Dynamics of Vortex Structures in a Stratified Rotating Fluid (original) (raw)
Related papers
Dynamics of baroclinic vortices in a rotating, stratified fluid: A numerical study
Physics of Fluids, 1997
This study deals with the instabilities that arise in the flow generated in a rotating tank by the evolution of a two-layer density stratified fluid. Numerical investigations have been performed by direct simulation of the Navier-Stokes equations for axisymmetric and fully three-dimensional flows. In the former case results have shown the attainment, in a very short time, of an equilibrium position and the formation of an anticyclonic structure in the upper light layer and a cyclonic one in the lower layer, consistently with the observation of Griffiths and Linden. In the long term, however, the Ekman layer at the bottom damps out the cyclone and a steady state with only an anticyclone in the upper layer is reached. In three-dimensions the flow is unstable to azimuthal disturbances and the steady state is no longer achieved. In particular a ring of cyclonic vorticity, surrounding the anticyclone, by the combined effects of baroclinic and barotropic processes, breaks, entrains vorticity from the anticyclone and eventually forms vortex pairs. As observed by Griffiths and Linden the azimuthal wave number (n*) of the instability depends on the Richardson number (Ri) and the ratio between the depth of the light fluid and the total depth (␦). However, since several modes, in addition to the most unstable, are amplified an initial perturbation whose energy is not equidistributed among the modes can lead to an instability with wave number different from the expected n*. Finally, the analysis of the equation for the energy of the instability has shown that the instability is initially driven by baroclinic effects, even for low values of ␦. The barotropic source, in contrast, sets in only in the large-amplitude phase of the instability and its effect is larger when ␦ is small.
Geophysical Research Letters, 2016
Wide compensated vortices are not able to remain circular in idealized two-layer models unless the ocean depth is assumed to be unrealistically large. Small perturbations on both cyclonic and anticyclonic eddies grow slower if a middle layer with uniform potential vorticity (PV) is added, owing to a weakening of the vertical coupling between the upper and lower layers and a reduction of the PV gradient in the deep layer. Numerical simulations show that the nonlinear development of the most unstable elliptical mode causes self-elongation of the upper vortex core and splitting of the deep PV anomaly into two corotating parts. The emerging tripolar flow pattern in the lower layer results in self-intensification of the fluid rotation in the water column around the vortex center. Further vortex evolution depends on the model parameters and initial conditions, which limits predictability owing to multiple equilibrium attractors existing in the dynamical system. The vortex core strips thin filaments, which roll up into submesoscale vortices to result in substantial mixing at the vortex periphery. Stirring and damping of vorticity by bottom friction are found to be essential for subsequent vortex stabilization. The development of sharp PV gradients leads to nearly solid-body rotation inside the vortex core and formation of transport barriers at the vortex periphery. These processes have important implications for understanding the longevity of real-ocean eddies.
Hydrodynamical Modeling Of Oceanic Vortices
Surveys in Geophysics - SURV GEOPHYS, 2001
Mesoscale coherent vortices are numerous in the ocean.Though they possess various structures in temperature and salinity,they are all long-lived, fairly intense and mostly circular. Thephysical variable which best describes the rotation and the density anomaly associated with coherent vortices is potential vorticity. It is diagnostically related to velocity and pressure, when the vortex is stationary. Stationary vortices can be monopolar (circular or elliptical) or multipolar; their stability analysis shows thattransitions between the various stationary shapes are possible when they become unstable. But stable vortices can also undergo unsteady evolutions when perturbed by environmental effects, likelarge-scale shear or strain fields, ß-effect or topography. Changes in vortex shapes can also result from vortex interactions. such as the pairing, merger or vertical alignment of two vortices, which depend on their relative polarities and depths. Such interactions transfer energy and en...
Geophysical & Astrophysical Fluid Dynamics, 2017
Analysis of the influence of condensation and related latent heat release upon developing barotropic and baroclinic instabilities of large-scale low Rossby-number shielded vortices on the f-plane is performed within the moist-convective rotating shallow water model, in its barotropic (one-layer) and baroclinic (two-layer) versions. Numerical simulations with a high-resolution well-balanced finite-volume code, using a relaxation parameterisation for condensation, are made. Evolution of the instability in four different environments, with humidity (i) behaving as passive scalar, (ii) subject to condensation beyond a saturation threshold, (iii) subject to condensation and evaporation, with two different parameterisations of the latter, are inter-compared. The simulations are initialised with unstable modes determined from the detailed linear stability analysis in the "dry" version of the model. In a configuration corresponding to low-level mid-latitude atmospheric vortices, it is shown that the known scenario of evolution of barotropically unstable vortices, consisting in formation of a pair of dipoles ("dipolar breakdown") is substantially modified by condensation and related moist convection, especially in the presence of surface evaporation. No enhancement of the instability due to precipitation was detected in this case. Cyclone-anticyclone asymmetry with respect to sensitivity to the moist effects is evidenced. It is shown that inertia-gravity wave emission during the vortex evolution is enhanced by the moist effects. In the baroclinic configuration corresponding to idealised cutoff lows in the atmosphere, it is shown that the azimuthal structure of the leading unstable mode is sensitive to the details of stratification. Scenarios of evolution are completely different for different azimuthal structures, one leading to dipolar breaking, and another to tripole formation. The effects of moisture considerably enhance the perturbations in the lower layer, especially in the tripole formation scenario.
Stabilization of Isolated Vortices in a Rotating Stratified Fluid
Fluids, 2016
The key element of Geophysical Fluid Dynamics-reorganization of potential vorticity (PV) by nonlinear processes-is studied numerically for isolated vortices in a uniform environment. Many theoretical studies and laboratory experiments suggest that axisymmetric vortices with a Gaussian shape are not able to remain circular owing to the growth of small perturbations in the typical parameter range of abundant long-lived vortices. An example of vortex destabilization and the eventual formation of more intense self-propagating structures is presented using a 3D rotating stratified Boussinesq numerical model. The peak vorticity growth found during the stages of strong elongation and fragmentation is related to the transfer of available potential energy into kinetic energy of vortices. In order to develop a theoretical model of a stable circular vortex with a small Burger number compatible with observations, we suggest a simple stabilizing procedure involving the modification of peripheral PV gradients. The results have important implications for better understanding of real-ocean eddies.
Vortex Generation by Topography in Locally Unstable Baroclinic Flows*
Journal of Physical Oceanography, 2003
The dynamics of a quasigeostrophic flow confined in a two-layer channel over variable topography on the beta plane is numerically investigated. The topography slopes uniformly upward in the north-south direction (in the beta sense) and is a smooth function of the zonal coordinate. The bottom slope controls the local supercriticality and is configured to destabilize the flow only in a central interval of limited zonal extent. Linearized solutions indicate that, for a wide enough channel, unstable modes exist for an arbitrary short interval of instability, confirming previous analysis on disturbances with no meridional variation. For small local maximum supercriticality, the instability is maintained by a short bottom-trapped wave localized at the downstream edge of the unstable region and oscillating in phase with the upper-layer disturbance. When nonlinearity is retained in the problem, the equilibration of the bottom-trapped wave is associated with the formation of coherent vortices. Both cyclones and anticyclones are formed continuously at the northeastern edge of the unstable interval. Through vortex stretching mechanisms, dipoles inside the interval of instability can split upon reaching the northern wall: Anticyclones move downstream along the north wall and propagate into the downstream stable region, while cyclonic structures tend to remain trapped inside the interval of instability. The authors suggest the relevance of their results to the observed eddy field of the Labrador Sea.
