Wave set up and set down due to a narrow frequency wave spectrum

Abstract

A narrow band wave spectrum was appIied to theoreticaI relationships previously developed for set down and set up in an attempt to find second order non-steady solutions for these concepts. The initial effort was to apply this spectrum to the radiation stress tensor using Iinear wave theory. Another development was attempted by incorporating the spectrum and the solution of the long wave equation into the BernoulIi and vertical momentum equations. Results obtained indicate that the solution for mean water level outside the surf zone is composed of a steady component and a periodic unsteady component; the periodic component being of the form of a long wave with a frequency lower than the components of the wave spectrum. The solution for set up is then composed of the same type components. The exact relationships depend on the patching process that is made for the solutions through the breaker line.