Discussion of `Note on a nonlinearity parameter of surface waves' by S. Beji

Abstract

A recently proposed rescaling of the governing equations for inviscid, irrotational, free surface hydrodynamics is reconsidered. A redefinition of the proposed scaling parameters leads to a nondimensionalized problem which contains both the usual intermediate depth scaling and the shallow water scaling as asymptotic limits, thus eliminating the need for a separate development of scaling arguments for the two regimes as given in most standard references.