Shock wave propagation past an ocean surface

Abstract

The diffraction of a shock of arbitrary strength by a plane interface separating two different fluids may be calculated for the general case. The restriction encountered in earlier work on a limiting maximum difference in shock velocities in the two media has been removed by a treatment at the interface which does not depend upon Whitham's method. Instead, the shock shape at the fluid discontinuity is determined simultaneously with the local wave system to ensure continuity of both pressure and normal fluid velocity. An example is presented for the propagation of a shock front of Mach number 8 past an ocean surface. It is shown that for later times, the shock shape becomes tangent to the interface with decreasing strength there.