Some aspects of the flip-through phenomenon: A numerical study based on the desingularized technique

Abstract

Flip-through is known as a rapidly focusing phenomenon at a wall leading to high loads without impact of liquid. In order to simulate numerically these highly nonlinear waves, the boundary value problem is formulated in potential theory without surface tension. A desingularized technique is used to compute the velocity potential. Conformal mappings of the fluid domain simplify the formulation of the solution. As shown by many contributors to the method of fundamental equations (another name to denote desingularized methods), the suitable desingularizing distance must be chosen with care. Here the criteria for choosing it follow from energy and mass conservation laws. This study shows what is the influence of an arbitrary additive constant to the velocity potential regarding conservation laws. Validation tests are performed on a focused wave. Recommendations are given regarding the choice of the desingularizing distance and the additive constant as well. In order to better control the initiation of flip-through, the simulations start from an initial free surface deformation in a rectangular tank, with or without varying bathymetry. The subsequent jet running along the wall, is described and the corresponding loads are discussed. In particular in the present configuration, it is shown that, along the wall, the maximum acceleration precedes the maximum of pressure contrary to the findings of previous studies. The sensitivity of the results with regard to the shape of the initial deformation and the local bathymetry is discussed.