The operation of second order wave modes on a uniformly sloping beach

Abstract

This paper addresses the theory concerning second order wave effects associated with water waves as the letter propagate through a uniformly sloping beach. A model beach with bottom contours parallel to the shoreline is used. It is also assumed that there exists a breaker zone in the neighborhood of the shoreline. lncidently, this ensures that the eigensolutions associated with primary wave motions are bounded.
Given the above considerations, it is shown that the second order modes of oscillations are excited and maintained by the energy derived from the non-linear interactions among the oscillatory wave profiles and the velocity of the primary wave components. Furthermore, numerical calculations suggest that the amplitudes of the second ordersr harmonics seem to steadily increase as they propagate towards the shoreline as well as increase with increasing beach gradient. In the range of tidal frequencies, the theory appears to have realistically predicted an estimate of (1) the width of the continental shelf over which propagating modes are likely to experience bottom effects, and ( 2) the rise and fall of the tidal modes as functions of the distance from the breaker zone.