Passive Scalar Spectra and Statistics In Steady Or Time-periodic 3d Laminar Chaotic Mixing
Abstract
New theoretical approaches for the problem of advection-diffusion of a passive scalar have been proposed in the literature (Cherkov et al., Phys. Rev. E, 51, 1995; Cherkov et al., Phys. Rev. Lett., 80, 1998; Balkovsky &Fouxon, Phys. Rev. E, 60, 1999). The more or the less, such works attempt to generalize the theory of Batchelor (J. Fluid Mech., 5, 1959) further extended by Kraichnan (Phys. Fluids, 11, 1968) which is intended to describe the behavior of the scalar in a turbulent flow at sub-Kolmogorov scales when low diffusivity (that is much smaller than kinematic viscosity) is involved. Universal properties of the scalar statistics are thought to characterize this so-called Batchelor regime. Among other results, in the freely decaying case (absence of scalar source), which is the topic in the following, exponential decay of the moments < q > is predicted at a rate which should be independent of q at large q while concentration PDF are expected to exhibit exponential tails. Note that, since they are mainly based on the existence of a local, maintained, stretching, most of these analysis, which primarily focus on turbulent flows, are expected to also describe mixing by laminar chaotic advection. Investigations have been performed recently to test for the relevance of such results. Experimental observations have been reported (Jullien et al, Phys. Rev. Lett., 85, 2000) for a 2D, weakly turbulent flow. Numerical results for a 2D laminar like flow (Pier- rehumbert, Chaos, 10, 2000) are also available. In the present work, we analyse in this context the concentration fields obtained by numerical simulation of 3D chaotic mixing. Previous results for steady state flows (Toussaint et al., Phys. Fluids, 7 (11), 1995; Toussaint et al., Phys. Fluids, 12 (11), 2000) as well as new results for time periodic flows are concerned. Time periodic flows are obtained by rotating the recir- culations axis at right angle from their previous orientation so that, three times after, the original orientation is recovered. Exponential decay of the variance at large times is still observed for this kind of 3D time periodic flows as in the case of 3D steady flows (previous references) and 2D unsteady ones (Pierrehumbert, Chaos, Solitons Fractals, 4, 1994; Antonsen et al., Phys. Fluids, 8, 1996). As well, large scale power law spectra are obtained as in the steady case (Toussaint et al., 2000) and compared with Batchelor-Kraichnan models. In the limit of the resolution, scalar PDF are found to have exponential tails while the rate of exponential decay of moments < q >, in agreement with Pierrehumbert (2000) results but in contradiction with the theoretical predictions of Balkovsky &Fouxon, are found to linearly depend on q.
- Publication:
-
EGS General Assembly Conference Abstracts
- Pub Date:
- 2002
- Bibcode:
- 2002EGSGA..27.6261C