木星“大红斑”的实验室模拟

在我们建立的旋转浅水实验系统上进行了可重复的系列模拟实验,成功地观测到大尺度持续存在的涡旋的产生、漂移与演化。在一定条件下,呈现出一个自持的、长寿命的、沿与整体旋转方向相反方向漂移的反气旋孤立波涡旋（Rossby soliton),这就是木星“大红斑”的实验室模型。     

Long-lived planetary vortices and their evolution: Conservative intermediate geostrophic model

Large, long-lived vortices, surviving during many turnaround times and far longer than the dispersive linear Rossby wave packets, are abundant in planetary atmospheres and oceans. Nonlinear effects which prevent dispersive decay of intense cyclones and anticyclones and provide their self-propelling propagation are revised here using shallow water equations and their balanced approximations. The main physical mechanism allowing vortical structures to be long-lived in planetary fluid is the quick fluid rotation inside their cores which prevents growth in the amplitude of asymmetric circulation arising due to the beta-effect. Intense vortices of both signs survive essentially longer than the linear Rossby wave packet if their azimuthal velocity is much larger than the Rossby wave speed. However, in the long-time evolution, cyclonic and anticyclonic vortices behave essentially differently that is illustrated by the conservative intermediate geostrophic model. Asymmetric circulation governing vortex propagation is described by the azimuthal mode m=1 for the initial value problem as well as for steadily propagating solutions. Cyclonic vortices move west-poleward decaying gradually due to Rossby wave radiation while anticyclonic ones adjust to non-radiating solitary vortices. Slow weakening of an intense cyclone with decreasing of its size and shrinking of the core is described assuming zero azimuthal velocity outside the core while drifting poleward. The poleward tendency of the cyclone motion relative to the stirring flow corresponds to characteristic trajectories of tropical cyclones in the Earth's atmosphere. The asymmetry in dispersion-nonlinear properties of cyclones and anticyclones is thought to be one of the essential reasons for the observed predominance of anticyclones among long-lived vortices in the atmospheres of the giant planets and also among intrathermoclinic eddies in the ocean.     

The coherent structures of shallow-water turbulence: Deformation-radius effects,cyclone/anticyclone asymmetry and gravity-wave generation

Over a large range of Rossby and Froude numbers, we investigate the dynamics of initially balanced decaying turbulence in a shallow rotating fluid layer. As in the case of incompressible two-dimensional decaying turbulence, coherent vortex structures spontaneously emerge from the initially random flow. However, owing to the presence of a free surface, a wealth of new phenomena appear in the shallow-water system. The upscale energy cascade, common to strongly rotating flows, is arrested by the presence of a finite Rossby deformation radius. Moreover, in contrast to near-geostrophic dynamics, a strong asymmetry is observed to develop as the Froude number is increased, leading to a clear dominance of anticyclonic vortices over cyclonic ones, even though no beta effect is present in the system. Finally, we observe gravity waves to be generated around the vortex structures, and, in the strongest cases, they appear in the form of shocks. We briefly discuss the relevance of this study to the vortices observed in Jupiter's atmosphere.     

Vortex patterns in quasi-two-dimensional flows of a viscous rotating fluid

A modified von Kármán problem that describes steady vortex flow in a rotating thin viscous fluid layer is solved. An analysis of the effect of bottom friction on the behavior of cyclonic and anticyclonic vortices at arbitrary values of the Rossby number is presented. Several anticyclonic flow patterns are examined. An approximate analytical solution obtained for steady flows is compared with numerical computations of a time-dependent problem. Experimental results on cyclonic and anticyclonic vortices in multiple-vortex quasi-turbulent flow are presented, and their interpretation based on the solution of the model problem is given.     

Some remarks on coherent structures out of chaos in planetary atmospheres and oceans

In the context of planetary atmospheres and oceans, it is natural to define "coherent structures" as "long-lived," or "solitary," Rossby vortices. These can be described by the generalized Charney-Obukhov equation (in fluid dynamics) or the analogous generalized Hasegawa-Mima equation (in plasma physics). These two equations contain KdV-type nonlinearities which (together with the compensating dispersive spreading) determine the formation of the coherent structures and explain the clear-cut cyclonic/anticyclonic asymmetry observed experimentally in long-lived planetary Rossby vortices. Examples are given of natural vortices which are (and which are not) coherent structures.     

