Run-up and backwash bore formation fromdam-break flow on an inclined plane

摘要

Nonlinear shallow water equations are employed to model the inviscid slumping offluid along an inclined plane and analytical solutions for the motion are derived usingthe hodograph transformation to reveal the run-up and the inception of a bore onthe backwash. Starting from rest, the fluid slumps along the inclined plane, attaininga maximum run-up, before receding and forming a relatively thin and fast movingbackwash. This interacts with the less rapidly moving fluid within the interior to forma bore. The evolution of the bore and the velocity and height fields either side of itare also calculated to reveal that it initially grows in magnitude before diminishingand intersecting with the shoreline. This analytical solution reveals features of thesolution, such as the onset of the bore and its growth and decline, previously knownonly through numerical computation and the method presented here may be appliedquite widely to the run-up of other initial distributions of fluid.