Residual circulation due to internal waves shoaling on a slope

Limnology and Oceanography

Volumn 55, Issue 3, 2010, Pages 1009-1023

  Nakayama, K ^a   Imberger, J ^b  

^a KITAMI INSTITUTE OF TECHNOLOGY   (Japan)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

BOUSSINESQ EQUATION; BREAKING WAVE; CIRCULATION; INTERNAL WAVE; NUMERICAL MODEL; SHOALING WAVE; SLOPE;

EID: 77955583815     PISSN: 00243590     EISSN: None     Source Type: Journal    
DOI: 10.4319/lo.2010.55.3.1009     Document Type: Article

References (57)

1. ANTENUCCI, J. P., AND J. IMBERGER. 2001. Energetics of long internal gravity waves in large lakes. Limnol. Oceanogr. 46: 1760-1773.
2. -, AND -. 2003. The seasonal evolution of wind/ internal wave resonance in Lake Kinneret. Limnol. Oceanogr. 48: 2055-2061.
3. -,-, A. SAGGIO. 2000. Seasonal evolution of the basin-scale internal wave field in a large stratified lake. Limnol. Oceanogr. 45: 1621-1638.
4. BOEGMAN, L., G. N. IVEY, AND J. IMBERGER. 2005. The degeneration of internal waves in lakes with sloping topography. Limnol. Oceanogr. 50: 1620-1637.
5. BROWN, D. J., AND D. R. CHRISTIE. 1998. Fully nonlinear solitary waves in continuously stratified incompressible Boussinesq fluids. Phys. Fluids 10: 2569-2586, doi:10.1063/1.869771
6. CACCIONE, D., AND C. WUNSCH. 1974. Experimental study of internal waves over a slope. J. Fluid Mech. 66: 223-239, doi:10.1017/S0022112074000164
7. CARRIER, G. F. 1966a. Gravity waves on water of variable depth. J. Fluid Mech. 24: 641-659, doi:10.1017/S0022112066000892
8. -. 1966b. Topics in applied mathematics, v. 2. Mathematical Association of America.
9. -, AND H. P. GREENSPAN. 1958. Water waves of finite amplitude on a sloping beach. J. Fluid Mech. 4: 97-109, doi:10.1017/S0022112058000331
10. DAVIS, R. E., AND A. ACRIVOS. 1967. Solitary internal waves in deep water. J. Fluid Mech. 29: 593-607, doi:10.1017/ S0022112067001041
11. FARMER, D. M. 1978. Observations of long nonlinear internal waves in a lake. J. Phys. Oceanogr. 8: 63-73, doi:10.1175/ 1520-0485(1978)008<0063: OOLNIW>2.0.CO;2
12. FRUCTUS, D., M. CARR, J. GRUE, A. JENSEN, AND P. A. DAVIES. 2009. Shear-induced breaking of large internal solitary waves. J. Fluid Mech. 620: 1-29, doi:10.1017/S0022112008004898
13. GALVIN, C. J. 1968. Breaker type classification on three laboratory beaches. J. Geophys. Res. 73: 3651-3659, doi:10.1029/ JB073i012p03651
14. GILL, A. E. 1982. Atmosphere-ocean dynamics. Academic Press.
15. GLOOR, M., A. WUEST, AND M. MUNNICH. 1994. Benthic boundary mixing and resuspension induced by internal seiches. Hydrobiologia 284: 59-68, doi:10.1007/BF00005731
16. GRUE, J., A. JENSEN, P. RUSAS, AND J. K. SVEEN. 2000. Breaking and broadening of internal solitary waves. J. Fluid Mech. 413: 181-217, doi: 10.1017/S0022112000008648
17. GUILLEMET, B., H. ISAKA, AND P. MASCART. 1983. Molecular dissipation of turbulent fluctuations in the convective mixed layer, i: Height variations of dissipation rates. Boundary-Layer Meteorol. 27: 141-162.
18. HAKANSON, L. 1982. Bottom dynamics in lakes. Hydrobiologia 9: 9-22.
19. HELFRICH, K. R. 1992. Internal solitary wave breaking and run-up on a uniform slope. J. Fluid Mech. 243:133-154, doi:10.1017/ S0022112092002660
