Examination of certain terms appearing in Reynolds' equations under unsteady conditions and their implications for micrometeorology

Reynolds' equations are generally valid only when the bar operator represents an ensemble average. Such averages are rarely calculated in practice, the usual approach (especially in micrometeorology) being to calculate a time average instead. When conditions are at all unsteady, this practice necessitates consideration of additional terms in the expression for the Reynolds flux. It is shown, with the aid of a series of rapid‐response measurements of wind and temperature, that these terms are not necessarily negligible and that under unsteady conditions the complete Reynolds flux expression may differ considerably from the quantity generally computed; also, the vertical gradients of the two quantities will differ. A quantitative criterion of steadiness is proposed and is shown to be highly correlated with the difference between the complete Reynolds flux and the quantity usually calculated.