Abstract
The modulation equations for Stokes waves in shallow water coupled to wave-generated meanflow, derived in Whitham (1967), based on an averaged Lagrangian are re-visited. 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 meanflow 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.(c) 2022 Published by Elsevier B.V.