Is turbulent mixing a self-convolution process?

Concentration Fluctuations from Localized Atmospheric Releases

We review the efforts made by the scientific community in more than seventy years to elucidate the behaviour of concentration fluctuations arising from localized atmospheric releases of dynamically passive and non-reactive scalars. Concentration fluctuations are relevant in many fields including the evaluation of toxicity, flammability, and odour nuisance. Characterizing concentration fluctuations requires not just the mean concentration but also at least the variance of the concentration in the location of interest. However, for most purposes the characterization of the concentration fluctuations requires knowledge of the concentration probability density function (PDF) in the point of interest and even the time evolution of the concentration. We firstly review the experimental works made both in the field and in the laboratory, and cover both point sources and line sources. Regarding modelling approaches, we cover analytical, semi-analytical, and numerical methods. For clarity of presentation we subdivide the models in two groups, models linked to a transport equation, which usually require a numerical resolution, and models mainly based on phenomenological aspects of dispersion, often providing analytical or semi-analytical relations. The former group includes: large-eddy simulations, Reynolds-averaged Navier-Stokes methods, two-particle Lagrangian stochastic models, PDF transport equation methods, and heuristic Lagrangian single-particle methods. The latter group includes: fluctuating plume models, semi-empirical models for the concentration moments, analytical models for the concentration PDF, and concentration time-series models. We close the review with a brief discussion highlighting possible useful additions to experiments and improvements to models.

Lamination and mixing in three fundamental flow sequences driven by electromagnetic body forces

This article pursues the idea that the degree of striations, called lamination, could be engineered to complement stretching and to design new sequential mixers. It explores lamination and mixing in three new mixing sequences experimentally driven by electromagnetic body forces. To generate these three mixing sequences, Lorentz body forces are dynamically controlled to vary the flow geometry produced by a pair of local jets. The first two sequences are inspired from the "tendril and whorl" and "blinking vortex" flows. The third novel sequence is called the "cat's eyes flip." These three mixing sequences exponentially stretch and laminate material lines representing the interface between two domains to be mixed. Moreover, the mixing coefficient (defined as 1-σ(2)/σ(0)(2) where σ(2)/σ(0)(2) is the rescaled variance) and its rate grow exponentially before saturation. This saturation of the mixing process is related to the departure of the mixing rate from an exponential growth when the striations' thicknesses reach the diffusive length scale of the measurements or species and dyes. Incidentally, in our experiments, for the same energy or forcing input, the cat's eyes flip sequence has higher lamination, stretching, and mixing rates than the tendril and whorl and the blinking vortex sequences. These features show that bakerlike in situ mixers can be conceived by dynamically controlling a pair of local jets and by integrating lamination during stirring stages with persistent geometries. Combined with novel insights provided by the quantification of the lamination, this paper should offer perspectives for the development of new sequential mixers, possibly on all scales.

Scalar fluctuations from a point source in a turbulent boundary layer

The downstream development of the concentration probability distribution along the mean-plume centerline of a dispersing plume in the wake of a ground-level continuous point source in a neutrally stratified wall-shear layer is studied. It is shown that the concentration distribution is well described by a family of one-parameter gamma distributions, as first suggested by Villermaux and Duplat [Phys. Rev. Lett. 91, 184501 (2003)] in the context of confined mixing. A prediction of the downstream evolution of the parameter k (which specifies the gamma distribution) is obtained. This prediction includes explicitly the effects of mean shear on the mean-square concentration.

Persistence of incomplete mixing: a key to anomalous transport

Anomalous dispersion in heterogeneous environments describes the anomalous growth of the macroscopic characteristic sizes of scalar fields. Here we show that this phenomenon is closely related to the persistence of local scale incomplete mixing. We introduce the mixing scale ε as the length for which the scalar distribution is locally uniform. We quantify its temporal evolution due to the competition of shear action and diffusion and compare it to the evolution of the global dispersion scale σ. In highly heterogeneous flow fields, for which the temporal evolution of σ is superdiffusive, we find that ε evolves subdiffusively. The anomalous evolutions of the dispersion and mixing scales are complementary, εσ ∝ t. This result relates anomalous global dispersion to the dynamics of local mixing.

Scaling laws of peripheral mixing of passive scalar in a wall-shear layer

The scaling laws governing the concentration moments of a passive scalar released from a ground-level localized source in a neutrally stratified wall-shear layer are investigated using a theoretical framework recently formulated by Lebedev and Turitsyn [Phys. Rev. E 69, 036301 (2004)]. For the current application, this theoretical framework is generalized from the smooth random velocity field applicable in the viscous sublayer to the nonsmooth random velocity field that applies to the bulk of the wall-shear layer. Theoretical relationships for the passive scalar concentration moments are compared to a water-channel simulation of turbulent diffusion from a ground-level source in a wall-shear layer. The diffusion measurements in the wall-shear layer are shown to be consistent with the theoretical description and also imply the robustness of the identified scaling laws for the scalar concentration moments.