Energy dissipation and flux laws for unsteady turbulence

• New energy dissipation law is verified for unsteady spatially periodic turbulence.
• New energy flux law for high Reynolds number unsteady turbulence is discovered.
• These laws hold both in forced and decaying turbulence.

Direct Numerical Simulations of unsteady spatially periodic turbulence with time-dependent rms velocity u′(t)u′(t) and integral length-scale L(t)L(t) show that not only the instantaneous energy dissipation rate but also the instantaneous energy flux at intermediate wavenumbers scales as U0L0u′(t)2/L(t)2 where U0U0 and L0L0 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)u′(t)3/L(t) cornerstone scalings of equilibrium turbulence where the energy flux and dissipation are exactly balanced at all times.