Abstract (Invited)

Role of Asymptotics in Nonlinear Acoustic Propagation

P.Hammerton (University of East Anglia, Norwich, England, UK)

e-mail: P.Hammerton@uea.ac.uk

From the mid-1970s until his untimely death in 2000, Professor David Crighton made a significant contribution to the study of nonlinear acoustic propagation using matched asymptotic expansions. This work, together with that of his collaborators will be discussed in this lecture. The derivation of model equations such as the Generalised Burgers Equation will be outlined, using multiple scales methods based on the slow distortion of a disturbance due to nonlinearity and dissipation/dispersion mechanisms. A variety of physical mechanisms such as molecular relaxation, relevant to atmospheric propagation, can also be included in a consistent asymptotic framework. In most physical cases of interest, diffusion mechanisms are small compared with nonlinear effects. Crighton and co-workers (Scott, Lee-Bapty and Hammerton) used asymptotic methods in order to classify the form of the propagating disturbance. These methods will be described. Results obtained agree well with numerical solutions, and indeed supplement numerical methods by providing solutions for parameter ranges which are computationally expensive. Finally, the recent use of such methods for physically realistic situations such as long-range propagation through a stratified atmosphere will be described.

Section : 6