CHAPTER 1 - INTRODUCTION

Abstract

This chapter presents the problems of ocean acoustic wave propagation, which deal with the solution of representative partial differential equations. These equations, which govern realistic physical ocean acoustic phenomena, are all regarded as wave equations. Because of the complex nature of the ocean, the various wave equations can be very complicated in nature and permit a closed form solution only in very simple cases. Numerical methods that have useful applications to ocean acoustic wave propagation problems did not receive much attention or interest until numerical ordinary differential equation methods and finite difference schemes were introduced for solving these problems. Because of the rapid growth of supercomputers and modern numerical techniques, solutions for complicated scientific problems are now possible. Appropriate initial and boundary conditions need to be prescribed for the problem to be well posed. The wave equation, conventionally regarded as the reduced wave equation, is a scalar elliptic equation whose solution consists of transmitted and reflected fields in three dimensions. It is convenient to express the wave equation in cylindrical coordinates in a three-dimensional ocean, as in most cases, the wave field has a very small azimuthal angular dependence. This reduces the three-dimensional problem to a two-dimensional one that is a little easier to handle.