Resonant Interactions of Inertial-Gravity and Rossby Waves

Abstract

The nonlinear dynamics of inertial-gravity and Rossby waves are studied via the asymptotic method of multiple scales. Two important parameters which enter the problem are the conventional Rossby number ? and a nondimensional measure of the northward variation of the Coriolis parameter ?. Restricted to the weakly nonlinear limit (??1), this paper examines three possible nonlinear wave motions: weakly non-linear interactions on an f-plane (?=0), very weakly interacting disturbances in a quiescent atmosphere [?=O(?2)], and nonlinear interactions of finite-amplitude disturbances [?=O(?)]. In particular, resonant interactions are studied and the slow modulations of the linear solutions due to the nonlinearity are found. Some of these nonlinear solutions are unstable, being able to feed their energy into a resonantly interacting pair of disturbances.