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On the Lagrangian description of steady surface gravity waves

Published online by Cambridge University Press:  08 October 2007

DIDIER CLAMOND
DIDIER CLAMOND*
Affiliation:
Institutt For Energiteknikk, P O Box 40, 2027 Kjeller, [email protected]
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Abstract

This paper concerns the mathematical formulation of two-dimensional steady surface gravity waves in a Lagrangian description of motion. It is demonstrated first that classical second-order Lagrangian Stokes-like approximations do not exactly represent a steady wave motion in the presence of net mass transport (Stokes drift). A general mathematically correct formulation is then derived. This derivation leads naturally to a Lagrangian Stokes-like perturbation scheme that is uniformly valid for all time – in other words, without secular terms. This scheme is illustrated, both for irrotational waves, with seventh-order and third-order approximations in deep water and finite depth, respectively, and for rotational waves with a third-order approximation of the Gerstner-like wave on finite depth. It is also shown that the Lagrangian approximations are more accurate than their Eulerian counterparts of the same order.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 589 , 25 October 2007 , pp. 433 - 454
Copyright
Copyright © Cambridge University Press 2007

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