Role of Nonmodal Growth and Nonlinearity in Cyclogenesis Initial-Value Problems

Abstract

Observationally motivated idealized initial-value problems of cyclogenesis are studied for quasigeostrophic dynamics. The goals of this investigation are to assess the contributions of normal-mode and nonmodal growth mechanisms and the influence of nonlinearity during incipient cyclogenesis. The initial condition is represented by a coherent vortex superposed on a zero potential vorticity parallel flow. Nonlinear solutions are qualitatively in accord with observations, producing typical deepening of the surface cyclone, an asymmetry in the strength of the cyclone and anticyclone, and the formation of an upper-level front downstream from the cyclogenesis. The growth rate for the projection of the model state vector onto the most unstable mode closely approximates the linear value during the early stages of surface development. Nonlinear dynamics become important after approximately 30 h, beyond which the modal-projection growth rate declines approximately 30%. Linear solutions accurately approximate the intensity and zonal location of the surface cyclone, as well as the asymmetry between the cyclone and upstream anticyclone. The development of the surface cyclone is explained, almost entirely, by the projection onto the growing normal modes. The growing normal modes also account for the development of a prominent ridge of high pressure that forms on the tropopause downstream from the vortex. Nonmodal processes (the complementary subset to the growing normal modes) capture the dispersion of the upper vortex but do not contribute to deepening the surface cyclone. The upper-level front is captured by the linear solutions, and results from a favorable superposition between the growing normal modes and the neutral modes. Tests reveal that surface development declines markedly for vortex length scales smaller than those of observed precursor disturbances. This effect is attributed to a reduction in the vortex projection onto the unstable normal-mode spectrum.