Theory of Nonlinear Acoustics in Fluids

1. Front Matter

   Pages i-xiii

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2. Introduction

   Pages 1-10

3. Physical theory of nonlinear acoustics

   Pages 11-29

4. Basic methods of nonlinear acoustics

   Pages 31-51

5. Nonlinear waves with zero and vanishing diffusion

   Pages 53-92

6. Nonlinear plane diffusive waves

   Pages 93-147

7. Nonlinear cylindrical and spherical diffusive waves

   Pages 149-197

8. Nonlinear bounded sound beams

   Pages 199-218

9. Nonlinear standing waves in closed tubes

   Pages 219-250

10. Back Matter

    Pages 251-282

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The aim of the present book is to present theoretical nonlinear aco- tics with equal stress on physical and mathematical foundations. We have attempted explicit and detailed accounting for the physical p- nomena treated in the book, as well as their modelling, and the f- mulation and solution of the mathematical models. The nonlinear acoustic phenomena described in the book are chosen to give phy- cally interesting illustrations of the mathematical theory. As active researchers in the mathematical theory of nonlinear acoustics we have found that there is a need for a coherent account of this theory from a unified point of view, covering both the phenomena studied and mathematical techniques developed in the last few decades. The most ambitious existing book on the subject of theoretical nonlinear acoustics is ”Theoretical Foundations of Nonlinear Aco- tics” by O. V. Rudenko and S. I. Soluyan (Plenum, New York, 1977). This book contains a variety of applications mainly described by Bu- ers’ equation or its generalizations. Still adhering to the subject - scribed in the title of the book of Rudenko and Soluyan, we attempt to include applications and techniques developed after the appearance of, or not included in, this book. Examples of such applications are resonators, shockwaves from supersonic projectiles and travelling of multifrequency waves. Examples of such techniques are derivation of exact solutions of Burgers’ equation, travelling wave solutions of Bu- ers’ equation in non-planar geometries and analytical techniques for the nonlinear acoustic beam (KZK) equation.

• Diffusion
• fluid mechanics
• mechanics
• stress
• thermodynamics
• wave
• wave equation
• partial differential equations

From the reviews:

"The authors present an elegant study on theoretical nonlinear acoustics … . The nonlinear acoustic phenomena described in the book are chosen to give physically interesting illustrations of mathematical theory. … Special for this book is its coherent account of nonlinear acoustic theory from a unified point of view and detailed presentations of mathematical techniques … . It is useful for practitioners and researchers in acoustics … . It can also be used as a textbook for graduate or advanced undergraduate students … ." (Ömer Kavaklioglu, Zentralblatt MATH, Vol. 1049 (24), 2004)

• Department of Mechanics, Kungl. Tekniska Högskolan, Stockholm, Sweden

  Bengt O. Enflo

• Department of Mechanical Engineering, Blekinge Tekniska Högskola, Karlskrona, Sweden

  Claes M. Hedberg

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