Theory of nonlinear acoustics in fluids.
type: Item
instance of: scholarly article
title: Theory of nonlinear acoustics in fluids.
zbMATH Open document ID: 1049.76001
author: Bengt O. Enflo
author: Claes M. Hedberg
published in: Fluid Mechanics and its Applications
publication date: 2003-12-21T00:00:00Z
review text: 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 applica…
Mathematics Subject Classification ID: 76-01
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 2020371
zbMATH Keywords: diffusive waves
zbMATH Keywords: Burgers' equation
zbMATH Keywords: shock waves
zbMATH Keywords: nonlinear acoustic beam equation
zbMATH Keywords: Kuznetsov's equation
reviewed by: Ömer Kavaklioglu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2020371