Abstract (Invited)

Entropy, Acoustic, and Vorticity Mode Decomposition as an Initial Step in Nonlinear Acoustics Formulations

A.Pierce (Department of Aerospace and Mechanical Engineering, Boston University, Boston, USA)

e-mail: adp@bu.edu

The idea that fluid dynamic disturbances can be decomposed into three fields goes back to Kirchhoff and to Chu and Kovasznay. The labeling of the three fields ensues from that, in the linear limit, the equations governing these fields correspond to thermal (entropy) diffusion, sound propagation, and vorticity diffusion. The restriction to Prandtl numbers of 3/4 is not necessary if the thermal conductivity and viscosity are "small" in an appropriate sense. The restriction to small disturbances is removed with the definition of mathematical operators acting on the total spatial dependence of the overall field, which project out each of the three fields. The formalism gives a clarified derivation of Lighthill's equation and also gives a framework for deriving wave equations that are used in nonlinear acoustics and in the propagation of sound in inhomogeneous moving media. The principal trick is to assign amplitude, length, and time scales to each of the fields separately, and then to identify dimensionless groups one might assume are small in expansions.

Section : 1