Stationary Solutions of Potential Equations

Abstract

For stationary equations, the proposed approach coincides with the conventional complex variable method. For this case, the numerical algorithms for solution of gravity (Stokes) and gravity-capillary wave equations are proposed, and the examples of numerical solutions are given. The results suggest that gravity-capillary waves do not approach Stokes waves as the capillarity coefficient decreases. Both stationary and non-stationary schemes use Fourier series representation for spatial approximation and the Fourier transform method to calculate the nonlinearities. The main properties of Stokes, gravity-capillary, and capillary waves for infinite depth are discussed. The properties of Stokes waves for finite depth are investigated.