The Cauchy surface wave problem from the viewpoint of a VOF method

摘要

Tidal waves produced in deep water by initial local disturbances of the surface are investigated by direct simulations using a volume-of-fluid method. Particular in case of finite disturbances this class of surface-waves has long been regarded as difficult, since the effort is substantial to obtain results in the framework of inviscid linearised potential flow theory. Due to the finite disturbances, the wave trains disappears. This phenomenon cannot be covered by the available closed analytical expressions, and it is hence investigated numerically in detail. The presented numerical approach employs a piecewise linear interface construction method. Cartesian and cylindrical cases are considered, and the numerical results are benchmarked with the analytical expressions and with experimental results. Based on this, a correlation for the maximum wave amplitude as function of the distance is derived.