On the application of the richardson criterion to large‐scale turbulence in the free atmosphere

A brief report on an investigation into the relationship between the wind shear and the static stability of the air in the layer immediately below the tropopause was presented to the Meteorological Research Committee in October 1942 (Swinbank, M.R.P. 51, unpublished). In the course of the ensuing discussion, members of the M.R.C. suggested that the investigation should be extended to cover the entire troposphere. This has been done particularly with a view to finding empirical relationships between stability and wind shear and comparing these with the results obtained by applying the Richardson criterion to actual observations. A further demand for investigating this problem arose in connection with an investigation of the turbulence conditions that obtain near the tropopause. In the present investigation use has been made of the reports from the British radio‐sonde stations for the period December 1942 to March 1943. The accuracy of the D/F method of determining the wind in the free atmosphere depends to a large extent upon the geometry of each case, and a tolerance figure is allotted to each observation assessing the accuracy. Only reports of the highest degree of accuracy ( i.e. vector errors less than 5 km/hour) have been used in this investigation. In all, 1,556 simultaneous observations of lapse rate and wind shear have been investigated. The observations have been grouped according to levels, and the results are illustrated in 12 diagrams in which lapse rate is the abscissa and wind shear the ordinate. The diagrams contain also the limiting curve between decrease and increase in turbulence as computed from Richardson's criterion. Since wind observations are made at intervals of 50 millibars, the diagrams represent the observed relationship between the mean wind shear and the mean lapse rate through layers of 50 mb. depth. The limiting curve in these diagrams would then represent the limit between the conditions that determine decrease and increase in the large‐scale turbulence of the atmosphere. The diagrams show that, with very few exceptions, for any degree of stability the observed wind shear is less than that required by Richardson's theory to cause the turbulence to increase. If the assumptions underlying the theory were correct and applicable to large‐scale turbulence, the diagrams would indicate that large‐scale turbulence almost invariably tends to decrease. Since this result appears improbable, it is shown that agreement between theory and observation can be obtained by dropping one of the assumptions made by Richardson; namely, that the coefficient.