20. HOLLOWAY, P. E., E. PELINOVSKY, T. TALIPOVA, AND B. BARNES. 1997. A nonlinear model of internal tide transformation on the Australian North West Shelf. J. Phys. Oceanogr. 27: 871-898, doi:10.1175/1520-0485(1997)027<0871: ANMOIT>2.0.CO;2
21. HORN, D. A., J. IMBERGER, AND G. N. IVEY. 2001. The degeneration of large-scale interfacial gravity waves in lakes. J. Fluid Mech. 434: 181-207, doi:10.1017/S0022112001003536
22. HUTHNANCE, J. M. 1989. Internal tides and waves near the continental shelf edge. Geophys. Astrophys. Fluid Dyn. 48: 81-106, doi: 10.1080/ 03091928908219527
23. IMBERGER, J., AND B. BOASHASH. 1986. Application of the Wigner-Ville distribution to temperature gradient micro structure: A new technique to study small-scale variations. J. Phys. Oceanogr. 16: 1997-2012, doi:10.1175/1520- 0485(1986)016 < 1997:AOTWDT>2.0.CO;2
24. -, AND G. N. IVEY. 1991. On the nature of turbulence in a stratified fluid. Part 2: Application to lakes. J. Phys. Oceanogr. 21: 659-680, doi:10.1175/1520-0485(1991)021 <0659:OTNOTI>2.0.CO;2
25. -, R. O. R. Y. THOMPSON, AND C. FANDRY. 1976. Selective withdrawal from a finite rectangular tank. J. Fluid Mech. 78: 489-512, doi:10.1017/ S0022112076002577
26. INALL, M. E. 2009. Internal wave induced dispersion and mixing on a sloping boundary. Geophys. Res. Lett. 36: L05604, doi:10.1029/2008GL036849
27. IVEY, G. N., AND J. IMBERGER. 1991. On the nature of turbulence in a stratified fluid. Part 1: Energetics of mixing. J. Phys. Oceanogr. 21: 650-658, doi:10.1175/1520-0485(1991)021 <0650:OTNOTI>2.0.CO;2
28. -, AND J. IMBERGER. 1991. On the nature of turbulence in a stratified fluid. Part 1: Energetics of mixing. J. Phys. Oceanogr. 21: 650-658, doi:10.1175/1520-0485(1991)021 <0650:OTNOTI>2.0.CO;2
29. -, AND R. I. NOKES. 1989. Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 204: 479-500, doi:10.1017/S0022112089001849
30. KAKINUMA, T., AND K. NAKAYAMA. 2008. Internal waves induced by typhoon, SUISUI Hydrol. Res. Lett. 1: 1-4.
31. KAO, T. W., F. S. PAN, AND D. RENOUARD. 1985. Internal solitons on the pycnocline: Generation, propagation, and shoaling and breaking over a slope. J. Fluid Mech. 159: 19-53, doi:10.1017/ S0022112085003081
32. LAMB, K. G. 2002. A numerical investigation of solitary internal waves with trapped cores formed via shoaling. J. Fluid Mech. 451: 109-144, doi:10.1017/S002211200100636X
33. LILLY, D. K., D. E. WACO, AND S. I. ADELFANG. 1967. The representation of small-scale turbulence in numerical simulation experiments. Proceedings of the IBM Science and Computer Symposium on Environmental Science.
34. LONGUET-HIGGINS, M. S. 1983. Wave set-up, percolation and undertow in the surf zone. Proc. R. Soc. Lond. 390: 283-291, doi:10.1098/rspa.1983.0132
35. MADSEN, O. S., AND C. C. MEI. 1969. The transformation of a solitary wave over an uneven bottom. J. Fluid Mech. 39: 781-791, doi: 10.1017/ S0022112069002461
36. MCPHEE-SHAW, E., AND E. KUNZE. 2002. Boundary layer intrusions from a sloping bottom: A mechanism for generating intermediate nepheloid layers. J. Geophys. Res. 107:1-16, doi:10.1029/2001JC000801
37. MEI, C. C. 1989. The applied dynamics of ocean surface waves. World Scientific.
38. MiCHALLET, H., AND G. N. IVEY. 1999. Experiments on mixing due to internal solitary waves breaking on uniform slopes. J. Geophys. Res. 104: 13467-13477, doi:10.1029/1999JC900037
