Surface waves on vertically sheared flows: Approximate dispersion relations
Article first published online: 20 SEP 2012
Copyright 1989 by the American Geophysical Union.
Journal of Geophysical Research: Oceans (1978–2012)
Volume 94, Issue C1, pages 1013–1027, 15 January 1989
How to Cite
1989), Surface waves on vertically sheared flows: Approximate dispersion relations, J. Geophys. Res., 94(C1), 1013–1027, doi:10.1029/JC094iC01p01013., and (
- Issue published online: 20 SEP 2012
- Article first published online: 20 SEP 2012
- Manuscript Accepted: 17 JUL 1988
- Manuscript Received: 16 MAR 1988
Assuming linear wave theory for waves riding on a weak current of 0(ε) compared to the wave phase speed, an approximate dispersion relation is developed to 0(ε2) for arbitrary current U(z) in water of finite depth. The 0(ε2) approximation is shown to be a significant improvement over the 0(ε) result, in comparison with numerical and analytic results for the full problem. Various current profiles in the full range of water depths are considered. Comments on approximate action conservation and application to depth-averaged wave models are included.