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

Abstract

The advection of a passive scalar through an initial flat interface separating two different isotropic decaying turbulent fields is investigated in two and three dimensions. Simulations have been performed for a range of Taylor’s microscale Reynolds numbers from 45 to 250 and for a Schmidt number equal to 1. Different to the case where the transport involves the momentum and kinetic energy only and one intermittency layer is formed in the low-turbulent energy side of the system, in the passive scalar concentration field two intermittent layers are observed to develop at the sides of the interface. The layers move normally to the interface in opposite directions. The dimensionality produces different time scaling of the passive scalar diffusion, which is much faster in the two-dimensional case. In two dimensions, the propagation of the intermittent layers exhibits a significant asymmetry with respect to the initial position of the interface and is deeper for the layer which moves towards the high kinetic energy side of the system. In three dimensions, the two intermittent layers propagate nearly symmetrically with respect the centre of the mixing region. During the temporal decay, inside the mixing, which is both inhomogeneous and anisotropic but devoid of a mean velocity shear, the passive scalar spectra are computed. In three dimensions, the exponent in the scaling range gets in time a value close to that of the kinetic energy spectrum of isotropic turbulence (−5/3). In two dimensions, instead the exponent settles down to a value that is about one-half of the corresponding isotropic case. By means of an analysis based on simple wavy perturbations of the interface we show that the formation of the double layer of intermittency is a dynamic general feature not specific to the turbulent transport. These results of our numerical study are discussed in the context of experimental results and numerical simulations.

Keywords:

• turbulent transport
• passive scalar
• shearless mixing
• intermittency
• spectral scaling

Acknowledgements

It is our great pleasure to dedicate this paper to this special journal issue celebrating Professor Robert Antonia’s outstanding contributions to fluid dynamics on the occasion of his 70th birthday. We thank Professor Antonia and his scientific work for giving a true inspiration.

We are grateful to Professor Zellman Warhaft of Cornell University who encouraged our study and shared the visualisation in Figure 3. We thank the referees for their constructive reviews and the many suggestions.

Additional information

Funding

This work was partially supported by the PRACE parternship (http://www.prace-ri.eu) [grant number 2011050773]; CINECA computing centre (http://www.cineca.it)[grant number ISCRA HP10ACLKN4]. We thank also HPC@POLITO (http://www.hpc.polito.it) for the availability of computational resources.