The linearised dambreak problem

[摘要] We employ the method of asymptotic coordinate expansions in time and space to determine the detailed structure of the solution to the linearised dambreak problem at the initial stage, in the far fields and at large time. We consider the situation where an inclined dam separates a horizontal layer of incompressible and inviscid fluid from a shallower horizontal layer of the fluid. The fluid is initially at rest, sits on a horizontal, impermeable base, and is bounded above by a free surface. We consider the linearised dambreak problem, which corresponds to a dam with a small step height and slope. We formulate the problem for the free surface and fluid velocity potential, to which the exact solution is found via the theory of complex Fourier transforms. This gives the free surface and fluid velocity potential in complex Fourier integral form. We examine the detailed asymptotic form of the exact solution for the free surface at the initial stage, in the far field and at large time. The asymptotic approximations are then compared to a numerical evaluation of the exact solution for the free surface, and to the case where the free surface is described by the linearised shallow water theory.

[发布机构] University:University of Birmingham;Department:School of Mathematics

[关键词] Q Science;QA Mathematics