Numerical studies on the degeneration of internal waves induced by an initial tilted pycnocline

LIN Zhenhua; SONG Jinbao

doi:10.1007/s13131-014-0503-9

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Article Navigation > Acta Oceanologica Sinica > 2014 > 33(7): 27-39

LIN Zhenhua, SONG Jinbao. Numerical studies on the degeneration of internal waves induced by an initial tilted pycnocline[J]. Acta Oceanologica Sinica, 2014, 33(7): 27-39. doi: 10.1007/s13131-014-0503-9

Citation:

LIN Zhenhua, SONG Jinbao. Numerical studies on the degeneration of internal waves induced by an initial tilted pycnocline[J]. Acta Oceanologica Sinica, 2014, 33(7): 27-39. doi: 10.1007/s13131-014-0503-9

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Numerical studies on the degeneration of internal waves induced by an initial tilted pycnocline

doi: 10.1007/s13131-014-0503-9

Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China;Key Laboratory of Ocean Circulation and Waves (KLOCAW), Chinese Academy of Sciences, Qingdao 266071, China

Received Date: 2013-08-28
Rev Recd Date: 2013-11-26

Abstract

Abstract

The pycnocline in a closed domain is tilted by external wind forcing and tends to restore to a level position when the wind falls. An internal seiche oscillation exhibits if the forcing is weak, otherwise internal surge and internal solitary waves emerge, which serve as a link to cascade energy to small-scale processes. A two-dimensional non-hydrostatic code with a turbulence closure model is constructed to extend previous laboratory studies. The model could reproduce all the key phenomena observed in the corresponding laboratory experiments. The model results further serve as a comprehensive and reliable data set for an in-depth understanding of the related dynamical process. The comparative analyses indicate that nonlinear term favors the generation of internal surge and subsequent internal solitary waves, and the linear model predicts the general trend reasonably well. The vertical boundary can approximately reflect all the incoming waves, while the slope boundary serves as an area for small-scale internal wave breaking and energy dissipation. The temporal evolutions of domain integrated kinetic and potential energy are also analyzed, and the results indicate that about 20% of the initial available potential energy is lost during the first internal wave breaking process. Some numerical tactics such as grid topology and model initialization are also briefly discussed.
- internal wave

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References(36)

References

Aghsaee P, Boegman L, Lamb K G. 2010. Breaking of shoaling internal solitary waves. J Fluid Mech, 659: 289-317

Boegman L, Imberger J, Ivey G N, et al. 2003. High-frequency internal waves in large stratified lakes. Limnol Oceanogr, 48: 895-919

Boegman L, Ivey G N, Imberger J. 2005a. The energetics of large-scale internal wave degeneration in lakes. J Fluid Mech, 531: 159-180

Boegman L, Ivey G N, Imberger J. 2005b. The degeneration of internal waves in lakes with sloping topography. Limnol Oceanogr, 50: 1620-1637

Boegman L, Ivey G N. 2009. Flow separation and resuspension beneath shoaling nonlinear internal waves. J Geophys Res, 114: C02018

Botelho, D, Imberger J, Dallimore C, et al. 2009. A hydrostatic/non-hydrostatic grid-switching strategy for computing high-frequency, high wave number motions embedded in geophysical flows. Environ Modell Softw, 24(4): 473-488

Cai Shuqun, Xie Jieshuo, He Jianling. 2012. An overview of internal solitary waves in the South China Sea. Surveys in Geophysics, 33(5): 927-943

Farmer D M. 1978. Observations of long nonlinear internal waves in a lake. J Phys Oceanogr, 8: 63-73

Fricker P D, Nepf H M. 2000. Bathymetry, stratification, and internal seiche structure. J Geophys Res, 105: 14237-14251

Fringer O B, Street R L. 2003. The dynamics of breaking progressive interfacial waves. J Fluid Mech, 494: 319-353

Heaps N S, Ramsbottom A E. 1966. Wind effects on the water in a narrow two-layered lake. Philos T R Soc: A, 259: 391-430

