Vortex stability in a multi-layer quasi-geostrophic model: application to Mediterranean Water eddies (original) (raw)
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Journal of Physical Oceanography, 2011
Large-scale vortices, that is, eddies whose characteristic length scale is larger than the local Rossby radius of deformation R d , 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.
Cyclone and anticyclone formation in a rotating stratified fluid over a sloping bottom
Journal of Fluid Mechanics, 1999
We discuss laboratory experiments with a continuous source or sink of fluid in a two-layer rotating environment which produces anticyclonic and cyclonic vortices, respectively. Experiments were carried out with a sloping bottom in order to simulate the β-effect and they were conducted for different values for the source/sink flow rate Q and the Coriolis parameter f. The Rossby number Ro of these vortices was small but finite and the flow was expected to be quasi-geostrophic. The qualitative behaviour of the anticyclonic and cyclonic vortices was generally similar, but it depended on the flow rate. For low flow rates, a single vortex formed at the source and extended to the west. At higher flow rates, the vortex broke free from the source and moved to the west; this vortex was then followed sequentially by other vortices behaving similarly. The westward velocity U of these vortices was calculated and compared with the speed Us of a linear topographic Rossby wave. For multiple vortice...
Anticyclonic selection by instability of parallel flows in a frontal regime
2007
Large-scale flows are known to present a predominance of anticyclonic vortices. A previous study (Perret et al. (2006)) showed a strong cyclone-anticyclone asymmetry in large-scale wakes, anticyclones are circular whereas cyclones are deformed. To determine the mechanisms responsible for the asymmetry, we perform a stability analysis of parallel wake flows associated with experimental velocity profiles. It is shown that the most unstable mode, in a frontal regime, is localized in the anticyclonic shear leading to a strong cyclone-anticyclone asymmetry in the nonlinear evolution of the perturbation. Moreover, the wake instability changes from the absolute instability in the quasigeostrophic regime to the strongly convective instability of the frontal regime. To determine whether the stability property of a parallel flow in a frontal regime could be a mechanism of anticyclones selection, we extend this stability analysis to parallel jets and shears. The anticyclonic shear, in a frontal regime, is much more unstable than the cyclonic one, but the nonlinear evolution of the flow leads, in both cases, to circular vortices.
Cyclone-anticyclone asymmetry of large-scale wakes in the laboratory
Physics of Fluids, 2006
We performed an experimental study of large-scale wakes in a rotating shallow-water layer. Standard particle image velocimetry was used to measure the horizontal velocity field, while a laser-induced fluorescence technique was used to measure the geopotential deviation ͑i.e., the interface deviation͒. According to these measurements, we were able to quantify the dynamics in a wide region of parameter space beyond the quasi-geostrophic regime. For obstacles larger than the deformation radius and with small Rossby numbers, a significant asymmetry occurs in the wake between cyclonic and anticyclonic vortices. These parameters correspond to a frontal geostrophic regime with the relative interface deviation being larger than 0.1-0.2. In this case, anticyclones remain coherent and circular, whereas cyclones tend to be elongated and distorted. More surprisingly, for some extreme cases, coherent cyclones do not emerge at all, and only an anticyclonic vortex street appears several diameters behind the obstacle. The transition from a quasi-geostrophic to a frontal geostrophic regime is characterized by a strong increase in the Strouhal number, which can reach a value up to 0.6. Hence, we found that a large-scale wake could differ strongly from the classical Karman street when the relative geopotential deviation becomes larger than the Rossby number.
Vortex evolution due to straining: a mechanism for dominance of strong, interior anticyclones
Geophysical & Astrophysical Fluid Dynamics, 2006
In this article we address two questions: Why do freely evolving vortices weaken on average, even when the viscosity is very small? Why, in the fluid's interior, away from vertical boundaries and under the influence of Earth's rotation and stable density stratification, do anticyclonic vortices become dominant over cyclonic ones when the Rossby number and deformation radius are finite? The context for answering these questions is a rotating, conservative, Shallow-water model with Asymmetric and Gradient-wind Balance approximations. The controlling mechanisms are vortex weakening under straining deformation (with a weakening that is substantially greater for strong cyclones than strong anticyclones) followed by a partially compensating vortex strengthening during a relaxation phase dominated by Vortex Rossby Waves (VRWs) and their eddy-mean interaction with the vortex. The outcome is a net, strain-induced vortex weakening that is greater for cyclones than anticyclones when the deformation radius is not large compared to the vortex radius and the Rossby number is not small. Furthermore, when the exterior strain flow is sustained, the vortex changes also are sustained: for small Rossby number (i.e., the quasigeostrophic limit, QG), vortices continue to weaken at a relatively modest rate, but for larger Rossby number, cyclones weaken strongly and anticyclones actually strengthen systematically when the deformation radius is comparable to the vortex radius. The sustained vortex changes are associated with strain-induced VRWs on the periphery of the mean vortex. It therefore seems likely that, in a complex flow with many vortices, anticyclonic dominance develops over a sequence of transient mutual straining events due to the greater robustness of anticyclones (and occasionally their net strengthening).
