Analysis of internally generated sound in continuous materials: 3. The momentum potential field description of fluctuating fluid motion as a basis for a unified theory of internally generated sound

Abstract

The reasons for a need for a unified theory of aerodynamic noise generation are discussed and justified. In a previous paper, existing theories of aerodynamic noise generation have been critically reviewed with special emphasis on conceptual adequacy and physical scope, and with special reference to supersonic jet noise. On the basis of the evidence provided by this critical review a new unified theory for internally generated sound in general, and jet noise in particular, has been devised. It is shown that the new, generalized theory, in which the previous work by Doak on the identification of acoustic, thermal and turbulent motions plays a fundamental role, includes all valid previous theories as special cases and that it can be explicitly formulated for general, non-linear fluctuating motion. A quasi-linear version of this new, generalized theoretical formulation of the problem of aerodynamic noise generation and propagation is presented. A detailed discussion is given of the manner in which Lilley's theory of mixing noise in a unidirectional, transversely sheared turbulent mixing layer arises as a special case of the new, generalized theory. The new theory is shown to be of a form in which no restrictions are implied on either mean velocity gradients or mean temperature gradients, with respect to either their magnitudes or directions.