Helfrich K R. 1992. Internal solitary wave breaking and run-up on a uniform slope. J Fluid Mech, 243: 133-154

Horn D A, Imberger J, Ivey G N. 2001. The degeneration of large-scale interfacial gravity waves in lakes. J Fluid Mech, 434: 181-207

Horn D A, Imberger J, Ivey G N, et al. 2002. A weakly nonlinear model of long internal waves in closed basins. J Fluid Mech, 467: 269-287

Horn W, Mortimer C H, Schwab D J. 1986. Wind-induced internal seiches in Lake Zurich observed and modeled. Limnol Oceanogr, 31: 1232-1254

Hunkins K, Fliegel M. 1973. Internal undular surges in Seneca Lake: a natural occurrence of solitons. J Geophys Res, 78: 539-548

Jasak H. 1996. Error analysis and estimation for the finite volume method with applications to fluid flows [dissertation]. London: Imperial College London, University of London

Lamb K G, Boegman L, Ivey G N. 2005. Numerical simulations of shoaling internal solitary waves in tilting tank experiments. In: Folkard, Jones I, Eds. Proceedings 9th European Workshop on Physical Processes in Natural Waters Lancaster: Lancaster University, 31-38

Lamb K G, Nguyen V T. 2009. Calculating energy flux in internal solitary waves with an application to reflectance. J Phys Oceanogr, 39: 559-580

Lemmin U. 1987. The structure and dynamics of internal waves in Baldeggersee. Limnol Oceanogr, 32: 43-61

Michallet H, Ivey G N. 1999. Experiments on mixing due to internal solitary waves breaking on uniform slopes. J Geophys Res, 104: 13467-13477

Mortimer C H. 1952. Water movements in lakes during summer stratification: evidence from the distribution of temperature in Windermere. Philos T R Soc: B, 236: 355-398

Monismith S. 1986. An experimental study of the upwelling response of stratified reservoirs to surface shear stress. J Fluid Mech, 171: 407-439

Sakai T, Redekopp L G. 2010. A parametric study of the generation and degeneration of wind-forced long internal waves in narrow lakes. J Fluid Mech, 645: 315

Spigel R H, Imberger J. 1980. The classification of mixed-layer dynamics of lakes of small to medium size. J Phys Oceanogr, 10: 1104-1121

Stashchuk N, Vlasenko V, Hutter K. 2005. Numerical modelling of disintegration of basin-scale internal waves in a tank filled with stratified water. Nonlinear Proc Geoph, 12: 955-964

Stevens C, Lawrence G, Hamblin P, et al. 1996. Wind forcing of internal waves in a long narrow stratified lake. Dynam Atmos Oceans, 24: 41-50

Stevens C, Lawrence G. 1997. Estimation of wind-forced internal seiche amplitudes in lakes and reservoirs, with data from British Columbia. Canada Aquat Sci, 59: 115-134

Thompson R O R Y, Imberger J. 1980. Response of a numerical model of a stratified lake to wind stress. In: Carstens T, McClimans T, eds. Second International Symposium on Stratified Flows. Trondheim, Norway: IAHR, 562-570

Thorpe S A. 1971. Asymmetry of the internal seiche in Loch Ness. Nature, 231: 306-308

Thorpe S A, Hall A, Crofts I. 1972. The internal surge in Loch Ness. Nature, 237: 96-98

Thorpe S A. 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 Venayagamoorthy S K, Fringer O B. 2007. On the formation and propagation of nonlinear internal boluses across a shelf break. J Fluid Mech, 577: 137-159

Vitousek S, Fringer O B. 2011. Physical vs. numerical dispersion in nonhydrostatic ocean modeling. Ocean Model, 40(1): 72-86

Weller H G, Tabor G, Jasak H, et al. 1998. A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys, 12: 620-631

Wiegand R C, Carmack E C. 1986. The climatology of internal waves in a deep temperate lake. J Geophys Res, 91: 3951-3958

Wu J. 1977. A note on the slope of a density interface between two stably stratified fluids under wind. J Fluid Mech, 81: 335-339

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