LAUSR

The Reynolds number dependence of the non-dimensional mean turbulent kinetic energy dissipation rate $C_{\unicode[STIX]{x1D716}}=\overline{\unicode[STIX]{x1D716}}L/u^{\prime 3}$ (where $\unicode[STIX]{x1D716}$ is the mean turbulent kinetic energy dissipation rate, $L$ is an integral length scale and $u^{\prime }$ is the velocity root-mean-square) is investigated in decaying turbulence. Expressions for $C_{\unicode[STIX]{x1D716}}$ in homogeneous isotropic turbulent (HIT), as approximated by grid turbulence, and in local HIT, as on the axis of the far field of a turbulent round jet, are developed from the Navier–Stokes equations within the framework of a scale-by-scale energy budget. The analysis shows that when turbulence decays/evolves in compliance with self-preservation (SP), $C_{\unicode[STIX]{x1D716}}$ remains constant for a given flow condition, e.g. a given initial Reynolds number. Measurements in grid turbulence, which does not satisfy SP, and on the axis in the far field of a round jet, which does comply with SP, show that $C_{\unicode[STIX]{x1D716}}$ decreases in the former case and remains constant in the latter, thus supporting the theoretical results. Further, while $C_{\unicode[STIX]{x1D716}}$ can remain constant during the decay for a given initial Reynolds number, both the theory and measurements show that it decreases towards a constant, $C_{\unicode[STIX]{x1D716},\infty }$ , as $Re_{\unicode[STIX]{x1D706}}$ increases. This trend, in agreement with existing data, is not inconsistent with the possibility that $C_{\unicode[STIX]{x1D716}}$ tends to a universal constant.