Velocity profiles of cyclones and anticyclones in a rotating turbulent flow
Physics of Fluids
Strong rotation makes an underlying turbulent flow quasi-two-dimensional that leads to the upscale energy transfer. Recent numerical simulations show that under certain conditions, the energy is accumulated at the largest scales of the system, forming coherent vortex structures known as condensates. We analytically describe the interaction of a strong condensate with weak small-scale turbulent pulsations and obtain an equation that allows us to determine the radial velocity profile U (r) of a coherent vortex. When external rotation is fast, the velocity profiles of cyclones and anticyclones are identical to each other and are well described by the dependence U (r) ∝ ±r ln(R/r), where R is the transverse size of the vortex. As the external rotation decreases, this symmetry disappears: the maximum velocity in cyclones is greater and the position of the maximum is closer to the axis of the vortex in comparison with anticyclones. Besides, our analysis shows that the size R of the anticyclone cannot exceed a certain critical value, which depends on the Rossby and Reynolds numbers. The maximum size of the cyclones is limited only by the system size under the same conditions. Our predictions are based on the linear evolution of turbulent pulsations on the background of the coherent vortex flow and are accompanied by estimates following from the nonlinear Navier-Stokes equation.
A New Look at the Problem of Tropical Cyclones in Vertical Shear Flow: Vortex Resiliency
Journal of The Atmospheric Sciences, 2004
A new paradigm for the resiliency of tropical cyclone (TC) vortices in vertical shear flow is presented. To elucidate the basic dynamics, the authors follow previous work and consider initially barotropic vortices on an f plane. It is argued that the diabatically driven secondary circulation of the TC is not directly responsible for maintaining the vertical alignment of the vortex. Rather, an inviscid damping mechanism intrinsic to the dry adiabatic dynamics of the TC vortex suppresses departures from the upright state. Recent work has demonstrated that tilted quasigeostrophic vortices consisting of a core of positive vorticity surrounded by a skirt of lesser positive vorticity align through projection of the tilt asymmetry onto vortex Rossby waves (VRWs) and their subsequent damping (VRW damping). This work is extended here to the finite Rossby number (Ro) regime characteristic of real TCs. It is shown that the VRW damping mechanism provides a direct means of reducing the tilt of intense cyclonic vortices (Ro > 1) in unidirectional vertical shear. Moreover, intense TC-like, but initially barotropic, vortices are shown to be much more resilient to vertical shearing than previously believed. For initially upright, observationally based TC-like vortices in vertical shear, the existence of a ‘‘downshear-left’’ tilt equilibrium is demonstrated when the VRW damping is nonnegligible. On the basis of these findings, the axisymmetric component of the diabatically driven secondary circulation is argued to contribute indirectly to vortex resiliency against shear by increasing Ro and enhancing the radial gradient of azimuthal-mean potential vorticity. This, in addition to the reduction of static stability in moist ascent regions, increases the efficiency of the VRW damping mechanism.
Inertial instability of intense stratified anticyclones. Part 1. Generalized stability criterion
Journal of Fluid Mechanics, 2013
The 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 ...
Cyclone-anticyclone asymmetry in decaying rotating turbulence
The statistics of the vorticity fluctuations in decaying rotating turbulence is experimentally investigated by means of particle image velocimetry. Two series of experiments have been carried out, one in a small-scale rotating water tank (FAST, Paris), with an aspect ratio ∼ O(1), and the other one in the large-scale 'Coriolis' plateform (LEGI, Grenoble), with an aspect ratio ∼ O(10). In both experiments, turbulence is generated by rapidly towing a grid through the fluid, providing an initial state which is approximately homogeneous and isotropic. The asymmetry between cyclones and anticyclones is characterized by the vorticity skewness S ω = ω 3 z / ω 2 z 3/2 (ω z is the vorticity component along the rotation axis). During the decay, for times up to the Ekman timescale, a growth of the asymmetry towards cyclonic vorticity is observed as S ω ∼ (Ωt) 0.7±0.1. For larger times, a re-symmetrization of the vorticity fluctuations take place, due to the non-linear Ekman pumping which preferentially affects the cyclonic vorticity. While the power-law growth is generic of both experiments, the maximum value of S ω is shown to depend on the experimental configuration.