An approximated method for the solution of elliptic problems in thin domains: Application to nonlinear internal waves

Ocean Modelling

Volumn 25, Issue 3-4, 2008, Pages 144-153

  Scotti, A ^a   Mitran, S ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Dispersion relationship; Nonhydrostatic approximation; Nonlinear internal waves

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION;

COMPUTATIONALLY EXPENSIVE; DIMENSIONAL PROBLEMS; DISPERSION RELATIONSHIP; ELLIPTIC PROBLEMS; HORIZONTAL GRID SPACING; NON-HYDROSTATIC MODEL; NONHYDROSTATIC APPROXIMATION; NONLINEAR INTERNAL WAVES; NONLINEAR STEEPENING; NUMERICAL SIMULATIONS; ONE-DIMENSIONAL; SECOND ORDERS; SURFACE BOUNDARIES; THIN DOMAINS; TOTAL DEPTH; VERTICAL DIRECTIONS;

DISPERSION (WAVES);

BOUNDARY CONDITION; COMPUTER SIMULATION; EXPERIMENTAL STUDY; HYDROSTATICS; INCOMPRESSIBLE FLOW; INTERNAL WAVE; NONLINEAR WAVE; ONE-DIMENSIONAL MODELING; WAVE DISPERSION; WAVE MODELING;

EID: 52149110933     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2008.07.005     Document Type: Article

References (47)

