SIMPLIFIED PROOF AND EXTENSION OF INTEGRAL PROPERTIES OF GRAVITY WAVES OF FINITE AMPLITUDE

By means of a rather simple and direct method, this paper deduces the relations between the kinetic energy of waves and the horizontial momentum, and between different kinds of energies of waves, thus greatly simplifying the corresponding processes of deduction given by Starr and others. Furthermore, several important integral properties of two-dimensional, irrotational, periodic and permanent waves, which are generalized to the case with uniform current existing, the concept of wave excess is established, and some important integral properties of wave excess are deduced.