On the Construction of Turbulent Transfer Spectral Models Using 3D Numerical Simulation of Taylor–Green Vortex Decay

Abstract

In the present paper we recall the classical Taylor–Green vortex turbulent decay in terms of isotropic turbulence theory. In particular, we calculate the spectral turbulent kinetic energy transfer \(T(k)\) and the spectral flux \({{\Pi }_{E}}(k)\) basing on the longitudinal triple correlation function (the two-point third-order velocity moment). These functions can be also obtained in other way via the generalized Karman–Howarth equation for homogeneous turbulence using integral of triple modes interaction. In both cases, the spectral transfer and the flux appear to be different from the characteristics of isotropic or homogeneous turbulence due to the peculiarities of the problem statement. The results obtained outline the range of obstacles associated with the construction of spectral turbulent models in complex heat and mass transfer problems arising due to periodicity effects, closeness of integral turbulent scales to modeling box size and lack of spectral resolution.