Crossover in the Enstrophy Decay in Two-Dimensional Turbulence in a Finite Box

Abstract

The numerical simulation of two-dimensional decaying turbulence in a large but finite box presented in this Letter uncovered two physically different regimes of enstrophy decay. During the initial stage, the enstrophy Omega, generated by a random Gaussian initial condition, decays as Omega(t) proportional variant t(-gamma) with gamma approximately 0.7-0.8. After that, the flow undergoes a transition to a gas or fluid composed of distinct vortices. Simultaneously, the magnitude of the decay exponent crosses over to gamma approximately 0.4. A theory predicting N(t) proportional variant t(-xi) and the magnitudes of exponents gamma=2/5 and xi=4/5 is presented.