Wilcox C.H. Sound Propagation in Stratified Fluids

Springer, 1984, 199 p., ISBN: 3540909869 0387909869 9780387909868Applied Mathematical Sciences, Volume 50The purpose of this monograph is to develop from first principles a theory of sound propagation in stratified fluids whose densities and sound speeds are essentially arbitrary functions of the depth. In physical terms, the propagation of both time-harmonic and transient fields is analyzed. The corresponding mathematical model leads to the study of boundary value problems for a scalar wave equation whose coefficients contain the prescribed density and sound speed functions.The intended audience for this monograph includes both those applied physicists and engineers who are concerned with sound propagation in stratified fluids and those mathematicians who are interested in spectral analysis and boundary value problems for partial differential operators.The propagation problems and their solutionsThe Acoustic Propagator
Solutions with Finite EnergySpectral analysis of sound propagation in stratified fluidsThe Reduced Propagator AU
Solutions of the Equation Auq
Spectral Properties of Au
Generalized Eigenfunctions of Au
The Spectral Family of Au
The Dispersion Relations
The Spectral Family of A
Normal Mode Expansions for A
Semi-Infinite and Finite LayersTransient sound field structure in stratified fluidsNormal Mode Expansions of Transient Sound Fields
Transient Free Waves
Transient Guided Waves
Asymptotic Energy Distributions
Semi-Infinite and Finite LayersScattering of signals by inhomogeneous layersSignals in Homogeneous Fluids
The Reflected and Transmitted Signals
Construction of the Scattering Operator
The Scattering Operator and Signal Structure