Non-circular baroclinic beta-plane modons: constructing stationary solutions

Abstract

Conditions determining the existence of localized steadily translating two-layer vortices (modons) of arbitrary symmetric form on the $\beta$-plane are considered. A numerical method for direct construction of modon solutions is suggested and its accuracy is analysed in relation to the parameters of the computational procedure and the geometrical and physical parameters of the modon sought. Using this method, several non-circular baroclinic solutions are constructed marked by nonlinearity of the dependence of the potential vorticity (PV) on the streamfunction in the trapped-fluid area of the modon, i.e. where the streamlines are closed. The linearity of this dependence and the circularity of the trapped-fluid area are shown to be equivalent properties of a modon. Special attention is given to elliptical modons – extended both in the direction of the modon propagation and in the orthogonal direction, the baroclinic PV component being assumed continuous. The differences between the two types of elliptical modons are discussed. The simplest vortical couples and shielded modons are considered. In the context of the continuity of the baroclinic PV field, the stability of modons is discussed based on numerical simulations.

Stability and evolution of uniform-vorticity dipoles

“…The first one is the reviled dependence of the dipole stability on the separation between the patches in all kinds of stationary dipoles: larger separation guarantees resistance to stronger perturbations. Such dependence has been observed in baroclinic modons and distributed hetons whose two vorticity 'masses' can overlap (Sokolovskiy & Verron 2000;Kizner et al 2002, Kizner, Berson & Khvoles 2003Kizner 2006Kizner , 2008. Here we have shown that the same is valid for non-overlapping barotropic dipoles.…”

Stability and transitions of hetonic quartets and baroclinic modons

“…To summarize, this vortical structure appears similar to the elliptical two-layer modons constructed by Kizner et al, 11 and can be considered a distributed ͑and smooth͒ analog of hetons.…”

“…However, numerical experiments showed that barotropic and baroclinic solutions with such a discontinuity are strongly unstable. [9][10][11] A heton is essentially baroclinic. It is comprised of two discrete vortices of equal strength but opposite signs confined to different layers of a two-layer fluid, and typically separated by a certain distance.…”

“…11 In a smooth elliptical modon, baroclinic and barotropic modes are interdependent, the amplitude of the baroclinic mode is not arbitrary and the modon's eastward translation is associated with both modes. Therefore, the baroclinic mode should not be referred to as a rider in this case.…”

“…When ellipses are sufficiently extended meridionally, the barotropic and baroclinic modes are close in magnitude, and such modons behave stably in numerical simulations. 11 With increasing separatrix aspect ratio , the northern ͑positive͒ and southern ͑negative͒ vortices become more and more localized ͑i.e., their vorticity peaks rise͒, whereas their overlap decreases and becomes negligible at Ϸ 1.1. These characteristics demonstrate that elliptical modons are affiliated with hetons.…”