Department of Mathematics and Computing Seminars

The This research is concerned with the steady and unsteady two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite depth. It is assumed that the fluid is incompressible and the flow is irrotational, and the effect of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. The aim of this research is to find the shape of the free surface created behind bodies and to use this knowledge to design a two-dimensional ship stern that minimises, or eliminates, the downstream waves. Different families of plate shapes are considered, and it is shown that the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

The steady two-dimensional free surface flow past bodies in a fluid of finite depth is investigated analytically using the Wiener-Hopf technique and numerically using the boundary integral technique. Furthermore, the weakly nonlinear solution is investigated using the forced Korteweg-de Vries equation (KDV) to describe the flow of the free surface. The problem of the free surface flow past a semi-infinite curved plate for the subcritical case when the Froude number F < 1 is solved. Linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level.

The unsteady two-dimensional free surface in a fluid of finite depth is investigated analytically using Laplace transform and the Wiener-Hopf technique. Apart from understanding of the physics, the analytical solution has shed some light on. solving a small and long time problem in the engineering practice of ship building, the optimisation of hull shape. The linear problem is formulated by assuming that the free surface is slightly perturbed a distance d by the stern, and is then solved for the case of the flat plate for the subcritical case F < 1. It is found that the unsteady solution approaches the steady state solution as t -> ∞.