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An expression for the dimensionless dissipation rate was derived from theKarman-Howarth equation by asymptotic expansion of the second- and third- orderstructure functions in powers of the inverse Reynolds number. The implicationsof the time-derivative term for the assumption of local stationarity (or localequilibrium) which underpins the derivation of the Kolmogorov `4/5' law for thethird-order structure function were studied. It was concluded that neglect ofthe time-derivative cannot be justified by reason of restriction to certainscales (the inertial range) nor to large Reynolds numbers. In principle,therefore, the hypothesis cannot be correct, although it may be a goodapproximation. It follows, at least in principle, that the quantitative aspectsof the hypothesis of local stationarity could be tested by a comparison of theasymptotic dimensionless dissipation rate for free decay with that for thestationary case. But in practice this is complicated by the absence of anagreed evolution time for making the measurements during the decay. However, wecan assess the quantitative error involved in using the hypothesis by comparingthe exact asymptotic value of the dimensionless dissipation in free decaycalculated on the assumption of local stationarity to the experimentallydetermined value (e.g. by means of direct numerical simulation), as thisrelationship holds for all measuring times. Should the assumption of localstationarity lead to significant error, then the `4/5' law needs to becorrected. Despite this, scale invariance in wavenumber space appears to holdin the formal limit of infinite Reynolds numbers, which implies that the `-5/3'energy spectrum does not require correction in this limit.

The dimensionless dissipation rate and the Kolmogorov (1941) hypothesis of local stationarity in freely decaying isotropic turbulence