A derivation of equations for wave propagation in water of variable depth

Abstract

Within the scope of the three-dimensional theory of homogeneous incompressible inviscid fluids, this paper contains a derivation of a system of equations for propagation of waves in water of variable depth. The derivation is effected by means of the incompressibility condition, the energy equation, the invariance requirements under superposed rigid-body motions, together with a single approximation for the (three-dimensional) velocity field.