Uniform asymptotics for spherical and cylindrical nonlinear acoustic waves generated by a sinusoidal source

Abstract

This paper is concerned with the nonlinear propagation of sound waves from spherical or cylindrical sinusoidal sources. This problem is governed by the two dimensionless parameters ε and R₀, and we seek asymptotic expansions valid uniformly in ε, R₀ (as well as in space-time) away from the irreducible domain where both ε and R₀ are of order unity. Various matching asymptotic domains of the parameter plane are defined and in each domain the space-time asymptotic structure is given: in many cases the leading term can actually be solved for analytically. Finally, the application of the results for spherical waves to the important problem of nonlinear acoustic beam spreading are discussed.