Turbulent mixing is ubiquitous in both nature and industrial applications. Most of them involve different fluids, therefore with variable physical properties (density and/or viscosity). The focus here is on variable-viscosity flows and mixing in density-matched fluids. The issue is whether or not these flows may be self-similar, or self-preserving. The importance of the question stands on the predictability of these flows; self-similar dynamical systems are much easier tractable from an analytical viewpoint. Self-similarity analysis, as first introduced by Townsend, is applied to the relevant transport equations of the velocity field (mean momentum, one-point energy budget equation as well as scale-by-scale energy transport equations-the latter represent the transport of energy at each scale and each point of the flow). Extensions of these equations for the transport of the scalar field are discussed, with particular focus on their mathematical analogy. It is stressed that neither local isotropy nor high Reynolds numbers are necessary conditions for the similarity to be valid. Scale-by-scale energy budget equations are developed for flows in which the viscosity varies as a result of heterogeneous mixture or temperature variations.  Additional terms are highlighted, accounting for the viscosity gradients, or fluctuations.  These terms are present at both small and large scales, thus rectifying the common belief that viscosity is a small-scale quantity. This will be illustrated with results obtained either experimentally (in a jet) or numerically (in a temporally evolving mixing layer). Scale-by-scale energy budget equations are written for the central region of a round jet evolving in a more viscous host fluid.  It is further shown that the condition of self-preservation on the jet axis is not necessarily satisfied in variable-viscosity jets. Indeed, the jet momentum conservation, as well as the constancy of the Reynolds number along the axis of the jet, cannot be satisfied simultaneously.  This points to the necessity of considering less stringent conditions (with respect to classical, single-fluid jets) when analytically tackling these flows and reinforces the idea that viscosity variations must be accounted for when modeling these flows.

Professor Luminita Danaila obtained her PhD from IRPHE, Université d'Aix-Marseille II, in 1998. She has been working in University of Rouen since 2000. Her research interests include fluid mechanics, turbulence.