Hydrodynamic collapse of a cylindrical cavity on dry sea bed

Abstract

A theory is developed on the generation and collapse of water craters created by explosions in shallow water. The crater lip generates a leading wave which radiates outward while the water cradle collapses towards the center. This collapse is similar to the dam break problem on a dry bed except for the cylindrical symmetry and is solved using the nonlinear long wave equations and the method of characteristics. When the water edge reaches the center, it rebounds on itself vertically and forms a cylindrical dissipative bore radiating outward. The bore height decays rapidly with distance from the center and is transformed into a nonlinear undular bore obeying the K dV equation. The K dV equation is extended to the Stokesian range for the higher frequency waves that follow. The theory is applicable in the reverse direction, i.e. for negative time steps. Therefore, given an experimental wave record obtained at a fixed distance from the center, it allows us to determine the size of the crater which would generate such a record. The method is applied to wave records obtained in the laboratory, ponds, and lakes with TNT explosions and also tested with the wave records from nuclear explosions, with yields ranging over 11 orders of magnitude. It is found consistently that the physical water crater created by underwater explosions in shallow water follows, R c = 4.4 · W 0.25, R c , in feet, and W is the explosion yield in lb of TNT. The relative hydrodynamic energy dissipation is nearly a constant 40% of the potential energy of the initial crater with lip.