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 View the MathML source where U0 and L0 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.