Waves on the Water Surface — Mathematical Models — Part 1

The work presents new expressions related to wave energy density and flux based on Stokes and cnoidal waves theories. It shows that as progressive waves of finite amplitude propagate a compensatory reverse flow is formed within the bottom fluid layers. The existence of such flow was experimentally confirmed. Modified mathematical models for surface waves over a non-uniform bottom and of a free plane configuration are suggested. A method of calculating the wave transformation and the currents in the surf zone is proposed. Computations made over a wide range of variations in wave parameters are presented.