FREE DECAY OF HIGH REYNOLDSNUMBERTWO DIMENSIONALTURBULENCE M.E. Brachet* and P.L. Sulem*;: *CNRS, Observatoire de Nice, France **School of Mathematical Sciences, Tel Aviv University Israel and CNRS, Observatoire de Nice, France ABSTRACT The free decay of high Reynolds two dimensional turbulence is simulated by direct numerical intergration of the Navier-Stokes equations at a resolution of 1024 x 1024 with symmetric random initial conditions. The following scenario is observed : At early times, large scale straining generates quasi-rectilinear vor- ticity gradient sheets with thickness decaying exponentially in time until dis- sipation becomes relevant. In Fourier space, the energy spectrum displays a k-n - range with n = 4, in agreement with Saffman's theory. Close to the time of maximum enstrophy dissipation, we observe a transition to an n = 3 inertial range, consis- tent which the Batchelor-Kraichnan theory of enstrophy cascade. In this regime, vorticity gradients are distributed on convoluted secondary dissipative structures resulting from folding and reconnection of early time sheets. 1 . INTRODUCTION A controversal question in high Reynolds number turbulence in two-dimensional incompressible flows is the behavior of the energy spectrum. Saffman (1971) argues that advection will bring different values of vorticity close together producing thin sheets of vorticity gradients and leading to a k-4 inertial energy spectrum. In contrast, the enstrophy cascade theory (Kraichnan, 1967 ; Batchelor, 1969) pre- dicts a k-3 - energy spectrum with a possible logarithmic correction due to non- local interactions (Kraichnan, 1971). Furthermore, Kraichnan (1975) predicts that because of this non-locality~ intermittency will not affect the energy spectrum. This point has been questioned by Basdevant, Legras, Sadourny and Beland (1981) who claim that intermittency will restore the predominance of local interactions and steepen the energy spectrum. Since the first calculations of Lilly (1969), it has been recognized that very high resolutions are required to property simulate an inertial range (Herring, Orszag, Kraichnan and Fox, 1974). Preliminary calculations at (512) 2 - resolution presented by Orszag (1977), showed that when the large scale Reynolds number is increased from 1100 to 25000, a distinct change is observed from a k -4 energy spec- trum to a spectrum roughly proportional to k-3. The present paper is devoted to simulations of spatially periodic solutions at (1024) 2 - resolution. To achieve this resolution on a IM - word CRAY i computer, 103