Influence of initial conditions on decaying two-dimensional turbulence

Abstract

A numerical study of freely decaying two-dimensional turbulence is presented to show how the time evolution of characteristic flow quantities is influenced by the initial conditions. The numerical method adopted is a standard two-dimensional (2D) Fourier pseudospectral algorithm with Newtonian viscosity. Vortex statistics are extracted using a vortex census method. Several characteristic initial vorticity distributions analogous to those employed in previous laboratory experiments are considered. Some of the initial vorticity distributions have in common a dominant subset of vortices. Reliable statistics are obtained for each characteristic distribution by ensemble averaging. For the dominant subset, the time evolutions of the global enstrophy and the number density, respectively, are found to collapse confirming the self-similarity of 2D turbulence, one of the starting points for the scaling theory proposed by Carnevale et al. [Phys. Rev. Lett. 66, 2735 (1991)]. The relationship between the relevant scaling exponents as predicted by the scaling theory is not confirmed, however, and thus seems questionable within the considered parameter range. Furthermore, power-law exponents for both the number density and the global enstrophy are found to be affected by the initial number density and the initial vortex size distribution. Our results thus suggest that for experiments in shallow fluid layers, any agreement with a universal scaling exponent seems coincidental.