LINEAR THEORY OF BOTTOM REFLECTIONS
NAVAL ORDNANCE LAB WHITE OAK MD
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The report gives a detailed mathematical development of a linear, spherical wave theory for the reflection of underwater explosion shock waves from plane bottoms of either fluid or rigid materials. The Laplace transform method of L. Cagniard is used to obtain integral solutions for the pressure which can be evaluated numerically. The paper begins with linear equations of motion and proceeds in steps through the derivation of the wave equations and finally to solutions of the wave equations. Two methods of integrating the integral solution are discussed. First, the real part of the integral is separated from the imaginary part to allow integration using real arithmetic. Second, a method of integration using complex arithmetic is described.
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