Abstract
The first prediction of the probability distribution function (PDF) of self-organized shear flows is presented in a nonlinear diffusion model where shear flows are generated by a stochastic forcing while diffused by a nonlinear eddy diffusivity. A novel nonperturbative method based on a coherent structure is utilized for the prediction of the strongly intermittent exponential PDF tails of the gradient of shear flows. Numerical simulations using Gaussian forcing not only confirm these predictions but also reveal the significant contribution from the PDF tails with a large population of supercritical gradients. The validity of the nonlinear diffusion model is then examined using a threshold model where eddy diffusivity is given by discontinuous values, elucidating an important role of relative time scales of relaxation and disturbance in the determination of the PDFs.
| Original language | English |
|---|---|
| Article number | 052304 |
| Journal | Physics of Plasmas |
| Volume | 16 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 10 Jun 2009 |
| Externally published | Yes |
Funding
This research was supported by the EPSRC (Grant No. EP/D064317/1) and RAS Travel Grant. The National Center for Atmospheric Research is sponsored by the NSF. FIG. 1. The solid line is the PDF from the numerical simulation of a nonlinear diffusion model (2) for a white noise. The dotted and dashed lines are the fits to Gaussian and exp ( − c u x 4 ) ( c = const ) . FIG. 2. The profile of u x corresponding to Fig. 1 . FIG. 3. Solid line is the PDF from a threshold model. Dotted and dashed-dotted-dotted-dotted lines are Gaussian fits; dashed and dashed-dotted lines are fits to exp ( − c u x 4 ) ( c = const ) .
ASJC Scopus subject areas
- Condensed Matter Physics