Water Waves Produced by Explosions

Abstract

Explicit formulas are found for the height of the water waves produced by an arbitrary axially symmetric initial disturbance in water of finite depth. The initial disturbance can be either a distribution of impulse or an elevation or depression of the surface or a combination of these. Upper bounds on the wave height are given to be used when the approximate size of the initial disturbance is known, but not its detailed shape. These results are applied to determine the wave resulting from the explosion of a typical large bomb above the surface. The corresponding formulas for waves in a one-dimensional channel are also derived and are compared with experimental results.