1. Apel J.R. A new analytical model for internal solitons in the oceans. J. Phys. Ocean. 33 (2003) 2247-2269
2. Aris R. Vectors, Tensors, and the Basic Equatios of Fluid Mechanics (1989), Dover
3. Benney D.J. Long nonlinear waves in fluid flows. J. Math. Phys. 45 (1966) 52-63
4. Bogucki D., Dickey T., and Redekopp L.F. Sediment resuspension and mixing by resonantly generated internal solitary waves. J. Phys. Ocean. 27 (1997) 1181
5. Butman B., Alexander P.S., Scotti A., Beardsley R.C., and Anderson S. Large internal waves in Massachusetts Bay transport sediments offshore. Cont. Shelf. Res. 26 (2006) 2029-2049
6. Canuto C., Hussaini M.Y., Quarteroni A., and Zang T.A. Spectral Methods in Fluid Dynamics (1987), Springer, Berlin
7. Choi W., and Camassa R. Fully nonlinear internal waves in a two-fluid system. J. Fluid Mech. 396 (1999) 1
8. Dubreil-Jacotin M.L. Sur les théorèmes d'existence relatifs aux ondes permanentes périodiques à deux dimensions dans les liquides hétérogènes. J. Math. Pures Appl. 19 9 (1937) 43
9. Durran D.R. Numerical Methods for Wave Equations in Geophysical Fluid Dynamics (1999), Springer, Berlin
10. Fringer O.B., Gerritsen M., and Street R.L. An unstructured-grid finite-volume nonhydrostatic parallel coastal ocean simulator. Ocean Modeling 14 (2006) 139-278
11. Griffies S.M. Fundamentals of Ocean Climate Models (2004), Princeton University Press
12. Grimshaw R. Internal solitary waves. In: Liu L.-F. (Ed). Advances in Coastal and Ocean Engineering vol. 3 (1997), World Scientific, Singapore 1-30
13. Grimshaw R. Environmental Stratified Flows (2001), Kluwer Academic Publishers, Dordrecht
14. Grimshaw R., Pelinovsky E., and Talipova T. Solitary wave transformation in a medium with sign-variable quadratic nonlinearity and cubic nonlinearity. Physica D 132 (1999) 40-62
15. Grimshaw R.H.J., and Smyth N. Resonant flow of a stratified fluid over topography. J. Fluid Mech. 169 (1986) 429
16. Gurevich A.V., and Pitaevskii L.P. Decay of initial discontinuity in the Korteweg-de Vries equation. JETP Lett. 17 (1973) 193-195
17. Gurevich A.V., and Pitaevskii L.P. Nonstationary structure of a collisionless shock wave. JETP Lett. (1973)
18. Haidvogel D.B., and Beckmann A. Numerical Ocean Circulation Modeling (1999), Imperial College Press
19. Halpern D. Semidiurnal tides in Massachusetts Bay. J. Geophys. Res. 76 (1971) 6573
20. Helfrich K. Decay and return of internal solitary waves with rotation. Phys. Fluids 19 2 (2007) 026601
21. Helfrich K.R., and Melville W.K. Long nonlinear internal waves. Ann. Rev. Fluid Mech. 38 1 (2006) 395-425
22. Helfrich K.R., and Pineda J. Accumulation of particles in propagating fronts. Limnol. Oceanogr. 48 4 (2003) 1509-1520
23. Holloway P.E., Pelinovsky E., and Talipova T. A generalized Korteweg-de Vries model of internal tide transformation in the coastal zone. J. Geophys. Res. 104 (1999) 18300
24. Holloway P.E., Pelinovsky E., Talipova T., and Barnes B. A nonlinear model of internal tide transformation on the Australian north west shelf. J. Phys. Ocean. 27 (1997) 871
25. Jackson C.R. An Atlas of Internal Solitary-like Internal Waves (2004), Global Ocean Associates
26. Klymak J.M., and Moum J.N. Internal solitary waves of elevation advancing on a shoaling shelf. Geophys. Res. Lett. 30 (2003) 2045 10.1029/2003GL017706
27. Korteweg D.J., and de Vries G. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philos. Mag. Ser. 39 (1895) 422-443
28. Kundu P.K., and Cohen I.M. Fluid Mechanic (2008), Academic Press, New York
29. Lamb K., and Wan B. Conjugate flows and flat solitary waves for a continuosly stratified fluid. Phys. Fluids 10 (1998) 2061
30. Leichter J.J., Stewart H.L., and Miller S.L. Episodic nutrient transport of Florida coral reefs. Limnol. Oceanogr. 48 4 (2003) 1394-1407
31. Liu A.K., and Benney D.J. The evolution of nonlinear wave trains in stratified shear flows. J. Phys. Ocean. 15 (1981) 1613-1624
32. Long R.R. Some aspects of the flow of stratified fluids. Part I. A theoretical investigation. Tellus 5 (1953) 42
33. MacKinnon J., and Gregg M. Mixing on the late-summer New England Shelf-Solibores, shear and stratification. J. Phys. Ocean. 33 (2003) 1476-1492
34. Marshall J.A., Adcroft A., Hill C., Perelman L., and Heisey C. A finite-volutme, incompressible Navier Stokes model of studies of the ocean on parallel computers. J. Geophys. Res. 102 C3 (1997) 5753-5766
35. Miller M.J., and White A.A. On the nonhydrostatic equatios pressure and sigma coordinates. Q.J.R. Meteorol. Soc. 110 (1984) 515-533
36. Moum J.N., Farmer D.M., Smyth W.D., Armi L., and Vagle S. Structure and generation of turbulence at interfaces strained by internal solitary waves propagating shoreward over the continental shelf. J. Phys. Ocean. 33 10 (2003)
37. Osborne A.R., and Burch T.I. Internal solitons in the Andaman Sea. Science 208 (1980) 451
38. Pedlosky J. Geophysical Fluid Dynamics (1986), Springer, Berlin
39. Pineda J. Circulation and larval distribution in internal tidal bore warm fronts. Limnol. Oceanogr. 44 6 (1999) 1400-1414
40. Rudin W. Real and Complex Analysis (1987), McGraw-Hill, New York
41. Scotti A., Beardsley R., and Butman B. On the interpretation of energy and energy fluxes of nonlinear internal waves: an example from Massachusetts Bay. J. Fluid Mech. 561 (2006) 103-112
42. Scotti A., Beardsley R.C., and Butman B. Generation and propagation of nonlinear internal waves in Massachusetts Bay. J. Geophys. Res. 112 (2007) C10001 10.1029/2007JC004313
43. Scotti A., and Pineda J. Obervation of very large and steep waves of elevation near the Massachusetts coast. Geophys. Res. Lett. 31 (2004) L22307
44. Scotti A., and Pineda J. Plankton accumulation and transport in propagating nonlinear internal fronts. J. Mar. Res. 65 (2007) 117-145
45. Smyth N.F., and Holloway P.E. Hydraulic jump and undular bore formation on a shelf break. J. Phys. Ocean. 18 (1988) 947-962
46. Stanton T.P., and Ostrovsky L.A. Observations of highly nonlinear, tidally forced solitons over the continental shelf. Geophys. Res. Lett. 25 (1998) 2695
47. Ziegenbein J. Short internal waves in the Strait of Gibraltar. Deep-sea Res. 16 (1969) 479