A stable precessing quasi-geostrophic vortex model with distributed potential vorticity

11 pages, 2 figures, 1 appendix, supplementary movies https://doi.org/10.1017/jfm.2020.130The permanent precession of a baroclinic geophysical vortex is reproduced, under he quasi-geostrophic approximation, using three potential vorticity anomaly modes in spherical geometry. The potential vorticity modes involve the spherical Bessel functions of the first kind jl(ρ)and the spherical harmonics Yml(θ, φ), where l is the degree, m is the order, and(ρ, θ, φ)are the spherical coordinates. The vortex precession is interpreted as the horizontal and circular advection by a large-amplitude background flow associated with the spherical modec0j0(ρ)of the small-amplitude zonal mode c2,0j2(ρ)Y02(θ) tilted by a small-amplitude mode c2,1j2(ρ)Y12(θ,φ), where {c0,c2,0,c2,1} are constant potential vorticity modal amplitudes. An approximate time-dependent, closed-form solution for the potential vorticity anomaly is given. In this solution the motion of the potential vorticity field is periodic but not rigid. The vortex precession frequencyω0depends linearly on the amplitudes c0 and c2,0 of the modal components of order 0, while the slope of the precessing axis depends on the ratio between the modal amplitude c2,1 and ω0.Partial support for this study was obtained through project RTI2018-100844-B-C33 (Spanish Ministry of Science, Innovation and UniversitiesWith the funding support of the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000928-S), of the Spanish Research Agency (AEI)Peer reviewe