Inertial instability of intense stratified anticyclones. Part 2. Laboratory experiments

Abstract

International audienceLarge-scale laboratory experiments were performed on the Coriolis rotating platform to study the stability of intense vortices in a thin stratified layer. A linear salt stratification was set in the upper layer on top of a thick barotropic layer, and a cylinder was towed in the upper layer to produce shallow cyclones and anticyclones of similar size and intensity. We focus our investigations on submesoscale eddies, where the radius is smaller than the baroclinic deformation radius. Towing speed, cylinder size and stratification were changed in order to cover a large range of the parameter space, staying in a relatively high horizontal Reynolds number (Re = 2000-7000). The Rayleigh criterion states that inertial instabilities should strongly destabilize intense anticyclonic eddies if the vorticity in the vortex core is negative enough zeta(0)/f < -1, where zeta(0) is the relative vorticity in the core of the vortex, and f is the Coriolis parameter. However, we found that some anticyclones remain stable even for very intense negative vorticity values, up to zeta(0)/f = -3.5, when the Burger number is large enough. This is in agreement with the linear stability analysis performed in part 1 (J. Fluid Mech., vol. 732, 2013, pp. 457-484), which shows that the combined effect of a strong stratification and a moderate vertical dissipation may stabilize even very intense anticyclones, and the unstable eddies we found were located close to the marginal stability limit. Hence, these experimental results agree well with the simple stability diagram proposed in the Rossby, Burger and Ekman parameter space for inertial destabilization of viscous anticyclones within a shallow and stratified layer

Oceanic Island Wake Flows in the Laboratory

“…This is in agreement with the two-dimensional nonrotating flow in the limit of large Reynolds number, for which the Strouhal number, S t = f s D/U 0 = D/L e 0.2 − 0.24, at large Reynolds numbers [Wen and Lin, 2001]. Both experimental [Boyer and Kmetz, 1983;Stegner et al, 2005;Teinturier et al, 2010;Lazar et al, 2013b] and numerical studies [Heywood et al, 1996;Perret et al, 2006a] confirm this result in a deepwater configuration when the bottom friction is negligible. Hence, a quasi-geostrophic wake will have the same pattern as the standard nonrotating Karman street even if the separation and the vortex shedding occur at higher critical Reynolds numbers [Boyer and Kmetz, 1983;Boyer et al, 1984].…”

“…However, it could be easier to perform PIV (particle image velocimetry) measurements with a top-view camera if the fluid layer is at rest, on the rotating turntable, and the cylinder is translated at a constant speed (Figure 14.2b). Such configurations with high-resolution PIV measurements were used in recent experiments [Stegner et al, 2005;Perret et al, 2006b;Teinturier et al, 2010;Lazar et al, 2013b], especially when the rotating fluid layer is stratified ( Figure 14.2c).…”

“…For a higher stratification, this stabilization is even more pronounced. Indeed, several intense anticyclones, having a relative core vorticity down to ζ 0 /f = −3, were found to be stable in a shallow and strongly stratified (N/f = 14) wake where Ro I = 1.7 and Re = 15, 000 [Lazar et al, 2013b]. Anticyclones become unstable for higher Rossby numbers (Ro I ≥ 2) but close to the marginal stability limit the signature of the inertial-centrifugal instability is not clearly visible on the vorticity field (Figure 14.8).…”

Submesoscale Instabilities in Mesoscale Eddies

“…They note that solving numerically for the linear stability of baroclinic vortices with continuous stratification is much more challenging, as the problem becomes nonseparable in the vertical and radial directions. The results here indicate a further complication compared to the large body of research of vortex stability (e.g., Kloosterziel and van Heijst 1991;Billant and Gallaire 2005;Lahaye and Zeitlin 2015;Lazar et al 2013;Smyth and McWilliams 1998) in that the stability of the vortices varies in the azimuthal direction. This variation occurs because of the opposing effect of the Ekman buoyancy flux on either side of a vortex.…”

Submesoscale Turbulence over a Topographic Slope

“…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].…”