Two Scaling Regimes in Two-Dimensional Turbulence

Abstract

In the present paper we have carefully examined the behavior of Q p ( r ), the moments of the enstrophy dissipation rate in two-dimensional turbulence averaged over squares of size r . We found a new scaling relation between Q p ( r ) and Q p -1 ( r ), which helps to establish the existence of two scaling regimes of Q p ( r ) in the large and small r region. The crossover scale is the length of the strips where the strong enstrophy dissipation occurs. If the length is much longer than the dissipation length corresponding to the width of the strips, such a scale is expected to naturally come in the scaling of Q p ( r ), casting a doubt on the usual statement that there is no characteristic length in turbulence. The implication of the result is discussed in relation to three-dimensional turbulence.