Spectral enstrophy budget in a shear-less flow with turbulent/non-turbulent interface

A numerical analysis of the interaction between decaying shear free turbulence and quiescent fluid is performed by means of global statistical budgets of enstrophy, both, at the single-point and two point levels. The single-point enstrophy budget allows us to recognize three physically relevant layers: a bulk turbulent region, an inhomogeneous turbulent layer, and an interfacial layer. Within these layers, enstrophy is produced, transferred, and finally destroyed while leading to a propagation of the turbulent front. These processes do not only depend on the position in the flow field but are also strongly scale dependent. In order to tackle this multi-dimensional behaviour of enstrophy in the space of scales and in physical space, we analyse the spectral enstrophy budget equation. The picture consists of an inviscid spatial cascade of enstrophy from large to small scales parallel to the interface moving towards the interface. At the interface, this phenomenon breaks, leaving place to an anisotropic cascade where large scale structures exhibit only a cascade process normal to the interface thus reducing their thickness while retaining their lengths parallel to the interface. The observed behaviour could be relevant for both the theoretical and the modelling approaches to flow with interacting turbulent/nonturbulent regions. The scale properties of the turbulent propagation mechanisms highlight that the inviscid turbulent transport is a large-scale phenomenon. On the contrary, the viscous diffusion, commonly associated with small scale mechanisms, highlights a much richer physics involving small lengths, normal to the interface, but at the same time large scales, parallel to the interface.