Eighteen hundred seventy-seven layers of turbulence, measured between 3000-18,300 m at four widely separated locations during all seasons by a parachuted telemetering instrument, have been analyzed by reducing the data to punched cards with the corresponding meteorological data. The altitude distribution of the layers exhibited three relative maxima (7400, 11,000, and 14,400 m), and three relative minima (6200, 9500, and 12,800 m). The first maximum, due to fronts, is the strongest. The other two are associated with the jet stream and probably represent clear-air turbulence. The trend is for turbulence to increase from 3000 to 7400 m, then to decrease slightly to 14,400 m, and then to decrease rapidly to 18,300 m. The average thickness of the layers was 239 m ; 87 per cent were less than 400 m thick. Most of this turbulence was indicated to be fairly persistent and moderate to heavy, having horizontal dimensions of at least 10 to 20 mi. This turbulence is below normal at the lowest freezing level. It is above normal at the base and top of well-marked tropospheric inversions, most of which are thought to be frontal inversions. No correlation was found with the base and top of the tropopause.

Correlations have been found between this turbulence and ranges of the following parameters: Richardson's number, vertical wind shear, lapse rate, wind speed and direction, temperature, and relative humidity. A theory of free-air turbulence, derived by analysis of the above-normal turbulence ranges for these parameters, has the following elements: 1. transitions occur in free-air turbulence flow, similar to transitions occurring in incompressible fluid flow; 2. transitions occur at certain values of Richardson's number R; 3. the vertical wind shear term is the most important parameter in R governing the turbulent flow. From the theory, it follows that the critical value of R can be taken to be unity, which means that the coefficients of turbulent diffusion for heat and momentum are equal in the free air.