Numerical experiments on the intermediate asymptotics of shear-free turbulent transport and diffusion

Abstract

A numerical experiment on the interaction between different decaying homogeneous and isotropic turbulence is described. In the absence of kinetic energy production, the intermediate asymptotics of the turbulent shear-free mixing layer can be observed. The first aim of the experiment is to verify the existence of the intermittency or of the Gaussian asymptotic state in the case of the absence, or weak presence, of a lengthscale gradient. The second aim is to analyse the effects that are due to the difference between the spectral distribution of the interacting turbulence fields, which introduces the presence of the gradient of integral scale into the initial condition. It can be observed that the homogeneity of the integral length across the shearless layer is not a sufficient condition to obtain the Gaussian asymptotic state. In fact, if the macroscale gradient is suppressed by considering turbulence with similar spectra, it is apparent that the intermittency increases with the energy gradient. Furthermore, by independently varying the initial energy level and distribution over the wavenumbers, two turbulence fields can be joined with an initial difference of integral scale either opposite to or concordant with the gradient of the turbulent kinetic energy. It is found that the intermittency and the depth of penetration by the eddies from the high-energy region increase when the energy and lengthscale gradients are concordant and decrease when they are opposite. Therefore, the most efficient process of mixing takes place when the spectra of two mixed fields differ in the lowest wavenumbers.