39. NADAOKA, K., AND T. KONDOH. 1982. Laboratory measurements of velocity field structure in the surf zone by ldv. Coast. Eng. Jpn. 25: 125-145.
40. NAKAMURA, T., K. KUDOH, AND T. ISHIKAWA. 2004. Development of CIP-reversed weighted residual method for water flow with free water surface and arbitrary topography. JASME Int. J. 47: 690-698, doi:10.1299/jsmeb.47.690
41. NAKAYAMA, K. 2006. Comparisons of using CIP, compact and CIP-CSL2 schemes for internal solitary waves. Int. J. Numer. Method F. 51: 197-219, doi:10.1002/fld.1112
42. -, T. OKADA, AND M. NOMURA. 2005. Mechanism responsible for fortnightly modulations in estuary circulation in Tokyo Bay. Estuar. Coast. Shelf Sci. 64: 459-466, doi: 10.1016/j.ecss.2005.03.002
43. OIKAWA, M., AND N. YAJIMA. 1973. Interaction of solitary waves-a perturbation approach to nonlinear system. J. Phys. Soc. Jpn. 34: 1093-1099, doi: 10.1143/JPSJ.34.1093
44. OKADA, T., AND K. NAKAYAMA. 2007. Modeling of dissolved oxygen in an enclosed bay with sill. J. Environ. Eng. Am. Soc. Civ. Eng. 133: 447-453.
45. OSTROVSKY, I., Y. Z. YACOBI, P. WALLINE, AND I. KALIKHMAN. 1996. Seiche-induced mixing-its impact on lake productivity. Limnol. Oceanogr. 41: 323-332.
46. OSTROVSKY, L. A., AND Y. A. STEPANYANTS. 1989. Do internal solitons exist in the ocean? Rev. Geophys. 27: 293-310, doi: 10.1029/RG027i003p00293
47. PEREGRINE, D. H. 1967. Long waves on a beach. J. Fluid Mech. 27: 815-827, doi:10.1017/S0022112067002605
48. PIERSON, D. C., AND G. A. WEYHENMEYER. 1994. High resolution measurements of sediment resuspension above an accumulation bottom in a stratified lake. Hydrobiologia 284: 43-57, doi:10.1007/BF00005730
49. SCHMIDT, H., AND U. SCHUMANN. 1989. Coherent structure of the convective boundary layer derived from large-eddy simulations. J. Fluid Mech. 200: 511-562, doi:10.1017/ S0022112089000753
50. SCHUMANN, U. 1991. Subgrid length-scales for large-eddy simulation of stratified turbulence. Theor. Comput. Fluid Dyn. 2: 279-290, doi:10.1007/BF00271468
51. SILVA, I. P. D. D., J. IMBERGER, AND G. N. IVEY. 1997. Localized mixing due to a breaking internal wave ray at a sloping bed. J. Fluid Mech. 350: 1-27, doi:10.1017/S0022112097006939
52. STAMP, A. P., AND M. JACKA. 1995. Deep-water internal solitary waves. J. Fluid Mech. 305: 347-371, doi:10.1017/ S0022112095004654
53. STEINMAN, B., W. ECKERT, S. KAGANOWSKY, AND T. ZOHARY. 1997. Seiche-induced resuspension in Lake Kinneret: A fluorescent tracer experiment. Water Air Soil Poll. 99: 123-131.
54. SVEEN, J. K., Y. Guo, P. A. DAVIES, AND J. GRUE. 2002. On the breaking of internal solitary waves at a ridge. J. Fluid Mech. 469: 161-188, doi:10.1017/S0022112002001556
55. THORPE, S. A. 1978. On the shape and breaking of finite amplitude internal gravity waves in a shear flow. J. Fluid Mech. 85: 7-31, doi:10.1017/S0022112078000518
56. WALLACE, B. C., AND D. L. WILKINSON. 1988. Run-up of internal waves on a gentle slope in a two-layered system. J. Fluid Mech. 191: 419-442, doi:10.1017/S0022112088001636
57. WESSELS, F., AND K. HUTTER. 1996. Interaction of internal waves with a topographic sill in a two-layered fluid. J. Phys. Oceanogr. 26: 5-20, doi: 10.1175/1520-0485(1996)026 <0005:IOIWWA>2.0.CO;2