Finite-amplitude deep-water waves on currents
- 31 August 1979
- journal article
- Published by The Royal Society in Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- Vol. 292 (1392) , 371-390
- https://doi.org/10.1098/rsta.1979.0066
Abstract
Accurate integral properties of plane periodic deep-water waves of amplitudes up to the steepest are tabulated by Longuet-Higgins (1975). These are used to define an averaged Lagrangian which, following Whitham, is used to describe the properties of slowly varying wave trains. Two examples of waves on large-scale currents are examined in detail. One flow is that of a shearing current, V ( x ) j , which causes waves to be refracted. The other flow, U ( x ) i , varies in the direction of wave propagation and causes waves to either steepen or become more gentle. Some surprising features are found.Keywords
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