Notes on Acoustics
Written by a noted authority in the subject area, this book is a comprehensive study of the theory and practical application of acoustics to numerous fields.
TABLE OF CONTENTS Notes on Acoustics
Chapter 10: Mean-flow Effects and Nonlinear Acoustics
10.1 Review of Fluid Equations
With the density, pressure, and fluid velocity denoted ?, P, and U i (component form), the equations for mass and momentum conservation are
where repeated indices (in this case j) implies summation over j = 1 , 2 , 3. The second equation can be rewritten as
and, combined with Eq. 10.1, as
where D/Dt ? ?/ ?t + U j ?/ ?x j (sum over j = 1 , 2 , 3).
The mass equation can be expressed in similar manner,
Next, we introduce the acoustic perturbations ?, p, and u i of the variables and put ? = ? 0 + ?, P = P 0 + p, and U i = U 0 i + u i with the subscript 0 signifying the unperturbed state. Now, there will products of the (first order) acoustic variables and the mean flow as well as products of acoustic variables. The first type of terms express the coupling or interaction between the sound field and the mean flow. The second type account for the coupling of the sound field with itself, so to speak, and expresses the nonlinearity of the field; in the linear theory of sound, these second order terms are neglected.
As discussed in Chapter 3, the relation between the density and pressure perturbation is ?
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