Projects per year
Abstract
We examine the basic properties and stability of isolated vortices having uniform potential vorticity (PV) in a nonhydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basicstate stratification for which both the Coriolis and buoyancy frequencies, f and N, are constant. Moreover, we take ƒ/N≪1,
as typically observed in the Earth’s atmosphere and oceans. In the small Rossby number ‘quasigeostrophic’ (QG) limit, when the flow is weak compared to the background rotation, there exist exact solutions for steadily rotating ellipsoidal volumes of uniform PV in an unbounded flow (Zhmur & Shchepetkin, Izv. Akad. Nauk SSSR Atmos. Ocean. Phys., vol. 27, 1991, pp. 492–503; Meacham, Dyn. Atmos. Oceans, vol. 16, 1992, pp. 189–223). Furthermore, a wide range of these solutions are stable as long as the horizontal and vertical aspect ratios λ and μ do not depart greatly from unity (Dritschel et al.,J. Fluid Mech., vol. 536, 2005, pp. 401–421). In the present study, we examine the behaviour of ellipsoidal vortices at Rossby numbers up to near unity in magnitude. We find that there is a monotonic increase in stability as one varies the Rossby number from nearly −1 (anticyclone) to nearly +1 (cyclone). That is, QG vortices are more stable than anticyclones at finite negative Rossby number, and generally less stable than cyclones at finite positive Rossby number. Ageostrophic effects strengthen both the rotation and the stratification within a cyclone, enhancing its stability. The converse is true for an anticyclone. For all Rossby numbers, stability is reinforced by increasing λ towards unity or decreasing μ. An unstable vortex often restabilises by developing a nearcircular crosssection, typically resulting in a roughly ellipsoidal vortex, but occasionally a binary system is formed. Throughout the nonlinear evolution of a vortex, the emission of inertia–gravity waves (IGWs) is negligible across the entire parameter space investigated. Thus, vortices at small to moderate Rossby numbers, and any associated instabilities, are (ageostrophically) balanced. A manifestation of this balance is that, at finite Rossby number, an anticyclone rotates faster than a cyclone.
Original language  English 

Pages (fromto)  196231 
Number of pages  36 
Journal  Journal of Fluid Mechanics 
Volume  762 
Early online date  2 Dec 2014 
DOIs  
Publication status  Published  Jan 2015 
Keywords
 Geophysical and geological flows
 Rotating flows
 Vortex dynamics
 Warmcore rings
 Geophysical flows
 Shallowwater
 Oceanic vortices
 Shearflow
 Vortex
 Balance
 Stability
 Evolution
 Equilibria
Fingerprint
Dive into the research topics of 'Ellipsoidal vortices in rotating stratified fluids: beyond the quasigeostrophic approximation'. Together they form a unique fingerprint.Projects
 1 Finished

Geophysical Vortices: The Structure, stability and interaction of geophysical vortices
Reinaud, J. N., Dritschel, D. G. & Scott, R. K.
5/01/10 → 1/11/13
Project: Standard