Flow noise and rapidly distorting turbulence in shear layers

Abstract

Rapid distortion theory (RDT) is a linear analytical framework for the formal split of a flow’s hydrodynamic sources from their acoustic effects. The former include time-varying vorticity, turbulence, and unsteady heat injection. Their acoustic effects manifest themselves through a generalized wave-propagation operator in the consistently separated equations of fluid mechanics. The present development reports on progress in extending RDT to include mean shear and associated macro-vorticity in the static but spatially nonuniform carrier flow. The analysis begins by fully recasting standard RDT [Goldstein, JFM (1978)] for irrotational backgrounds in tensor-dyadic form for the curvilinear coordinates of the streamlines of the background flow. This complete geometrization of the background offers clues for achieving a similar split in the time-varying acoustical and turbulent variables that perturb the more general sheared freestream. The new development could eventually be applied to turbulent boundary layers, and particularly to spatial discontinuities such as steps and gaps that (rapidly) distort the statistics of the perturbed rotational flow and thereby lead to additional broadband noise via RDT’s generalized wave-equation operator and geometrized source terms.