Momentum and energy of a solitary wave interacting with a submerged semi-circular cylinder

Abstract

AbstractThe interaction of a weakly viscous solitary wave with a submerged semi-circular cylinder was examined using high-resolution two-dimensional numerical calculations. Two simulations were carried out: (a) as a baseline calculation, the propagation of a solitary wave over uniform depth; and (b) a solitary wave interacting with a submerged semi-circular cylinder. Large-scale simulations were performed to resolve the viscous boundary layers on the free surface, bottom and around the obstacle. Integral measures such as momentum and energy are analysed and compared against analytical approximations. For uniform depth, the loss in momentum and energy arises from the traction caused by the finite length of the domain bottom and the dissipation which is predominantly within the bottom boundary layer, respectively. The force on the cylinder is composed of (form) drag, inertial and hydrostatic components, the last factor arising from gradients in the height of the free surface. Morison’s semi-empirical equation is shown to provide a leading-order description of the force on the semi-circular cylinder. These elevated rates of change (momentum and energy) return to uniform depth values after a short period of time, indicating a localized effect of the obstacle. To interpret the flow field, vorticity, streamline and second invariant of the velocity gradient tensor plots were used to highlight relative thickness of boundary layers, vorticity distribution throughout the domain and stagnation points in the flow.