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This paper presents additional information of a theoretical nature and a synoptic case study concerning the nature of the generation of Clear Air Turbulence. The hypothesis in this paper is that (a) Shear is generated rapidly in a specific region of the atmosphere. (b) The shear reaches a critical value and the flow field becomes turbulent. (c) The turbulent flow field, in the form of a cell or eddy, is carried away from the source region and gradually decays. The theory on which the prediction of shear is based is developed on a nonlinear basis to show that if convection of vorticity is neglected, the vertical component of the vorticity depends quadratically with time on the solenoids of temperature and divergence of velocity, plus another smaller term. Thus the horizontal shear of the velocity may be expected in certain large scale synoptic situations to grow nonlinearly. Synoptic analysis has been made by computer program of a well-known case of CAT: April, 1962.