Level Crossing Analysis of Burgers Equation in 1+1 Dimensions

Abstract

We investigate the average frequency of positive slope ${\nu }_{\alpha }^{+}$, crossing the velocity field $u(x)-\bar{u}=\alpha$ in the Burgers equation. The level crossing analysis in the inviscid limit and total number of positive crossing of velocity field before creation of singularities are given. The main goal of this paper is to show that this quantity, ${\nu }_{\alpha }^{+}$, is a good measure for the fluctuations of velocity fields in the Burgers turbulence.

5 pages, 3 figures