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Reappraisal of Whitham's 1967 theory for wave-mean flow interaction in shallow water by Bridges, Thomas J.; Ratliff, Daniel J. is a scholarly article available to read on EtoBox.

What is Reappraisal of Whitham's 1967 theory for wave-mean flow interaction in shallow water about?

The modulation equations for Stokes waves in shallow water coupled to wave generated mean flow, derived in Whitham (1967), based on an averaged Lagrangian are revisited. Firstly, it is shown that they can be recast into two coupled classical shallow water equations, with modified gravity having the sign of the Whitham index: sign($\omega_0'' \omega_2$). Secondly, it is shown that the amplitude of the mean flow and amplitude of the wave are, in general, independent. Thirdly, the implications of the coalescing characteristics, whose unfolding is associated with the Benjamin-Feir instability, are studied.

Author

Bridges, Thomas J.; Ratliff, Daniel J.

Published

2022

Language

EN