Acoustic radiation by a Hill vortex in viscous heat-conducting gas

Abstract

Acoustic radiation by a Hill vortex has been studied on the basis of the Navier – Stokes equations. We used the expansion of unknown functions into power series of the initial vorticity which was assumed to be small. The Navier-Stokes equations were reduced to a parabolic system with constant coefficients for higher derivatives. The problem is set in such a manner. The vorticity is defined inside a sphere at t = 0. The initial density and the temperature are assumed to be constant throughout the whole space. The solution is represented as a power series whose coefficients are multiple integrals. They have been calculated with the aid of Korobov grids. The density oscillations have been investigated. The frequency spectra were studied at various distances from the vortex. The results may be useful for modelling decaying grid turbulence.