On the adjustment of azimuthally perturbed vortices

Abstract

A series of numerical experiments with a reduced‐gravity, quasi‐geostrophic model were performed to investigate the adjustment of vortices to large‐amplitude perturbations of azimuthal modes 2 and 3. The results indicate that for vortices with length scales near the radius of deformation, almost 100% of the azimuthal mode energy is transferred to the axisymmetric flow. The time scale is of the order of the circulation time scale but exhibits a strong dependence on the perturbation mode number. The β plane cases show that this strong axisymmetrization tendency is almost completely unaffected by variations in the Coriolis parameter. The energetics of the perturbed β plane cases are virtually indistinguishable from the energetics of the unperturbed cases after 2–3 circulation periods, except for the cases with the strongest perturbations. Vorticity plots reveal that in the most perturbed cases, excess vorticity in the ends of the ellipse is removed in the form of elongated streamers. In some regions of the parameter space, these streamers roll up into cyclone‐anticyclone pairs.

Vortex motion in a weak background shear flow

“…Such vorticity might be present through perturbations to a vortex, for example if a vortex is immersed in weak ambient strain generated by other vortices, by vortex interactions, or by a vortex moving in a background of weak, filamented vorticity. These situations can occur in two-dimensional turbulence (for example Fornberg 1977;McWilliams 1984;Brachet et al 1988;Dritschel 1989) but also have wider applicability to the modelling of vortices in general geophysical fluid flows (for example, Rhines & Young 1982;McCalpin 1987;Smith & Montgomery 1995;.…”

The spiral wind-up and dissipation of vorticity and a passive scalar in a strained planar vortex

“…Such vortices cannot show the process of relaxation to axisymmetry which commonly † occurs for smooth vortices (for example McCalpin 1987;Melander, McWilliams & Zabusky 1987;Smith & Montgomery 1995;Yao & Zabusky 1996). As an instance of such 'axisymmetrization', consider a Gaussian vortex exposed to an impulsive external strain field (Bernoff & Lingevitch 1994, henceforth referred to as BL94).…”

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.…”