TY - JOUR
T1 - The instability and breakdown of tall columnar vortices in a quasi-geostrophic fluid.
AU - Dritschel, David Gerard
AU - de la Torre Juárez, Manuel
PY - 1996/12/10
Y1 - 1996/12/10
N2 - We examine the linear stability of elliptical columns of uniform potential vorticity subject to two-dimensional (horizontal) straining within a rapidly rotating, stratified (quasi-geostrophic) fluid. We find that horizontal straining can promote the exponential growth of three-dimensional disturbances when the vortex height-to-width aspect ratio exceeds, qualitatively, three times the ratio of the Coriolis parameter to the buoyancy frequency. This instability is not related to the usual baroclinic instability which operates on shallow vortex columns whose potential vorticity changes sign with height. The nonlinear development of these instabilities is investigated numerically using a high-resolution contour surgery algorithm. Simulations are conducted for both a Boussinesq (ocean-like) fluid and a compressible (atmospheric-like) fluid having exponentially decreasing density with height. The simulations reveal a generic nonlinear development that results in a semi-ellipsoidal baroclinic vortex dome at the lower surface and, in the case of a Boussinesq fluid, another such dome at the upper surface.The related problem of two interacting vortex columns is also examined. A generic three-dimensional instability and nonlinear development occurs no matter how great the distance between the vortex columns, provided that they are sufficiently tall.Our results may bear upon the observed structure of many atmospheric and oceanic vortices, whose height-to-width aspect ratios are consistent with our findings. Remarkably, even strongly ageostrophic vortices, such as tropical cyclones, fit the pattern. Our results furthermore re-open questions about the long-time nature of freely decaying quasi-geostrophic turbulence, for which recent simulations indicate a progressive two-dimensionalization by vortex alignment, while earlier simulations have indicated long-lived baroclinic vortices, not unlike what we find here.
AB - We examine the linear stability of elliptical columns of uniform potential vorticity subject to two-dimensional (horizontal) straining within a rapidly rotating, stratified (quasi-geostrophic) fluid. We find that horizontal straining can promote the exponential growth of three-dimensional disturbances when the vortex height-to-width aspect ratio exceeds, qualitatively, three times the ratio of the Coriolis parameter to the buoyancy frequency. This instability is not related to the usual baroclinic instability which operates on shallow vortex columns whose potential vorticity changes sign with height. The nonlinear development of these instabilities is investigated numerically using a high-resolution contour surgery algorithm. Simulations are conducted for both a Boussinesq (ocean-like) fluid and a compressible (atmospheric-like) fluid having exponentially decreasing density with height. The simulations reveal a generic nonlinear development that results in a semi-ellipsoidal baroclinic vortex dome at the lower surface and, in the case of a Boussinesq fluid, another such dome at the upper surface.The related problem of two interacting vortex columns is also examined. A generic three-dimensional instability and nonlinear development occurs no matter how great the distance between the vortex columns, provided that they are sufficiently tall.Our results may bear upon the observed structure of many atmospheric and oceanic vortices, whose height-to-width aspect ratios are consistent with our findings. Remarkably, even strongly ageostrophic vortices, such as tropical cyclones, fit the pattern. Our results furthermore re-open questions about the long-time nature of freely decaying quasi-geostrophic turbulence, for which recent simulations indicate a progressive two-dimensionalization by vortex alignment, while earlier simulations have indicated long-lived baroclinic vortices, not unlike what we find here.
KW - 2-DIMENSIONAL VORTEX DYNAMICS
KW - KIRCHHOFF ELLIPTIC VORTEX
KW - CONTOUR DYNAMICS
KW - V-STATES
KW - TURBULENCE
KW - FLOWS
KW - ALIGNMENT
KW - MODEL
UR - http://www.scopus.com/inward/record.url?scp=0030441243&partnerID=8YFLogxK
U2 - 10.1017/S0022112096008671
DO - 10.1017/S0022112096008671
M3 - Article
SN - 0022-1120
VL - 328
SP - 129
EP - 160
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -