Analytical calculation of turbulence parameters on axisymmetric distortion

Abstract

A method of closing the equations of locally-isotropic turbulence is proposed. The method is based on the use of the most general properties of spectral functions on the longwave range, namely, the scale invariance and the behavior in the krc → 0 limit. Within the framework of the reduced description methodology the governing fields, namely, the orientation amplitudes fi j of the spectral functions and the integral turbulence scale rc, are established. The arguments of these fields, namely, the coordinates x and the wave vector orientation θ, are assumed to be slow, as distinct from the wavenumber k, in the sense that a universal quasi-equilibrium distribution with respect to k is achieved much more rapidly than relaxation with respect to the variables x and θ. A closed system of equations, which does not include model constants, is derived directly from the spectral equations for the governing fields. The solutions of this system are analyzed for the general case of irrotational distortion of developed turbulence.