부산대학교 도서관

Many environmental fluid flows are strongly influenced by the presence of bed topography, which we investigate in the context of idealised shallow water models considering a range of topographical effects. First, a barrier that controls the dynamics as the fluid overtops, which appears in models of a partially collapsed dam, and of a confined gravity current. Next, an edge over which the fluid drains, which is investigated in axisymmetric geometry demonstrating the spontaneous development of supercritical outflow, and then for a spreading current that drains from its rear. Finally, we consider obstacles that may be mobilised by the presence of the fluid, including an obstacle that slides under friction, and one that is destroyed by the current. Several of the problems feature the spontaneous development of a shock in the interior of the domain due to the sharpening of a gradient discontinuity, an unusual effect. We use a variety of analytical tools to elucidate the dynamics, including the method of characteristics and the hodograph transformation, similarity analysis, and multi-scale asymptotics, along with numerical simulations. The simulations were performed using a bespoke code with several novel developments which are also presented, including a custom implementation of the boundary conditions, and the ability to resolve steady states at high accuracy.