The "zeroth law" of turbulence: Isotropic turbulence simulations revisited

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The dimensionless kinetic energy dissipation rate Cₑpsilon is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number Reₗambda range is 20 < Reₗambda < 220 and the statistical stationarity is achieved with a random phase forcing method. The strong Reₗambda dependence of Cₑpsilon abates when Reₗambda approx. 100 after which Cₑpsilon slowly approaches approx 0.5 a value slightly different to previously reported simulations but in good agreement with experimental results. If Cₑpsilon is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to +-30%. This may explain the spread in results from previously published estimates of Cₑpsilon.