  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.
