Abstract:

The paper deals with fluid dynamical disturbances governed by the full nonlinear set of equations for a compressible fluid with viscosity and thermal conductivity included with arbitrary Prandtl number. The field governed by these equations is regarded as being a set of five functions of space and time, these functions being the three fluid velocity components, the pressure, and the entropy. A projection operator formalism is defined which uniquely separates the five-component field at any instant into three component fields, labeled for convenience as acoustic, vorticity, and entropy modes. The equations coupling these can be developed to any order of nonlinearity, but the superposition principle applies regardless of order. Lighthill's formulation of sound generated by flow falls easily out of the formulation without any intrinsic arbitrariness. Applications to computational aero-acoustics are discussed, with some numerical results for the case of sound generated by two adjacent line vortices.