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 di↵usion, 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.

We study the physics of turbulent/non-turbulent interface (TNTI) of an isolated turbulent region in dilute polymer solutions and Newtonian fluid. We designed an experimental setup of a turbulent patch growing in water/dilute polymer solution, without mean shear and far from the walls. The observations from the experiments are complemented and expanded by simulations performed using a localised homogeneous forcing to generate the turbulent front and the FENE-P model for the polymer stress. The comparison, which shows that when Newtonian and viscoelastic TNTIs are fed by the same energy they behave in similar manner both in the experiments and in the simulations, permits to extend the applicability, on a qualitative basis, of single relaxation time polymer models also to turbulent/non-turbulent interfaces.From the detailed analysis offered by the numerical results, the alterations in the dynamics between strain and vorticity help understanding the mechanics of the polymer action on the TNTI without mean shear. The reduced vorticity stretching and increased vorticity compression terms are found to be due to the modified degrees of alignment between vorticity, polymer conformation tensor and rate-of-strain tensor eigenvectors observed especially near the interface. These alignments at the smallest scales of the non-Newtonian turbulent flow lead to a reduced production of enstrophy and consequently to a reduced entrainment, that in this problem are seen as reduced advancement of a turbulent region.

We present measurements of the fine structure of a passive scalar plume in uniformly sheared turbulence generated in a water tunnel. We report on the mixed velocity-scalar statistics of the plume, including the probability density functions of the velocity, scalar, and scalar derivatives, as well as conditional expectations of the velocity and the scalar derivatives, conditioned upon the scalar fluctuations. Such results are particularly relevant to models that are intended to be used for solving the balance equation of the scalar pdf. Specifically, we address the effect of having a highly intermittent scalar field, in which case the scalar pdf is highly skewed, the joint velocity and scalar pdfs are non-Gaussian, and conditional expectations of the velocity components are distinctly non-linear. Details on the fine structure of turbulent mixing are particularly relevant for the modelling of chemical reactions and combustion. A popular approach for analyzing reactive flows is to consider the balance equation of the scalar probability density function (pdf) [1, 2, 3]. Although these equations have certain advantages over conventional Reynolds-averaged balance equations of velocity and scalar moments, they are complicated by the appearance of conditional expectations of the velocity and the scalar dissipation values, conditioned upon the scalar fluctuations. Most previous studies have focused on flows in which the velocity and scalar are nearly homogeneous and jointly-Gaussian, in which case these conditional expectations would be linear functions of the scalar value [2, 3, 4]; however, this would not necessarily be the case for inhomogeneous scalar fields as they would appear in indus

A DNS simulation of an interface between a decaying turbulent flow without mean shear and a quiescent non-turbulent region is presented here. The analysis of the instantaneous fields highlight a complex multi-scale behaviour at the turbulent/non-turbulent interface. According to previous results in the literature, by analysing the enstrophy budgets it is possible to observe that enstrophy propagate from the turbulent region mainly by inviscid process while viscous diffusion is relevant only at the interface.