Nonlinear Acoustics. Part 1. Physical Phenomena, Exact Basic Equations, and Problems in Formulation and Solution of Approximate Equations.
NAVAL RESEARCH LAB WASHINGTON D C
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The basic equations of classical hydrodynamics of fluids, together with constitutive relations of the medium, have been reviewed. By perturbation expansions the nonlinear equations of acoustic wave propagation currently in use were derived using the acoustic Mach number and Strouhal number as measures of scale method of Goldberg. Several derivations of Burgers-type equations have been presented, together with a review of solution methods introduced by Hopf and Cole and of the method of characteristics. The classic problem of a piston in a tube was reviewed, with the theoretical extensions of Blackstock. The complexity of all methods led to a search for new approaches. A promising development is Whithams theory of nonlinear partial differential equations. Elements of this theory are discussed. It is concluded that theoretical difficulties in nonlinear acoustics remain to be solved.
- Numerical Mathematics
- Fluid Mechanics