Nonlinear shear instabilities of alongshore currents on plane beaches

Journal of Fluid Mechanics

Volumn 310, Issue , 1996, Pages 181-213

  Allen, J S ^a   Newberger, P A ^a   Holman, R A ^a  

^a OREGON STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BEACHES; BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; FRICTION; PROBLEM SOLVING; SURFACE WAVES;

ALONGSHORE CURRENTS; NONLINEAR SHEAR INSTABILITIES; PLANE BEACHES;

OCEAN CURRENTS;

ALONGSHORE; BEACHES; CURRENTS; NONLINEAR INSTABILITY; PLANE; SHEAR STABILITY;

KELVIN-HELMHOLTZ INSTABILITY; NEARSHORE CURRENTS; NONLINEAR DYNAMICS; SHALLOW-WATER EQUATIONS; SURF ZONE;

EID: 0029656639     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096001772     Document Type: Article

References (21)

1. ARAKAWA, A. & LAMB, V. R. 1977 Computational design of the basic dynamical processes of the UCLA general circulation model. Meth. Comput. Phys, 17, 173-265.
2. ARNEODO, A., COULLET, P., TRESSER, C., LIBCHABER, A., MAURER, J. & D'HUMIÈRES, D. 1983 On the observation of an uncompleted cascade in a Raleigh-Bènard experiment. Physica 6D, 385-392.
3. BENNETTIN, G., GALGANI, L. & STRELCYN, J.-M. 1976 Kolmogorov entropy and numerical experiments. Phys. Rev. A 14, 2338-2345.
4. BOWEN, A. J. & HOLMAN, R. A. 1989 Shear instabilities of the mean longshore current, 1. Theory. J. Geophys. Res. 94(C12), 18023-18030.
5. DEIGAARD, R., CHRISTENSEN, E. D., DAMGAARD, J. S. & FREDSØE, J. 1994 Numerical simulation of finite amplitude shear waves and sediment transport. Proc. 24th Intl Conf. Coastal Engng, pp. 1919-1933. ASCE.
6. DODD, N. 1994 On the destabilization of a longshore current on a plane beach: Bottom shear stress, critical conditions, and onset of instability, J. Geophys. Res. 99(C1), 811-828.
7. DODD, N., OLTMAN-SHAY, J. & THORNTON, E. B. 1992 Shear instabilities in the longshore current: A comparison of observation and theory. J. Phys. Oceanogr. 22, 62-82.
8. DODD, N. & THORNTON, E. B. 1990 Growth and energetics of shear waves in the nearshore. J. Geophys. Res. 95(C9), 16075-16083.
9. DODD, N. & THORNTON, E. B. 1992 Longshore current instabilities: growth to finite amplitude. Proc. 23rd Intl. Conf. Coastal Engng, pp. 2655-2668. ASCE.
10. DRAZIN, P. G. & REID, W. H. 1981 Hydrodynamic Stability Cambridge University Press.
11. FALQUÉS, A. & IRANZO, V. 1994 Numerical simulation of vorticity waves in the nearshore. J. Geophys. Res. 99(C1), 825-841.
12. FALQUÉS, A., IRANZO, V. & CABALLERIA, M. 1994 Shear instability of longshore currents: effects of dissipation and non-linearity. Proc. 24th Intl Conf. Coastal Engng, pp. 1983-1997. ASCE.
13. GOLDHIRSCH, I., SULEM, P-L. & ORSZAG, S. A. 1987 Stability and Lyapunov stability of dynamical systems: A differential approach and a numerical method. Physica 27D, 311-337.
14. FEIGENBAUM, M. J. 1978. Quantitative universality for a class of nonlinear transformations. J. Statist. Phys. 19, 25-52.
15. FEIGENBAUM, M. J. 1983 Universal behaviour in nonlinear systems. Physica 7D, 16-39.
16. Ho, C.-M. & HUERRE, P. 1984 Perturbed free shear layers. Ann Rev. Fluid Mech. 16, 365-424.
17. KLAASSEN, G. P. & PELTIER, W. R. 1989 The role of transverse secondary instabilities in the evolution of free shear layers. J. Fluid Mech. 202, 367-402.
18. LIBCHABER, A. & MAURER, J. 1982 A Rayleigh-Bénard experiment: helium in a small box. In Nonlinear Phenomena at Phase Transitions and Instabilities (ed. T. Riste), pp. 259-286. Plenum.
19. OLTMAN-SHAY, J., HOWD, P. A. & BIRKEMEIER, W. A. 1989 Shear instabilities of the mean longshore current, 2. Field data. J. Geophys. Res. 94(C12), 18031-18042.
20. SIROVICH, L. & DEANE, A. E. 1991. A computational study of Rayleigh-Bénard convection. Part 2. Dimension considerations. J. Fluid Mech. 222, 251-265.
21. WOLF, A., SWIFT, J. B., SWINNEY, H. L. & VASTANO, J. A. 1985 Determining Lyapunov exponents from a time series. Physica 16D, 285-317.