Free decay of high reynolds number two dimensional turbulence
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 vorticity gradient sheets with thickness decaying exponentially in time until dissipation 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, consistent 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.
KeywordsEnergy Spectrum Spectral Exponent Free Decay Cascade Theory Vorticity Gradient
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