Numerical Simulation of Generation Processes of Mach Stems

Abstract

Mach stems generated by the oblique interaction of waves were numerically simulated using a set of nonlinear equations derived on the basis of a variational principle without any assumptions concerning wave nonlinearity and dispersion. The Mach stems showed a larger amplification rate defined along the nondimensional time as the incident wave height to water depth ratio was larger and the water depth to incident wave length ratio was smaller. When the Mach stem reflected at a vertical wall, its wave height became remarkably large without wave breaking. A new method was proposed to consider the boundary conditions on a vertical wall which was set diagonally across computational grids. The wave amplification at the head of a bay depended on not only the incident-wave parameters but also how large the Mach stem was amplified.