Propagation and Overturning of Localized Anelastic Internal Gravity Wavepackets

Abstract

As internal gravity wavepackets propagate upward in the atmosphere, their amplitude experiences exponential growth so that nonlinear effects influence their evolution. This thesis examines the weakly and fully nonlinear evolution, stability, and overturning of horizontally and vertically localized internal gravity wavepackets propagating in a stationary, non-rotating anelastic model atmosphere. The weakly nonlinear evolution is examined through the derivation of an expression for the flow induced by the propagating wavepacket, which is used to formulate a nonlinear Schrödinger equation. The induced flow is manifest as a long, hydrostatic disturbance qualitatively resembling a bow wake. The direction of this flow transitions from positive on the leading flank of the wavepacket to negative on the trailing flank. As such, we find that two-dimensional internal gravity wavepackets are always modulationally unstable. Consequently, enhanced amplitude growth is focused either on the leading or the trailing flank of the wavepacket. When combined with exponential amplitude growth predicted by linear theory, we anticipate that two-dimensional wavepackets will overturn either somewhat below or just above the overturning heights predicted by linear theory. The nonlinear Schrödinger equation is solved numerically, and its solutions are compared with the results of fully nonlinear simulations of the equations of motion to establish the validity of weakly nonlinear theory. Actual wave overturning heights are determined quantitatively from a range of fully nonlinear simulations.