Level Crossing Analysis of Burgers Equation in 1+1 Dimensions
We investigate the average frequency of positive slope $ν_α^{+}$, crossing the velocity field $u(x)- \bar u = α$ 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, $ν_α^{+}$, is a good measure for the fluctuations of velocity fields in the Burgers turbulence.
cond-mat.stat-mech↗