Acoustic Radiation by 3D Vortex Rings in Air

Abstract

Acoustic radiation emitted by three-dimensional (3D) vortex rings in air has been investigated on the basis of the unsteady Navier-Stokes equations. Power series expansions of the unknown functions with respect to the initial vorticity which is supposed to be small are used. In such a manner the system of the Navier-Stokes equations is reduced to a parabolic system with constant coefficients at high derivatives. The initial value problem is as follows. The vorticity is defined inside a toroid at t = 0. Other gas parameters are assumed to be constant throughout the whole space at t = 0. The solution is expressed by multiple integrals which are evaluated with the aid of the Korobov grids. Density oscillations are analyzed. The results show that the frequency band depends on the initial size of the vortex ring and its helicity. The presented data may be applied to the study of a flow in a wake region behind an aerodynamic body.

'One Note Samba' Approach to Cosmology: How to Connect Bose-Einstein Condensate, Ermakov-Pinney Equation, Scalar Field Cosmology and Feshbach Resonance All at Once

“…In such a manner the system of the Navier-Stokes equations is reduced to a parabolic system with constant coefficients at high derivatives. [11] o Rozanova-Pierrat's Kuznetsov equation: she analysed the existing derivation of the models of non-linear acoustics such as the Kuznetsov equation, the NPE equation and the KZK equation. The technique of introducing a corrector in the derivation ansatz allows to consider the solutions of these equations as approximations of the solution of the initial system (a compressible Navier-Stokes/Euler system).…”