A New Surface Model for Cyclone–Anticyclone Asymmetry

Abstract

Cyclonic vortices on the tropopause are characterized by compact structure and larger pressure, wind, and temperature perturbations when compared to broader and weaker anticyclones. Neither the origin of these vortices nor the reasons for the preferred asymmetries are completely understood; quasigeostrophic dynamics, in particular, have cyclone-anticyclone symmetry.In order to explore these and related problems, a novel small Rossby number approximation is introduced to the primitive equations applied to a simple model of the tropopause in continuously stratified fluid. This model resolves dynamics that give rise to vortical asymmetries, while retaining both the conceptual simplicity of quasigeostrophic dynamics and the computational economy of two-dimensional flows. The model contains no depth-independent (barotropic) flow, and thus may provide a useful comparison to two-dimensional flows dominated by this flow component.Solutions for random initial conditions (i.e., freely decaying turbulence) exhibit vortical asymmetries typical of tropopause observations, with strong localized cyclones, and weaker diffuse anticyclones. Cyclones cluster around a distinct length scale at a given time, whereas anticyclones do not. These results differ significantly from previous studies of cyclone-anticyclone asymmetry in the shallow-water primitive equations and the periodic balance equations. An important source of asymmetry in the present solutions is divergent flow associated with frontogenesis and the forward cascade of tropopause potential temperature variance. This thermally direct flow changes the mean potential temperature of the tropopause, selectively maintains anticyclonic filaments relative to cyclonic filaments, and appears to promote the merger of anticyclones relative to cyclones.

Submesoscale turbulence in the upper ocean

“…These predictions carry over to more complete dynamics, which lead to corrections at small submesoscales (order 1 km) but generally agree with surface quasi-geostrophic dynamics at larger scales (e.g. Hakim et al, 2002;Klein et al, 2008;Capet et al, 2008e).…”

“…Primitive equation and Boussinesq simulations can also address how non-QG effects modify mesoscale-driven surface frontogenesis and allow an estimate of the importance of corrections to surface QG turbulence (cf. Hakim et al, 2002;Capet et al, 2008b;Klein et al, 2008;Roullet et al, 2012;Badin, 2012), providing another stepping stone for understanding observations.…”

On the formation of cyclones and anticyclones in a rotating fluid

“…(See, for example, Refs. [10][11][12][13]. This is an altogether more complex problem, where stratification and surface waves can play an important role.…”

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.…”