An Application of the Modified Zero-Fourth-Cumulant Approximation to Homogeneous Axisymmetric Turbulence

Abstract

Equations of energy spectra in homogeneous axisymmetric turbulence are formulated by applying the modified zero-fourth-cumulant approximation and numerically solved under the three different initial conditions: (A) three-dimensional anisotropic turbulence; (B) two-dimensional isotropic velocity fluctuations transverse to the direction of axisymmetry λ; (C) one directional homogeneous fluctuations parallel to λ. The results show that in the case (A) Herring’s over-relaxation is observed, and that in the case (B) an inverse energy cascade characteristic of two-dimensional isotropic turbulence is observed. Also, it is shown that for strongly anisotropic cases (B) and (C) an approach to isotropy is much slower than for less anisotropic case (A).