Asymmetric evolution of eddies in rotating shallow water

Abstract

It is demonstrated that cyclones evolve in a way different from that of anticyclones in rotating shallow water. The anticyclones merge and eventually take circular coherent forms, but cyclones are elongated with active enstrophy cascading. This asymmetric evolution is strengthened with increasing surface displacements. When the initial surface displacement exceeds a certain critical value, the initial elongation of a cyclonic ellipse ends up with splitting in two cyclones. This splitting of the cyclonic ellipse is always associated with the first appearance of a saddle point inside the core, due to irrotational, ageostrophic motion. The appearance of the saddle point inside the core seems to be a necessary condition for splitting of the core of the cyclonic ellipse with surface displacements. The linear stability analysis of the elliptical vortex is consistent qualitatively with both of the simulation results and the kinematic axisymmetrization/elongation principle.

Numerical Simulations of Forced Shallow-Water Turbulence: Effects of Moist Convection on the Large-Scale Circulation of Jupiter and Saturn

“…Decaying shallowwater simulations initialized with equal-strength cyclones and anticyclones show that, as the flow evolves, the anticyclones become stronger and more compact than the cyclones (Arai and Yamagata 1994;Cho and Polvani 1996b;Polvani et al 1994;Stegner and Dritschel 2000). In decaying turbulence simulations initialized with zero skewness, the asymmetry only develops when F 2 /Ro Ͼ 0.13, where F ϭ U/͌gh and Ro ϭ U/2⍀L are the Froude and Rossby numbers, respectively, and L is a characteristic horizontal length scale of the flow (Cho and Polvani 1996b;Iacono et al 1999a).…”

“…In contrast to the quasigeostrophic system (which restricts vertical stretching to small fractional amplitude), fluid columns in shallow water can undergo order-unity changes in vertical thickness; however, baroclinic effects such as column twisting and tilting are excluded. There exist several decaying (Arai and Yamagata 1994;Farge and Sadourny 1989;Polvani et al 1994;Spall and McWilliams 1992) and forced (Yuan and Hamilton 1994) shallow-water turbulence investigations on the f plane that investigate the interaction between slowmoving vortex structures and high-frequency gravity waves. However, only a few turbulent shallow-water investigations have been published that focus on jets, and all of these investigated decaying rather than forced turbulence (Cho and Polvani 1996a,b;Iacono et al 1999a,b;Peltier and Stuhne 2002).…”

Stability of parallel wake flows in quasigeostrophic and frontal regimes

“…2,3 For small Rossby numbers, the geopotential fluctuations can be significant for large-scale flows, i.e., when the local deformation radius R d is smaller than the size of the vortices, where R d = ͱ gH 0 / f, g is the gravity, and H 0 is the layer depth. In that case, anticyclonic vortices tend to be more robust 4 and stable [5][6][7] than cyclones. As far as large-scale wakes are concerned, a recent experimental study 8 shows that the vortex street greatly differs from the classical von Karman street.…”

A Formal Theory for Vortex Rossby Waves and Vortex Evolution

“…The motivations for having such a theory are manifold. Among the phenomena that may be addressed by applications of this theory are the following: horizontal vortex axisymmetrization (McCalpin, 1987;Melander et al, 1987;Sutyrin, 1989;MK97;Bassom and Gilbert, 1998;Brunet and Montgomery, 2002); vortex spiral evolution (Lundgren, 1982;Moffat, 1986;Gilbert, 1988); vertical alignment (i.e., relaxation of perturbations that tilt the vortex axis away from the vertical Sutyrin et al, 1998;Polvani and Saravanan, 2000;Reasor and Montgomery, 2001;; evolutionary parity selection of either anticyclonic vortices away from boundaries (CushmanRoisin and Tang, 1990;Polvani et al, 1994;Arai and Yamagata, 1994;Yavneh et al, 1997;Stegner and Dritschel, 2000) or cyclonic vortices adjacent to solid horizontal boundaries (Simmons and Hoskins, 1978;Snyder et al, 1991;Rotunno et al, 2000;Hakim et al, 2002), both due to their greater robustness to perturbations at finite Rossby number; conservative vortex dynamics in shearing or straining flows (Marcus, 1990;Bassom and Gilbert, 1999); tropical cyclone development and potential vorticity redistribution (Guinn and Schubert, 1993;Montgomery and Enagonio, 1998;Schubert et al, 1999;Montgomery, 1999, 2000); and astrophysical accretion and protoplanetary disks (Bracco et al, 1999;Mayer et al, 2002;Nauta, 1999). It is not our present purpose to report particular solutions of the formal theory required for these various applications.…”