##
**Sound propagation in stratified fluids.**
*(English)*
Zbl 0543.76107

Applied Mathematical Sciences, 50. New York etc.: Springer-Verlag. IX, 198 p. DM. 56.00; $ 20.40 (1984).

This monograph is essentially a treatise on wave propagation in a horizontally stratified medium seen from a functional analysis viewpoint. Though the subject is interesting to engineers and physicists involved with sound propagation on the ocean, I fear that the author is correct in speculating that a great gulf separates them from those addressing similar problems from this relatively pure mathematical base. It is even difficult to see at the outset just how many of the wave phenomena encountered in the ocean are contained in the model. The coupling of sound with surface waves, and with internal waves, is outside the scope of the model as is the scattering interactions of sound with inhomogeneous surfaces and ocean turbulence.

But the homogeneous problem of linear wave propagation through a stratified fluid at rest and the study of waves induced by force distributions within that medium are both extremely rich in phenomena that can only be analysed satisfactorily through the powerful spectral techniques of this book. This is a book for mathematical technicians and forms the sound foundation of proofs, lemmas, corollaries and the like needed to tackle the detailed analysis of a definite model problem. It is not a place where the applied mathematician concerned with the creation of relevant models will find much insight.

But the homogeneous problem of linear wave propagation through a stratified fluid at rest and the study of waves induced by force distributions within that medium are both extremely rich in phenomena that can only be analysed satisfactorily through the powerful spectral techniques of this book. This is a book for mathematical technicians and forms the sound foundation of proofs, lemmas, corollaries and the like needed to tackle the detailed analysis of a definite model problem. It is not a place where the applied mathematician concerned with the creation of relevant models will find much insight.

Reviewer: J.E.Ffowcs Williams

### MSC:

76Q05 | Hydro- and aero-acoustics |

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |