Inertial instability of intense stratified anticyclones. Part 1. Generalized stability criterion

Abstract

International audienceThe stability of axisymmetric vortices to inertial perturbations is investigated by means of linear stability analysis, taking into account stratification, vertical eddy viscosity, as well as finite depth of the flow. We consider different types of circular barotropic vortices in a linearly stratified shallow layer confined with rigid lids. For the simplest case of the Rankine vortex we develop an asymptotic analytic dispersion relation and a marginal stability criterion, which compares well with numerical results. This is a further generalization to the well-known generalized Rayleigh criterion, which is only valid for non-dissipative and non-stratified eddies. Unlike the Rayleigh criterion, it predicts that intense anticyclones may be stable even with a core region of negative absolute vorticity, and that the dissipation and stratification work together to stabilize the flow. Numerical analysis reveals that the stability diagrams for various types of vortices are almost identical in the Rossby, Burger and Ekman parameter space. This allows extension of our analytical solutions for the Rankine vortex to a wide variety of vortices. Furthermore, we show that a more suitable parameter for the intensity of the vortex is the vortex Rossby number, while for the inviscid case it is the local normalized vorticity. These predictions are in agreement with laboratory experiments presented in part 2

Submesoscale Turbulence over a Topographic Slope

“…In all experiments, cyclonic vortices are more prevalent near the surface than anticyclonic vortices, resulting in a preference for positive Ro. As mentioned in the introduction, this is consistent with many previous studies (Munk et al [35], Lazar et al [32], Buckingham et al [37] to name a few), and is a possible signature of the flow's geostrophic imbalance. In each of our simulations, we choose a shallow layer at 10 m depth and calculate the Ro probability density functions (PDF) as shown in Figure 6a Away from the surface, Ro decays to smaller values, roughly by a factor of 3 at 180 m depth (Figure 6b, also shown in Klein et al [3]).…”

“…Both theoretical predictions [31,32] and laboratory experiments [33,34] have shown that anticyclonic vortices are more susceptible to inertial instability. This has been used to explain the preponderance of cyclonic submesoscale eddies observed at the ocean surface [35].…”

The Azores Confluence Zone

“…Contrary to Barbosa et al (2011), however, Cyclonic eddies rotated and also propagated faster than anticyclones. As in Barbosa et al (2011), the local "vortex Rossby number" (Ro) was calculated as a function of ζ /f redefined by Lazar et al (2013) as Ro = V max /f r max ; where ζ is the vortex core vorticity; f is the Coriolis parameter; V max is the maximum "swirl velocity" of the eddy; and r max is the radius corresponding to the maximum velocity. Rossby numbers were slightly higher but of the same order of magnitude as of those previously reported, indicating a strong influence of planetary rotation (Barbosa et al, 2011).…”

Effect of Prandtl’s ratio on balance in geophysical turbulence

“…Such instability is often preceded by a period when the vorticity-based Rossby number Ro = ζ /f is less than −1 somewhere in the flow (a necessary condition for inertial instability, cf. Knox (1997), Lazar, Stegner & Heifetz (2013)) or by a period when the Richardson number Ri = N 2 (1 + S)/|∂u h /∂z| 2 is less than 1/4 (a necessary condition for shear or Kelvin-Helmholtz instability, cf. Howard (1961), Miles (1961), Hazel (1972).…”

“…However, arguably, inertial instability is not relevant to stratified threedimensional vortices: one cannot ignore the stabilising effects of stratification. Instead, instability requires that the (total) PV be negative: Π < 0 (Sawyer 1947;Ooyama 1966;Charney 1973) (this is called 'symmetric instability' -see Lazar et al (2013) for a detailed discussion). Notably, this never occurs in our simulations since PV is conserved and Π > 0 in all cases.…”