On the Theory of Disturbances in a Conditionally Unstable Atmosphere

A perturbation model is developed which is applicable to small-amplitude moist convcctive disturbances of scales ranging from those of squall lines t o tropical cyclones. In a11 extension of the works of SyBno and Haque, disturbance development is studied for an atmosphere in which static stabi1it)y may vary with height and with the sense of the vertical motion, being in general negative for upward motion in some substantial layer. Closed solutions for simplified cases are exhibited as well as results of nurrlerical integration of a more realistic case. The dynamic stability criterion depends on the static stabilities in the ascending and descmding currents and their dimensions and geometric relationships. Cloud-scale and meso-scale disturbances arc’ more unstable than those of cyclone-scale, and presence of the former may tend to destroy conditions favoring development of the latter. Evaluation is made of, the linearized effects of parallel convective bands, an “eye”, the tropopause, nonhydrostatic motions, surface friction, and various boundary conditions. Comparison of solutions with observational features shows fair agreement in some respects, improving considerably when nonlinear effects are qualitatively considered. The disturbances are effective in transporting kinetic and potential energy outward from the actively unstable updraft. Nonlinear interactions tend to transport heat upward to modify the initial static stability distribution. A second-order dynamic stability criterion, obtained by consideration of nonlinear effects, tends to favor development of an existing finite-amplitude disturbance of tropical cyclone scale.