The dimensionless kinetic energy dissipation rate $C_{\epsilon }$ is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number $\left({\mathrm{Re}}_{\lambda }\right)$ range is $20\lesssim {\mathrm{Re}}_{\lambda }\lesssim 220$ and the statistical stationarity is achieved with a random phase forcing method. The strong ${\mathrm{Re}}_{\lambda }$ dependence of $C_{\epsilon }$ abates when ${\mathrm{Re}}_{\lambda }\approx 100$ after which $C_{\epsilon }$ slowly approaches $\approx 0.5$, a value slightly different from previously reported simulations but in good agreement with experimental results. If $C_{\epsilon }$ 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 $\pm 30\%$. This may explain the spread in results from previously published estimates of $C_{\epsilon }$.

• Received 23 April 2004

DOI:https://doi.org/10.1103/PhysRevE.70.056301