Equations Of Long Waves With A Free Surface IV. The Case of Constant Shear

Abstract

A large class of two-dimensional free-surface hydrodynamical systems is determined that can be self-consistently reduced by the condition that the velocity profile has a constant shear. The reduced systems turn out to be Hamiltonian, and so does the reduction process itself. All reducible systems, Hamiltonian or not, are determined and %%@ shown to form a Lie algebra. All this is then generalized to the multilayer/multi-species representations.