An approximate analytical solution on the scattering of sound by a Taylor Vortex

Abstract

Currently state-of-the-art approximate analytical solutions for the scattering of sound by a vortex are primarily based on the Plane-Wave Point Vortex (PWPV) model. In this model, the velocity of the point vortex flow field decays slowly over an infinite range, which leads to the scattered integral is ill-posed; the flow field velocity approaches infinity at the vortex core, which leads to the forward singularity. To address these two issues, based on the Plane-Wave Taylor Vortex (PWTV) model, we develop an approximate analytical solution for the scattering of sound by a vortex. In our model, the velocity of Taylor vortex flow field decays rapidly within a finite range, which can ensure the scattered integral is well-posed; the flow field velocity approaches zero at the vortex core, which can eliminate the forward singularity. We divide a Taylor vortex into a rigid vortex and a linear circular shear flow to make the scattering equation solvable. We reconstruct the composition of scattered waves and analyze the important impacts of diffraction on them. Next, after analyzing the reasons of the generation of side-lobes, we propose to replace Bessel diffraction term with the Gaussian function, which can eliminate side-lobes, thus to enhance the accuracy of the approximate solution. It is shown that the proposed approximate analytical solution is highly consistent with the numerical solution, which indicates this analytical solution can advance theoretical research on the scattering of sound by a vortex.