We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For the PDFs of velocity and its derivatives u\(k\) = ∂kxu, the general formula is found: lnP\(\|u\(k\)\|\)~-\(\|u\(k\)\|/Rek\)3/\(k+1\).
Physical Review Letters
- Pub Date:
- February 1997
- Nonlinear Sciences - Chaotic Dynamics;
- Condensed Matter;
- High Energy Physics - Theory
- 4 pages, RevTeX 3.0, short version of chao-dyn/9603015, submitted to Phys. Rev. Lett