Mach Reflection of Sinusoidally-Modulated Nonlinear Stokes Waves by a Thin Wedge

By using multiple-scale expansion techniques, the Mach reflection of sinusoidally- modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is shown that the evolution of diffracted wave amplitude can be described by the Zakharov equation to the loading order and that It reduces to the cubic Schrodinger equation with an additional linear term in the case of stable modulations. Computations are made for the cubic Schrodinger equation for different values of nonlinear and dispersion parameters. Numerical results reflect the experimental findings in terms of the amplitude and width of generated stem waves. Based on the computations it is concluded that the nonlinearity dominates the wave field, while the dispersion does not significantly affect the wave evolution.