Refraction of Continuous Ocean Wave Spectra

The governing equation describing the propagation of a continuous ocean wave spectrum in water of any depth is derived and analyzed. The derivation of the equation is based upon the assumption that each component of the spectrum, defined by a given direction and frequency, is propagated according to linear-wave theory, and single period regular wave refraction relationships are employed. A computer program has been prepared to solve the equation numerically for steady-state conditions where no wind, friction, or currents are present to modify the spectrum. These are the same conditions that are usually assumed in single period wave refraction studies. From a known distribution of the deep water wave spectrum the program predicts the changes in the spectrum as it travels into shallow water of a given bottom topography. Results of a few numerical examples are presented.