Doakʹs momentum potential theory of energy flux used to study a solenoidal wavepacket

Doakʹs momentum potential theory of energy flux is explored using a model problem constructed to facilitate the introduction of solenoidal perturbations, in a controlled manner, to an otherwise well-understood sound generation problem: that of an irrotational, subsonically convecting wavepacket. The solenoidal wavepacket has, in addition to a downstream radiation lobe similar to its irrotational counterpart, lower level radiation in the sideline direction. Helmholtz decomposition of the linear momentum and subsequent exploration of the various source and flux terms that participate, according to Doakʹs fluctuation-energy balance, in the generation and transport of total fluctuating enthalpy (TFE) reveal a rich inner structure involving work performed on, and extracted from, the fluid system by means of the irrotational and solenoidal components of the wavepacket. The response of the fluid involves the internal transport and attentuation of trapped TFE, as well as the radiation of a small amount of radiating TFE. The analysis shows how the downstream radiation is associated with a mechanism similar to that of the irrotational wavepacket, while the sideline radiation arises due to the scattering of irrotational wavepacket fluctuations by solenoidal momentum fluctuations. It is postulated that such a mechanism might play a role in the sideline radiation of subsonic jets.