Is Turbulent Mixing a Self-Convolution Process?

In the absence of kinetic energy production, we consider that the influence of the initial conditions is characterized by the presence of an energy gradient or by the concurrency of an energy and a macroscale gradient on turbulent transport. Here, we present a similarity analysis that interprets two new results on the subject recently obtained by means of numerical experiments on shearless mixing (Tordella & Iovieno, 2005). In short, the two results are: i-The absence of the macroscale gradient is not a sufficient condition for the setting of the asymptotic Gaussian state hypothesized by Veeravalli and Warhaft (1989), where, regardless of the existence of velocity variance distributions, turbulent transport is mainly diffusive and the intermittency is nearly zero up to moments of order four. In fact, it was observed that the intermittency increases with the energy gradient, with a scaling exponent of about 0.29; ii-If the macroscale gradient is present, referring to the situation where the macroscale gradient is zero but the energy gradient is not, the intermittency is higher if the energy and scale gradients are concordant and is lower if they are opposite. The similarity analysis, which is in fair agreement with the previous experiments, is based on the use of the kinetic energy and the two-point correlation equations, which contain information on the second and third order moments of the velocity fluctuations. The analysis is based on two main hypotheses: first, the decays of the turbulences being mixed are nearly equal (as suggested by the experiments), second, the pressure-velocity correlation is almost proportional to the convective transport associated to fluctuations (Yoshizawa, 2002).

Experimental Thermal and Fluid Science, 2010

A turbulent mixing layer develops along stream wise direction through successively distinct regions, namely the near-field and self-preserving regions. Its flow field is composed of two different flow types, namely a shear layer and two outer free stream regions. The (stream wise) evolution from the near-field region to the self-preserving region and the (transverse) evolution from the shear layer to the two free stream sides in the mixing layer are experimentally investigated by using the information of joint probability density function (PDF) of velocity fields under the two flow conditions of (Re h = U H Á h 0 /m = 1100, r = (U H À U L )/(U H + U L ) = 0.72) and (370, 0.39), respectively. It is demonstrated that the transition from the near-field region to the self-preserving region can be precisely monitored through the stream wise variation of the inclined angle of the joint PDF distribution at the position of g = 0 where its mean stream wise velocity is equal to half of the sum of the high-and low-speed free stream velocities. In contrast, the transition from the shear layer to the two outer free stream regions can be monitored through the transverse variation of the roundness of the joint PDF distribution.

Physical Review Letters, 1997

We study the statistics of a passive scalar mixed by a turbulent flow that contains coherent structures (Görtler vortices). These structures entrain the passive scalar in such a way that its one-point probability density function (pdf) has a nonstandard shape that can be explained as a superposition of a background Gaussian mixing on the one hand, and the action of the Görtler vortices on the other. We propose a "mean field" approach to predict this pdf. This study (applicable to a wider class of systems) constitutes the first experimental example for which the conditional expectation of the second temporal derivative of the concentration of a passive scalar given the concentration deviates from a linear behavior.

Journal of Fluid Mechanics, 1999

We investigate the temporal evolution of the geometrical distribution of a passive scalar injected continuously into the far field of a turbulent water jet at a scale d smaller than the local integral scale of the turbulence. The concentration field is studied quantitatively by a laser-induced-fluorescence technique on a plane cut containing the jet axis. Global features such as the scalar dispersion from the source, as well as the fine structure of the scalar field, are analysed. In particular, we define the volume occupied by the regions whose concentration is larger than a given concentration threshold (support of the scalar field) and the surface in which this volume is enclosed (boundary of the support). The volume and surface extents, and their respective fractal dimensions are measured as a function of time t, and the concentration threshold is normalized by the initial concentration C s /C 0 for different injection sizes d. All of these quantities display a clear dependence on t, d and C s , and their evolutions rescale with the variable ξ = (ut/d)(C s /C 0 ), the fractal dimension being, in addition, scale dependent. The surface-to-volume ratio and the fractal dimension of both the volume and the surface tend towards unity at large ξ, reflecting the sheet-like structure of the scalar at small scales. These findings suggest an original picture of the kinetics of turbulent mixing.

2021

We investigate the dynamics of turbulent dispersion by means of direct numerical simulations of a passive tracer released in a homogeneous isotropic turbulent flow. We focus on the link between the probability density function (PDF) of the passive scalar concentration and its mixing properties. In particular, we show how the gamma distribution can be used as a suitable model for the PDF, as has been previously verified in wind tunnel experiments in wall-bounded turbulent flows. Finally, we develop a simple mixing model to estimate the time scale that regulates the decay rate of the intensity of concentration fluctuations.

Physics of Fluids, 2021

Contemporary Mathematics, 2007

We outline a program for the study of turbulent mixing of compressible fluids. We emphasize recent progress and steps still to be taken.

Physics of Fluids, 1996

Scalar mixing models are required to model turbulent molecular mixing in full probability density function ͑pdf͒ simulations of turbulent reacting flows. Despite the existence of direct numerical simulation ͑DNS͒ data suggesting the contrary, most scalar mixing models assume that molecular mixing is independent of the instantaneous velocity, i.e., ͗Dٌ 2 ͉V,͘ϭ͗Dٌ 2 ͉͘. Since in a joint velocity, composition pdf calculation the velocity is known, this assumption is unnecessary and leads to a lack of local isotropy in the scalar field. Moreover, since velocity conditioning offers a numerically tractable approach for including the effects of local anisotropy and mean velocity gradients on scalar mixing, it should be of considerable interest for the numerical simulation of scalar mixing in inhomogeneous turbulent flows. An efficient numerical implementation of velocity-conditioned scalar mixing for full pdf simulations is proposed and verified against DNS data for homogeneous turbulence ͑isotropic and shear flow͒ with a uniform mean scalar gradient. A second-moment closure relating the velocity-conditioned scalar dissipation to the scalar fluxes and Reynolds stresses that is exact in the limit of a joint Gaussian pdf is also derived for use with moment closure models.

Proceedings of the National Academy of Sciences, 2018

Mixing of initially distinct substances plays an important role in our daily lives as well as in ecological and technological worlds. From the continuum point of view, which we adopt here, mixing is complete when the substances come together across smallest flow scales determined in part by molecular mechanisms, but important stages of the process occur via the advection of substances by an underlying flow. We know how smooth flows enable mixing but less well the manner in which a turbulent flow influences it; but the latter is the more common occurrence on Earth and in the universe. We focus here on turbulent mixing, with more attention paid to the postmixing state than to the transient process of initiation. In particular, we examine turbulent mixing when the substance is a scalar (i.e., characterized only by the scalar property of its concentration), and the mixing process does not influence the flow itself (i.e., the scalar is “passive”). This is the simplest paradigm of turbule...

In studies of a turbulent flow with mixing-sensitive chemical reactions, the equations for the PDF of scalars (temperature and mixture component concentrations) are applied in combination with the conventional turbulence models that contain the equations for statistical moments. The PDF method advantage is an accurate representation of the chemistry influence in model equations. However, to calculate correlations responsible for an averaged chemical reaction rate, one needs a more thorough description of micromixing. As micromixing is governed by the small-scale flow structure, the latter can be considered statistically homogeneous. So, the well-developed homogeneous turbulence theory is used for closing the micromixing models. Just the adequate description of micromixing connected not only with the successful modeling of the chemistry influence, but first with a reasonable analysis of the entire mixing process, remains a stumbling block for the PDF method. This problem has received...