Theory of Development and of Thickness Patterns

The equations of motion, of continuity, of vorticity and of heat-transfer are transformed from coordinates (x, y, z) to coordinates (x, y, p) without the use of the hydrostatic equation in the vertical. An approximation based on the empirical fact that the isobaric surfaces are slightly inclined to the horizontal together with the use of dimensionless variables, gives the hydrostatic equation and simplifies the fundamental equations by the rejection of many of their terms. Thereafter definitions of certain types of geostrophic and nongeostrophic motions lead, respectively, to (a) Rossby's potential-vorticity equation; (b) the development and thickness-patterns theory of R. C. Sutcliffe, which is discussed in detail; and (c) J. G. Charney's (1949) treatment of the equivalent barotropic atmosphere. These models of atmospheric motions are compared and contrasted.