Sound, Vorticity, Entropy

Abstract

Up to recent times acoustics was primarily concerned with small amplitude irrotational motion of a compressible medium and fluid mechanics dealt with incompressible flow, consequently there was no overlapping area between those two disciplines. Presently, however, the importance of understanding both compressible flow and large amplitude waves in the presence of important viscous and heat conduction effects created a real need for a single unified discipline that includes both small amplitude irrotation waves and incompressible flow as special limiting cases. The full Navier-Stokes equations of a viscous heat conductive gas are strongly nonlinear. For weak fields, however, the solutions reduce to three independent “modes” and those can be identified as vorticity, sound waves, and entropy spots. A second-order theory indicates interaction between all the modes and the familiar examples such as sound generation by vorticity, sound scattering on entropy nonuniformities, heat convection by turbulence, etc., can all be accounted for by a single unified theory.