  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.
