Energy dissipation and flux laws for unsteady turbulence

Direct Numerical Simulations of unsteady spatially periodic turbulence with time-dependent rms velocity u'(t) and integral length-scale L(t) show that not only the instantaneous energy dissipation rate but also the instantaneous energy flux at intermediate wavenumbers scales as U0L0 u'(t)(2)/L(t)(2) where U-0 and L-0 are velocity and length scales characterizing initial or overall unsteady turbulence conditions. These high Reynolds number scalings are qualitatively different from the well-known u'(t)(3)/L(t) cornerstone scalings of equilibrium turbulence where the energy flux and dissipation are exactly balanced at all times. (C) 2015 Elsevier B.V. All rights reserved.