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⁾0ex0ex=0ex0ex∂ₓᵏu, the general formula is found: lnP(|u⁽ᵏ⁾|)∝-(|u⁽ᵏ⁾|/Reᵏ)3/(k+1).
No takes yet. Share an insight, caveat, or question.
A 1997 study studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: