Natural SciencesOcean EngineeringOceanographyComputational Fluid DynamicsOcean WavesLinear Wave TheorySurface Wave DynamicsSurface Wave MethodsWave DispersionFinite Depth Wave SpectrumWave Propagation Modeling
Numerical Fourier solutions for time-dependent two-dimensional standing gravity waves of finite amplitude in water of uniform depth are presented in this paper. While using a truncated double Fourier series for the velocity potential which satisfies the Laplace equation, an implicit function, rather than a series approximation for the surface elevation, is preserved in the nonlinear free surface boundary conditions. An algorithm involving Newton's iteration method is developed to calculate the unknown Fourier coefficients. The properties of standing waves in water of finite depth, including variations of angular frequency, surface profiles and wave forces,f and even the maximum wave steepness are then calculated. The accuracy of the truncated series is validated by the convergence of the solutions for the angular frequency. The null residual pressure at the free surface then implies high accuracy of the Fourier solutions. The results agree well with the experimental data available.