Generation of waves at an inertial surface due to explosions

B N Mandal,N K Ghosh

doi:10.1155/s0161171290000837

B N Mandal, N K Ghosh

Open Access

https://doi.org/10.1155/s0161171290000837

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Abstract

This paper is concerned with the generation of surface waves by an axially symmetric initial disturbance applied at an inertial surface in an ocean of finite depth. This initial disturbance can be either in the form of an impulse or an elevation or depression. The depression of the inertial surface is obtained as an infinite integral in each case. The method of stationary phase is applied to evaluate the integral for large values of time and distance.

Highlights

Waves are generated by an explosion above or within an ocean
The formulation of the problems associated with the generation of these waves as an initial value problem is based on the linear theory of surface water waves
If the explosion occurs above the ocean surface, the initial condition on the surface is taken as an initial impulse distributed over a certain region while for the case when the explosion occurs at or below the ocean surface, the initial condition is taken as an initial elevation or depression of the same surface

Summary

INTRODUCTION

Waves are generated by an explosion above or within an ocean. The formulation of the problems associated with the generation of these waves as an initial value problem is based on the linear theory of surface water waves. Kranzer and Keller [3] considered the three dimensional unsteady motion due to an arbitrary axially symmetric initial surface disturbance in an ocean of uniform finite depth and gave explicit formula for the surface elevation and compared the theory with experimental results. This may be viewed as an extension of the problem of generation of water waves at the free surface of an ocean of finite depth considered by Kranzer and Keller [3] to an ocean covered by an inertial surface After formulating it within the framework of llnearized theory as an initial value problem, it is reduced to a boundary value problem by taking the Laplace transform in time. (k) Here (k) and are the Hankel transforms of C(r) and F(r) respectively

Then g

Using the result