On the decay of two-dimensional homogeneous turbulence

Direct numerical simulations of decaying two-dimensional turbulence in a fluid of large extent are performed primarily to ascertain the asymptotic decay laws of the energy and enstrophy. It is determined that a critical Reynolds number R(c) exists such that for initial Reynolds numbers with R(0)<R(c) final period of decay solutions result, whereas for R(0)>R(c) the flow field evolves with increasing Reynolds number. Exactly at R(0)=R(c), the turbulence evolves with constant Reynolds number and the energy decays as t(-1) and the enstrophy as t(-2). A t(-2) decay law for the enstrophy was originally predicted by Batchelor for large Reynolds numbers [Phys. Fluids Suppl. II, 12, 233 (1969)]. Numerical simulations are then performed for a wide range of initial Reynolds numbers with R(0)>R(c) to study whether a universal power-law decay for the energy and enstrophy exist as t-->infinity. Different scaling laws are observed for R(0) moderately larger than R(c). When R(0) be comes sufficiently large so that the energy remains essentially constant, the enstrophy decays at large times as approximately t(-0.8). (C) 1997 American Institute of Physics.