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.

Mixing of a passive scalar across a thin shearless layer: concentration of intermittency on the sides of the turbulent interface

“…In all flow configurations, the velocity mixing layer was observed to be highly intermittent and the velocity fluctuations in the x-direction have large skewness and kurtosis, see [13,14,24]. Across the mixing layer, the second, the third, and the fourth velocity moments collapse using a single lengthscale; the mixing width E , conventionally defined as the distance between the points with normalised energy (E(x, t) − E 2 (t))/(E 1 (t) − E 2 (t)) equal to 0.75 and 0.25.…”

“…The coordinate Downloaded by [Heriot-Watt University] at 13:01 02 January 2015 system is chosen with the x-axis along the direction of the kinetic energy gradient, axes y 1 and y 2 along the homogeneous directions. The initial condition is obtained by matching two homogeneous and isotropic fields with the same integral scale but each with different turbulent kinetic energy as in [13,14]. In practice, the initial condition is generated as…”

“…A description of how the presence of different integral scales can influence the turbulent kinetic energy diffusion can be found in [13,16].…”

“…The domain used in the 2D simulation has the same aspect ratio: it is 4π × 2π . For further details on the numerical technique and the initial condition generation, see [13,21,22].…”

“…The field that transports it is formed by one high kinetic energy turbulent isotropic field which is left to convectively diffuse into a lower energy one. In this shear-free velocity field, the region where the two turbulences interact is preceded by a highly intermittent thin layer -where the energy flux is maximum -that propagates into the low-energy region (see [13][14][15][16]). It should be noticed that this particular fluctuation field features a compression of the fluid filaments normal to the interface, that is along the direction of the mean gradient of both the scalar and kinetic energy fields.…”