Propagation of barotropic vortices over topography in a rotating tank
Journal of Fluid Mechanics, 1991
A small-scale cyclonic vortex in a relatively broad valley tends to climb up and out of the valley in a cyclonic spiral about the centre, and when over a relatively broad hill it tends to climb toward the top in an anticyclonic spiral around the peak. This phenomenon is examined here through two-dimensional numerical simulations and rotating-tank experiments. The basic mechanism involved is shown to be the same as that which accounts for the northwest propagation of cyclones on a 8-plane. This inviscid nonlinear effect is also shown to be responsible for the observed translationary motion of barotropic vortices in a free-surface rotating tank. The behaviour of isolated vortices is contrasted with that of vortices with non-vanishing circulation. vortices on the P-plane. On displacements and intensity changes of atmospheric vortices. J . Mar. Res. J . Fluid Mech. 78, 12S154. flow over topography. J . Fluid Mech. 175, 157-181. modons over topography. Geophye. Astrophys. Fluid Dyn. 41, 45-101. axisymmetry. J . Atmos. Sci. 46, 3177-3191. tropical cyclone motion. Part I : Zero mean flow. J . Atmos. Sci. 44, 1257-1265. Oceanogr. 6, 57-65. J . Phys. Oceanogr. 7, 365-379. laboratory experiments and general integral constraints. Dyn. Atmos. Oceans 7, 233-263. Astrophys. Fluid Dyn. 35, 209-233. 73-97. 569-57 1. J . Atmos. Sci. 34, 1731-1750. an isolated eddy. Dyn. Atmos. Oceans 10, 165-184. VII, 175-187.
Journal of Fluid Mechanics, 1997
This paper deals with the self-induced translation of intense vortices on the β-plane in the framework of the multi-layer quasi-geostrophic approximation. An analytical theory is presented and compared to numerical experiments. To predict the vortex trajectories, we consider initially monopolar vortices, with a core of piecewise-constant potential vorticity, and calculate the evolution of the dipolar circulation which advects the vortex core. This multi-layer model yields analytical solutions for a period while the Rossby wave radiation is small.The development of the dipolar circulation and corresponding vortex translation are described as the results of three effects. The first and second are similar to what was found in earlier studies with a one-layer model: advection of the planetary vorticity by the symmetric vortex circulation, and horizonal deformations of the vortex core. In addition, when stratification is taken into account, the vertical tilting of the vortex core also pl...
Baroclinic instability of two-layer vortices in laboratory experiments
Journal of Fluid Mechanics, 2005
The dynamics of a baroclinic vortex in a two-layer rotating stratified fluid is investigated. The vortex is produced by the classical geostrophic adjustment process, starting from an initial step in the layer interface. The experiments are performed on the 13 m diameter Coriolis turntable, allowing investigation of inertial regimes, in which viscous friction effects are negligible. The velocity fields are measured in both layers by employing particle image velocimetry, thus providing a quantitative measure of the flow evolution. The baroclinic instability occurs much later in time than the initial inertial oscillations. The growth occurs in a hydrostatic regime, with velocity being independent of height in each layer. This process is described well by linear stability theory for a quasi-geostrophic disk vortex, or by the classical model of Phillips (1954) empirically adapted to the circular geometry. This stability prediction from the quasigeostrophic model remains relevant even for a large initial interfacial step. For strong cyclones, the instability grows roughly twice as fast as these predictions. In the nonlinear stage of the instability, the initial vortex splits and reorganizes into vortex pairs propagating outward. These dipoles involve the interactions of positive and negative vortices, with components in the upper and in the lower layer. In the case of a large initial interface step, a clear asymmetry between anticyclones and cyclones is observed: the latter are more intense and compact, with a more barotropic structure. Our results are compared with numerical simulations, using a two-layer isopycnal model. Data assimilation is used to initiate the model with the same perturbations as in the laboratory experiments, thus providing a quantitative test of the dynamics. Furthermore, data assimilation is used to extrapolate the measurements, yielding the interface position and potential vorticity fields.