Skip to main content Accessibility help

Improved linear representation of surface waves. Part 2. Slowly varying bottoms and currents

  • Jon Wright (a1) and Dennis B. Creamer (a2)


We extend the results of a previous paper to fluids of finite depth. We consider the Hamiltonian theory of waves on the free surface of an incompressible fluid, and derive the canonical transformation that eliminates the leading order of nonlinearity for finite depth. As in the previous paper we propose using the Lie transformation method since it seems to include a nearly correct implementation of short waves interacting with long waves. We show how to use the Eikonal method for slowly varying currents and/or depths in combination with the nonlinear transformation. We note that nonlinear effects are more important in water of finite depth. We note that a nonlinear action conservation law can be derived.



Hide All
Creamer, D. B., Henyey, F., Schult, R. & Wright, J. 1989 Improved linear representation of ocean surface waves. J. Fluid Mech. 205, 135161 (referred to herein as Paper I).
Ding, L. & Farmer, D. M. 1993 A Monte-Carlo study on breaking wave statistics and comparison with field observations. Preprint, Institute of Ocean Sciences, Sidney, B. C., Canada.
Henyey, F. S., Creamer, D. B., Dysthe, K. B., Schult, R. L. & Wright, J. A. 1988 The energy and action of small waves riding on large waves. J. Fluid Mech. 189, 443462.
Miles, J. W. 1977 On Hamilton's principle for surface waves. J. Fluid Mech. 83, 153158.
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. J. Fluid Mech. 9, 193217.
Watson, K. M. & McBride, J. 1993 Excitation of capillary waves by longer waves. J. Fluid Mech. 250, 103119.
West, B. J. 1981 Deep Water Gravity Waves, p. 33. Springer.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190194.
Zakharov, V. E. 1991 Inverse and direct cascade in the wind-driven surface turbulence and wave breaking. Proc. IUTAM Congress on Wave Breaking, Sydney, Australia.
MathJax is a JavaScript display engine for mathematics. For more information see

Improved linear representation of surface waves. Part 2. Slowly varying bottoms and currents

  • Jon Wright (a1) and Dennis B. Creamer (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed