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Hot-wire measurements are carried out in grid-generated turbulence at moderate to low Taylor microscale Reynolds number $Re_{{\it\lambda}}$ to assess the appropriateness of the commonly used power-law decay for the mean turbulent kinetic energy (e.g. $k\sim x^{n}$, with $n\leqslant -1$). It is found that in the region outside the initial and final periods of decay, which we designate a transition region, a power law with a constant exponent $n$ cannot describe adequately the decay of turbulence from its initial to final stages. One is forced to use a family of power laws of the form $x^{n_{i}}$, where $n_{i}$ is a different constant over a portion $i$ of the decay time during the decay period. Accordingly, it is currently not possible to determine whether any grid-generated turbulence reported in the literature decays according to Saffman or Batchelor because the reported data fall in the transition period where $n$ differs from its initial and final values. It is suggested that a power law of the form $k\sim x^{n_{init}+m(x)}$, where $m(x)$ is a continuous function of $x$, could be used to describe the decay from the initial period to the final stage. The present results, which corroborate the numerical simulations of decaying homogeneous isotropic turbulence of Orlandi & Antonia (J. Turbul., vol. 5, 2004, doi:10.1088/1468-5248/5/1/009) and Meldi & Sagaut (J. Turbul., vol. 14, 2013, pp. 24–53), show that the values of $n$ reported in the literature, and which fall in the transition region, have been mistakenly assigned to the initial stage of decay.

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.

between the boundary layer developing over this wall and the smooth-wall turbulent boundary layer.