Small-Scale Dynamics of High-Reynolds-Number Two-Dimensional Turbulence

The free decay of two-dimensional turbulence is simulated by direct numerical integration of the incompressible Navier-Stokes equations at resolutions 512² and, for flows with symmetries, 1024². At early times, quasirectilinear vorticity-gradient sheets develop, with a thickness decaying exponentially in time until dissipation becomes relevant. The energy spectrum then displays a kⁿ range with n-4. At later times, we observe a transition to n-3. Vorticity gradients are then distributed on reconnecting, elongated, dissipative structures.