Abstract:

Longuet-Higgins (1977) observed in a two-dimensional shallow tank that a sandbar model moves with mean speed as high as 1.2 cm/sec. towards the weatherside, while incident waves break on the leeside of the sandbar. In this paper we intended to examine the problem numerically by using boundary integral method. Computations are made based on a mixed EulerianLagrangian solution scheme under the assumptions of potential flow. Wave forces acting on the sandbar including hydrostatic contributions are evaluated and assessed to quantify the experimental- finding of Longuet-Higgins. It is found that the time-derivative and hydrostatic components in Bernoulli" s equation dominate the total force acting on the sandbar. The force becomes negative, i.e. directs the weatherside, mainly due to the resulting hydrostatic unbalance, when waves break on the leeside of the sandbar.

1. Introduction

The semi-Lagrangian time-stepping procedure initiated by Longuet-Higgins and Cokelet (1976) provided a sound basis for investigating non-linear water wave problems, because it can be implemented to exactly satisfy both the dynamic and the kinematic conditions on the free surface in numerical sense. Faltin- sen (1977) reformulated the method on the physical plane and successfully applied to wave-body interaction problems. Vinje and Brevig (1980a) incorporated Cauchy" s theorem into the method in order to derive boundary integral equations for the complex potential. They employed it to simulate plunger-type breaking waves in two dimensions with the assumption of spatial periodicity. In their method, the stream function is prescribed on the boundaries, where the normal velocity is known, while the velocity potential on the free surface. In extending their approach to the case of a floating body, Vinje and Brevig (1980b) regarded the intersection points between the body and the free surface as a part of kinematic boundary, where the normal velocity is to be prescribed.

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