Theory of nonlinear acoustics in fluids.

*(English)*Zbl 1049.76001
Fluid Mechanics and its Applications 67. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0572-5/hbk). xiii, 282 p. (2002).

The authors present an elegant study on theoretical nonlinear acoustics with equal stress on physical and mathematical foundations. They have attempted explicit and detailed accounting for physical phenomena, as well as for their modelling and solution of mathematical models. The nonlinear acoustic phenomena described in the book are chosen to give physically interesting illustrations of mathematical theory.

The book contains a variety of applications mainly described by Burgers’ equation or by its generalizations. The authors include recent applications and newly developed techniques on the subject of theoretical nonlinear acoustics. Examples of such applications are resonators, shock waves from supersonic projectiles, and travelling of multifrequency waves. Examples of such techniques are derivation of exact solutions of Burgers’ equation, travelling wave solutions of Burgers’ equation in non-planar geometries, and analytical techniques for nonlinear acoustic beam equation. The analytical techniques are developed from first principles, i.e. from the continuity equation, Navier-Stokes equations, heat conduction equation and the constitutive equation of the medium in which the nonlinear acoustic waves propagate. From these principles in fluid mechanics and thermodynamics, a universal mathematical model of nonlinear acoustics (Kuznetsov’s equation) is derived.

Special for this book is its coherent account of nonlinear acoustic theory from a unified point of view and detailed presentations of mathematical techniques of solving the nonlinear acoustic equations. The present book differs from the books on nonlinear acoustics concentrating on mathematics by the derivations of model equations from physical laws and principles, and it differs from the books dealing with a wide range of applications by its attempt to give a coherent theory of the fewer phenomena accounted for. On the other hand, the present book is less specialized than the books dealing with special applications. It is useful for practitioners and researchers in acoustics who feel a need for more theoretical understanding. It can be also used as a textbook for graduate or advanced undergraduate students with adequate background in physics and mathematical analysis, specializing in acoustics, mechanics or applied mathematics.

The book contains a variety of applications mainly described by Burgers’ equation or by its generalizations. The authors include recent applications and newly developed techniques on the subject of theoretical nonlinear acoustics. Examples of such applications are resonators, shock waves from supersonic projectiles, and travelling of multifrequency waves. Examples of such techniques are derivation of exact solutions of Burgers’ equation, travelling wave solutions of Burgers’ equation in non-planar geometries, and analytical techniques for nonlinear acoustic beam equation. The analytical techniques are developed from first principles, i.e. from the continuity equation, Navier-Stokes equations, heat conduction equation and the constitutive equation of the medium in which the nonlinear acoustic waves propagate. From these principles in fluid mechanics and thermodynamics, a universal mathematical model of nonlinear acoustics (Kuznetsov’s equation) is derived.

Special for this book is its coherent account of nonlinear acoustic theory from a unified point of view and detailed presentations of mathematical techniques of solving the nonlinear acoustic equations. The present book differs from the books on nonlinear acoustics concentrating on mathematics by the derivations of model equations from physical laws and principles, and it differs from the books dealing with a wide range of applications by its attempt to give a coherent theory of the fewer phenomena accounted for. On the other hand, the present book is less specialized than the books dealing with special applications. It is useful for practitioners and researchers in acoustics who feel a need for more theoretical understanding. It can be also used as a textbook for graduate or advanced undergraduate students with adequate background in physics and mathematical analysis, specializing in acoustics, mechanics or applied mathematics.

Reviewer: Ömer Kavaklioglu (Izmir)

##### MSC:

76-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics |

76Q05 | Hydro- and aero-acoustics |

76L05 | Shock waves and blast waves in fluid mechanics |

35Q53 | KdV equations (Korteweg-de Vries equations) |