Similarity in decaying isotropic turbulence: functional forms, constraints in single- and two-time evolution, and DNS results*

A similarity solution is proposed for two-space, two-time decaying isotropic turbulence. Constraint equations for the temporal evolution of the turbulence intensity and characteristic length scale are found and determine the decay exponent for the turbulence. These constraints and temporal evolution equations furthermore specify the evolution of the dissipation without any additional fitting parameters. A new non-dimensional time variable is found that characterizes self-similar behavior across logarithmic differences in time. The similarity solutions and constraints are applied to a Direct Numerical Simulation (DNS) of decaying isotropic turbulence at two grid resolutions (1024³ and 1536³) and different Reynolds numbers. The decay exponent is found to be determined solely from the evolution of the length scale and is dependent on the Reynolds number.