Introduction

The difficulty of the subject of sound propagation through the stochastic ocean owes much of its complexity to the fact that sound transmission in the ocean occurs in a waveguide. Sound waves are continuously refracted and diffracted by the sound channel and the waves are bounded on the edges by the sea floor and surface. Therefore, this chapter provides an overview of the basic ocean acoustics concepts of guided propagation that are needed as a foundation to understand transmission through the fluctuating ocean waveguide. The key propagation methodologies to be covered in this chapter include ray theory, the Born approximation, Feynman path integrals, and the method of normal modes. Most of the background information provided here will involve sound propagation concepts in a vertically stratified ocean, but an effort is made to present the fundamental range-dependent equations for each propagation methodology and to briefly discuss implications for acoustic scattering.

Those readers with a solid background in underwater acoustics may not find anything particularly new in this chapter, but studying the following material is encouraged to foster a familiarity with the notation and broad approach of the monograph. By necessity this is an abridged treatment of the subject of underwater acoustics, and the reader is referred to numerous quality texts dedicated to this subject (see, for example, Brekhovskikh and Lysanov, 1991; Frisk, 1994; Jensen et al., 1994; Munk et al., 1995; Katznelson et al., 2012).

Fundamental Equations of Hydrodynamics

For ocean sound propagation the fundamental hydrodynamic equations are the continuity equation (conservation of mass), the momentum equation (Newton'sLaw), and the adiabatic equation of state (pressure as a function of density and entropy). These are written

where p′ is the pressure, ρ′ is the density, u′ is the fluid velocity, and in the equation of state changes in pressure and density involve no heat conduction, that is, entropy (s) following a water parcel is constant (e.g., ∂s/∂t + u′∇s=0). Because most ocean acoustic problems involve propagation over many wavelengths, nonlinear effects are small. Further assuming a fluid otherwise at rest and expanding the pressure, density and entropy fields about a time independent state p0(r), ρ0(r), and s0(r) the following linearized acoustic equations are obtained: