Didier Clamond: Lagrangian description of steady waves

This presentation concerns the mathematical formulation of steady surface gravity waves in a Lagrangian description of motion. It will be demonstrated that classical second-order Lagrangian Stokes-like approximations do not 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, i.e. 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 same order.

Didier Clamond has been a post.-doc. at the Department at Mathematics, UiO. He is now faculty member at the University of Nice, Sophia-Antipolis.