The free decay of two-dimensional turbulence is simulated by direct numerical integration of the incompressible Navier-Stokes equations at resolutions ${512}^2$ and, for flows with symmetries, ${1024}^2$. 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 $k^n$ range with $n\simeq -4\mathrm{}$. At later times, we observe a transition to $n\simeq -3\mathrm{}$. Vorticity gradients are then distributed on reconnecting, elongated, dissipative structures.

• Received 12 August 1985

DOI:https://doi.org/10.1103/PhysRevLett.57.683