Abstract

Local density of turbulent kinetic helicity, defined by the correlation between velocity and vorticity, is a measure of breakage of mirror-symmetry and provides structural information of turbulence. With the aid of a closure theory for inhomogeneous, anisotropic, and non-equilibrium turbulence: multiple-scale renormalised perturbation expansion theory, inhomogeneous rotating turbulence is investigated. The analytical expression for the Reynolds stress and vortex-motive (or ponderomotive) force is derived from the fundamental equations. This expression includes the inhomogeneous helicity coupled with the mean absolute vorticiy (the anti-symmetric part of mean shear) as well as the usual eddy viscosity coupled with the mean velocity strain (the symmetric part of mean shear). The validity of this expression is confirmed through applications of the turbulence model to turbulent swirling flow in a pipe, and direct numerical simulations of a rotating box turbulence with inhomogeneous turbulent helicity injected by external forcing. Several possible applications to the geophysical and astrophysical turbulent flows will be presented, followed by some proposals for the subgrid-scale (SGS) turbulence modelling with structure effects incorporated through SGS turbulent helicity.