14, 849–871 (2014). https://doi.org/10.1007/s10652-013-9329-9

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  • DOI: https://doi.org/10.1007/s10652-013-9329-9

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