The dynamics of breaking progressive interfacial waves

Journal of Fluid Mechanics

Volumn 494, Issue , 2003, Pages 319-353

  Fringer, Oliver B ^a   Street, Robert L ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; MIXING; NUMERICAL METHODS; SHEAR STRESS; WAVES;

INTERFACIAL WAVES;

FLUID DYNAMICS;

ENERGY DISSIPATION; FLUID MECHANICS; INSTABILITY; MATHEMATICAL MODELING; MIXING; WAVE BREAKING; WAVE ENERGY;

EID: 0345530058     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003006189     Document Type: Article

References (43)

1. ARMFIELD, S. W. & STREET, R. L. 2000 Fractional step methods for the Navier-Stokes equations on non-staggered grids. ANZIAM J. 42(E), C134-C156.
2. BAKER, B. R., MEIRON, D. I. & ORSZAG, S. A. 1982 Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477-501.
3. CHEN, G., KHARIF, C., ZALESKI, S. & LI, J. 1999 Two-dimensional Navier-Stokes simulation of breaking waves. Phys. Fluids 11, 121-133.
4. COKELET, E. D. 1977 Breaking waves. Nature 267, 769-774.
5. DÖRNBRACK, A. 1998 Turbulent mixing by breaking gravity waves. J. Fluid Mech. 375, 113-141.
6. DÖRNBRACK, A. & GERZ, T. 1995 Generation of turbulence by overturning gravity waves below a critical level. In Proc. 11th Symposium on Boundary Layers and Turbulence, pp. 576-579. American Meteorological Society.
7. DRAZIN, P. G. 1977 On the instability of an internal gravity wave. Proc. R. Soc. Lond. A 356, 411-432.
8. FRINGER, O. B. 2003 Numerical simulations of breaking interfacial waves. PhD dissertation, Stanford University.
9. HARLOW, F. H. & WELCH, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of a fluid with free surface. Phys. Fluids 8, 2182-2189.
10. HAZEL, P. 1972 Numerical studies of the stability of inviscid stratified shear flows. J. Fluid Mech. 51, 39-61.
11. HODGES, B. R. & STREET, R. L. 1999 On simulation of turbulent nonlinear free-surface flows. J. Comput. Phys. 151, 425-457.
12. HOLYER, J. Y. 1979 Large amplitude progressive interfacial waves. J. Fluid Mech. 93, 433-448.
13. IVEY, G. N. & IMBERGER, J. 1991 On the nature of turbulence in a stratified fluid. Part I: The energetics of mixing. J. Phys. Oceanogr. 21, 650-658.
14. JOU, W. & WEISSMAN, M. A. 1987 A perturbation solution for long internal waves. Phys. Fluids 30, 1699-1707.
15. LEONARD, B. P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Meth. Appl. Mech. 19, 59-98.
16. LEONARD, B. P. 1987 Sharp simulation of discontinuities in highly convective steady flow. NASA Techn. Mem. 100240.
17. LIN, C. L., FERZIGER, J. H., KOSEFF, J. R. & MONISMITH, S. G. 1993 Simulation and stability of two-dimensional internal gravity waves in a stratified shear flow. Dyn. Atmos. Oceans 19, 325-366.
18. LINDEN, P. F. & REDONDO, J. J. 1991 Molecular mixing in Rayleigh-Taylor instability. Phys. Fluids A 3, 1269-1277.
19. MCEWAN, A. D. 1983a Internal mixing in stratified fluids. J. Fluid Mech. 128, 59-80.
20. MCEWAN, A. D. 1983b The kinematics of stratified mixing through internal wave breaking. J. Fluid Mech. 128, 47-48.
21. MEIRON, D. I. & SAFFMAN, P. G. 1983 Overhanging interfacial gravity waves of large amplitude. J. Fluid Mech. 129, 213-218.
22. MICHALLET, H. & IVEY, G. N. 1999 Experiments on mixing due to internal solitary waves breaking on uniform slopes. J. Geophys. Res. 104, 13,467-13,477.
23. MUNK, W. & WUNSCH, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. 45, 1977-2010.
24. PETRUNCIO, E. T., ROSENFELD, L. K. & PADUAN, J. D. 1998 Observations of the internal tide in Monterey Canyon. J. Phys. Oceanogr. 28, 1873-1903.
25. PHILLIPS, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.
26. PUCKETT, E. G., ALMGREN, A. S., BELL, J. B., MARCUS, D. L. & RIDER, W. J. 1997 A high-order projection method for tracking fluid interfaces in variable density incompressible flows. J. Comput. Phys. 130, 269-282.
27. REHMANN, C. R. 1995 Effects of stratification and molecular diffusivity on the mixing efficiency of decaying grid turbulence. PhD dissertation, Stanford University.
28. ROBERTS, E. S. 1998 Programming Abstractions in C. Addison-Wesley.
29. ROSENFELD, L. & KUNZE, E. 1998 Internal waves in Monterey Canyon. Coastal Ocean Processes Symp., Woods Hole, MA, Woods Hole Oceanographic Institution. Extended abstracts.
30. SLINN, D. N. & RILEY, J. J. 1998a Turbulent dynamics of a critically reflecting internal gravity wave. Theor. Comput. Fluid Dyn. 11, 281-303.
31. SLINN, D. N. & RILEY, J. J. 1998b A model for the simulation of turbulent boundary layers in an incompressible stratified flow. J. Comput. Phys. 144, 550-602.
32. SMYTH, W. D. & WINTERS, K. B. 2003 Turbulence and mixing in Holmboe waves. J. Phys. Oceanogr. 33, 694-711.
33. STANTON, T. P. & OSTROVSKY, L. A. 1998 Observations of highly nonlinear interal solitons over the continental shelf. Geophys. Res. Lett. 25, 2695-2698.
34. STOKES, G. G. 1880 Considerations relative to the greatest height of oscillatory irrotational waves. Mathematical and Physical Papers, vol. 1, pp. 225-228. Cambridge University Press.
35. THOMPSON, R. O. R. Y. 1980 Efficiency of conversion of kinetic energy to potential energy by a breaking internal gravity wave. J. Geophys. Res. 85, 6631-6635.
36. 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.
37. TROY, C. D. 2003 The breaking and mixing of interfacial waves. PhD dissertation, Stanford University.
38. TSUGI, Y. & NAGATA, Y. 1973 Stokes' expansion of internal deep water waves to the fifth order. J. Oceanogr. Soc. Japan 29, 61-69.
39. WINTERS, K. B. & D'ASARO, E. A. 1989 Two-dimensional instability of finite amplitude internal gravity wave packets near a critical level. J. Geophys. Res. 94, 12,709-12,719.
40. WINTERS, K. B. & D'ASARO, E. A. 1994 Three-dimensional wave instability near a critical level. J. Fluid Mech. 272, 255-284.
41. WINTERS, K. B., LOMBARD, P. N., RILEY, J. J. & D'ASARO, E. A. 1995 Available potential energy and mixing in density-stratified flows. J. Fluid Mech. 289, 115-128.
42. WINTERS, K. B. & RILEY, J. J. 1992 Instability of internal waves near a critical level. Dyn. Atmos. Oceans 16, 249-278.
43. ZANG, Y., STREET, R. L. & KOSEFF, J. R. 1994 A non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 18-33.