Numerical Calculations of Periodic Gravity-Capillary Waves.

The general problem of steady, two dimensional, gravity-capillary waves on an interface between two fluids of different densities is formulated in terms of a pair of nonlinear integro-differential equations. The pair of equations is shown to reduce to a single integro-differential equation for the special case of free surface waves. Perturbation solutions of these equations are found and are seen to agree with existing small amplitude approximation solutions. An iterative method for the accurate numerical solution of these equations is developed and a procedure for estimating the error in the method is presented. The method is applied to a number of different cases of periodic waves in an unbounded fluid.