Dissipation Statistics of a Passive Scalar in a Multidimensional Smooth Flow
Abstract
We compute analytically the probability distribution function P( ɛ) of the dissipation field ɛ=(∇ θ)2 of a passive scalar θ 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 ɛ→∞, ln P( ɛ)∼-( d 2 ɛ)1/3.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- March 1999
- DOI:
- 10.1023/A:1004522830805
- arXiv:
- arXiv:chao-dyn/9808001
- Bibcode:
- 1999JSP....94..759G
- Keywords:
-
- dissipation statistics;
- passive scalar;
- turbulence;
- intermittency;
- functional integral;
- Nonlinear Sciences - Chaotic Dynamics;
- Condensed Matter - Statistical Mechanics
- E-Print:
- Latex, 20 pages, submitted to J. Stat. Phys