Dissipation statistics of a passive scalar in a multidimensional smooth flow

Abstract

We compute analytically the probability distribution function $\mathcal{P}(\epsilon )$ of the dissipation field $\epsilon =(\nabla \theta {)}^2$ of a passive scalar $\theta$ advected by a $d$-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime). The tail of the distribution is a stretched exponential: for $\epsilon \to \infty$, $\ln \mathcal{P}(\epsilon )\sim -(d^2\epsilon {)}^{1/3}$.

Latex, 20 pages, submitted to J. Stat. Phys

References in corpus (5)

• Slow modes in passive advection
• Intermittent dissipation of a passive scalar in turbulence
• Inverse versus direct cascades in turbulent advection
• Inverse cascade and intermittency of passive scalar in 1d smooth flow
• Two complementary descriptions of intermittency

Cited by in corpus (6)

• Particles and fields in fluid turbulence
• Fine-scale statistics of temperature and its derivatives in convective turbulence
• Statistics and geometry of passive scalars in turbulence
• Lagrangian views on turbulent mixing of passive scalars
• Dissipation Scale Fluctuations and Chemical Reaction Rates in Turbulent Flows
• Characterization of the stretched exponential trap-time distributions in one-dimensional coupled map lattices