Abstract
Abstract Large-scale vortices, that is, eddies whose characteristic length scale is larger than the local Rossby radius of deformation Rd, are ubiquitous in the oceans, with anticyclonic vortices more prevalent than cyclonic ones. Stability or robustness properties of already formed shallow-water vortices have been investigated to explain this cyclone–anticyclone asymmetry. Here the focus is on possible asymmetries during the generation of vortices through barotropic instability of a parallel flow. The initial stage and the nonlinear stage of the instability are studied by means of linear stability analysis and direct numerical simulations of the one-layer rotating shallow-water equations, respectively. A wide variety of parallel flows are studied: isolated shears, the Bickley jet, and a family of wakes obtained by combining two shears of opposite signs. The results show that, when the flow is characterized by finite relative isopycnal deviation, the barotropic instability favors the formation of large-scale anticyclonic eddies. The authors emphasize here that the cyclone–anticyclone asymmetry of parallel flows may appear at the linear stage of the instability. This asymmetry finds its origin in the linear stability property of localized shear flows. Indeed, for both the cyclogeostrophic regime (finite Rossby number) and the frontal geostrophic regime (small Burger number), an anticyclonic shear flow has higher linear growth rates than an equivalent cyclonic shear flow. The nonlinear saturation then leads to the formation of almost axisymmetric anticyclones, while the cyclones tend to be more elongated in the shear direction. However, although some unstable parallel flows exhibit the asymmetry at the linear stage, others exhibit such asymmetry at the nonlinear stage only. If the distance separating two shear regions is large enough, the barotropic instability develops independently in each shear, leading in the frontal and the cyclogeostrophic regime to a significant cyclone–anticyclone asymmetry at the linear stage. Conversely, if the two shear regions are close to each other, the shears tend to be coupled at the linear stage. The most unstable perturbation then resembles the sinuous mode of the Bickley jet, making no distinction between regions of cyclonic or anticyclonic vorticity. Nevertheless, when the nonlinear saturation occurs, large-scale anticyclones tend to be axisymmetric while the cyclonic structures are highly distorted and elongated along the jet meander.
Highlights
Various wake profiles are constructed as a combination of two localized shears. At this stage we introduce a new dynamical parameter to quantify the distance between the two shears and analyze its impact on the stability of the parallel wake flows
While the growth rate in the anticyclonic shear decreases by only 30% from its quasigeostrophic value, the unstable growth rate within the cyclonic shear strongly decreases
In the cyclogeostrophic regime, corresponding here to Bu 5 1 and Ro ’ 1, we found a more pronounced asymmetry between the unstable growth rate of the cyclonic and the anticyclonic shears (Fig. 3)
Summary
For all of these various configurations the coastal boundary of the archipelago or a cape induces significant shear flows in the open ocean far away from the coast. To explain the predominance of anticyclones among large-scale eddies, several studies were devoted to the specific stability of anticyclonic vortices in rotating shallow-water flows (Arai and Yamagata 1994; Stegner and Dritschel 2000; Baey and Carton 2002). Taking into account the weak beta effect, which may affect large-scale oceanic eddies, reveals that only anticyclones are weakly affected by the Rossby wave dispersion relation for a long time (Matsuura and Yamagata 1982; Nycander and Sutyrin 1992; Stegner and Zeitlin 1995, 1996). The departure from the QG regime (finite isopycnal displacement and/or finite Rossby number) may induce a specific cyclone–anticyclone asymmetry
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