## Abstract

Vortex displacement stratospheric sudden warmings (SSWs) are studied in an idealized model of a quasigeostrophic columnar vortex in an anelastic atmosphere. Motivated by the fact that observed events occur at a fixed orientation to the earth’s surface and have a strongly baroclinic vertical structure, vortex Rossby waves are forced by a stationary topographic forcing designed to minimize excursions of the vortex from its initial position. Variations in the background stratospheric “climate” are represented by means of an additional flow in solid body rotation. The vortex response is determined numerically as a function of the forcing strength *M* and the background flow strength Ω.

At moderate *M* it is found that a large response, with many features resembling observed displacement SSWs, occurs only for a narrow range of Ω. Linear analysis reveals that for this range of Ω the first baroclinic azimuthal wave-1 Rossby wave mode is close to being resonantly excited. A forced nonlinear oscillator equation is proposed to describe the nonlinear behavior, and a method for determining the relevant coefficients numerically, using unforced calculations of steadily propagating vortex “V states,” is adopted. The nonlinear equation predicts some qualitative details of the variation in the response at finite *M*. However, it is concluded that strongly nonlinear processes, such as wave breaking and filament formation, are necessarily quantitatively important in determining the amplitude of the near-resonant response at finite *M*.

*Corresponding author address:*Gavin Esler, Department of Mathematics, University College London, 25 Gower Street, London WC1E 6BT, United Kingdom. E-mail: gavin@math.ucl.ac.uk