Wave Numbers of Linear Progressive Waves

Abstract

An explicit solution for wave number and wave speed is derived. The method of solution is to expand the linear wave dispersion relation in Taylor series in the neighborhoods of deep and shallow water limits. The two series are matched at the inflection point of the dispersion function, where the shoaling wave height is a minimum value. Numerical comparisons indicate that the present solution is computationally efficient and has an error of less than 0.05%. Two applications are made to solve problems, involving nearshore spectral analysis and refraction of ocean waves.