MOMENTUM POTENTIAL-THEORY OF ENERGY FLUX CARRIED BY MOMENTUM FLUCTUATIONS

The momentum potential theory of time-stationary fluctuating flows is briefly reviewed and then extended to include energy flux carried by momentum fluctuations. It is shown that the mean (time-averaged) energy flux can be expressed as a linear superposition of mean, turbulent, acoustic and thermal components. A mean energy flux balance relating turbulent, acoustic and thermal energy fluxes only is obtained. For homentropic flows the Cantrell and Hart expression for acoustic intensity is obtained as a special case. Physical and analog interpretations of the mean energy flux balance are presented for the general case. A formal solution of the equation for mean flow of energy due to momentum fluctuations is presented, leading to a definition of local fluctuating dynamical equilibrium of a time-stationary flow and an identification of sources of far field radiated acoustic power. In the Appendix, the momentum potential theory version of Jenvey's partitioning of the stagnation enthalpy into mean, turbulent, acoustic and thermal parts is presented.