Evolution of vortices formed in Jupiter’s atmosphere after the collision of the planet with Comet Shoemaker-Levy 9

The evolution of disturbances formed in the Jovian atmosphere after the collision with large fragments of Comet Shoemaker-Levy is investigated. Simplified equations for the evolution of large vortices in a shallow, horizontally inhomogeneous atmosphere are derived taking account of the latitudinal nonuniformity of the zonal wind and also taking account of viscosity and heat conduction. The results of the numerical simulation of the evolution of the vortices are in good agreement with observations from the Hubble platform. It is shown that the evolution of the vortex structure depends strongly on the zonal wind velocity field in the fall region of a comet fragment. The threshold energy of the initial disturbance at which large, long-lived vortices, such as the Great Red Spot, can form is estimated to be E∼ 10²⁴ ergs. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 324–329 (10 September 1996)     

Statistical mechanical theory of the great red spot of jupiter

In a previous study a permanent isolated vortex like the Great Red Spot of Jupiter was obtained as a statistical equilibrium for the classical quasigeostrophic model of atmospheric motion on rapidly rotating planets. We provide here a theoretical basis for this work and relate it to a previous model of the spot (Rossby soliton).     

Centrifugal-dissipative instability of Rossby vortices and their cyclonic-anticyclonic asymmetry

A new linear centrifugal-dissipative mechanism is proposed that explains the vortex asymmetry observed, in particular, in the structure of low-frequency anticyclonic Rossby vortices. It is shown that the relevant centrifugal-dissipative instability, which spontaneously breaks the chiral symmetry of the vortices, takes place only in the range ω<Ω, where ω is the frequency of small oscillations corresponding to the effective solid-body rotation of a vortex and Ω is the rotation rate of a noninertial frame of reference. The onset of the instability is associated with the existence of an optimum magnitude of the frictional force. In the vortex model based on a two-dimensional oscillator with the natural frequency ω in a noninertial reference frame rotating at the rate Ω, the instability shows up as an exponential increase in the total angular momentum. It is noted that the centrifugal dissipative instability may also manifest itself in the seismically active regions of the world.     

Jupiter's Great Red Spot and zonal winds as a self-consistent,one-layer,quasigeostrophic flow

We present the point of view that both the vortices and the east-west zonal winds of Jupiter are confined to the planet's shallow weather layer and that their dynamics is completely described by the weakly dissipated, weakly forced quasigeostrophic (QG) equation. The weather layer is the region just below the tropopause and contains the visible clouds. The forcing mimics the overshoot of fluid from an underlying convection zone. The late-time solutions of the weakly forced and dissipated QG equations appear to be a small subset of the unforced and undissipated equations and are robust attractors. We illustrate QG vortex dynamics and attempt to explain the important features of Jupiter's Great Red Spot and other vortices: their shapes, locations with respect to the extrema of the east-west winds, stagnation points, numbers as a function of latitude, mergers, break-ups, cloud morphologies, internal distributions of vorticity, and signs of rotation with respect to both the planet's rotation and the shear of their surrounding east-west winds. Initial-value calculations in which the weather layer starts at rest produce oscillatory east-west winds. Like the Jovian winds, the winds are east-west asymmetric and have Karman vortex streets located only at the west-going jets. From numerical calculations we present an empirically derived energy criterion that determines whether QG vortices survive in oscillatory zonal flows with nonzero potential vorticity gradients. We show that a recent proof that claims that all QG vortices decay when embedded in oscillatory zonal flows is too restrictive in its assumptions. We show that the asymmetries in the cloud morphologies and numbers of cyclones and anticyclones can be accounted for by a QG model of the Jovian atmosphere, and we compare the QG model with competing models.     

Coherent structures and their stability in ion temperature gradient turbulence

Periodic arrays of large scale coherent vortices and their stability have been investigated, within the framework of /spl eta//sub i/ turbulence, using two-dimensional fluid simulation in slab geometry. These vortices, in combination with viscosity damping of small scales, contribute to the formation of a steady state in a system with linearly unstable modes. The steady state comprises of a few vortex convective turn over times and seems to be fairly robust. It has been recognized that a vortex chain, consisting of positive and negative vorticities, continues to move stably in the poloidal direction (along periodic direction). On the other hand, an initial isolated monopole vortex is unstable and leads to a long-lived stable dipolar structure after a few vortex turnover periods. A variety of simple collisional interaction processes among these coherent vortices have also been explored numerically.     

Steady vortices in plasmas and geophysical flows

A number of two-dimensional fluid models in geophysical fluid dynamics and plasma physics are examined to find out whether they have steady and localized monopole vortex solutions. A simple and general method that consists of two steps is used. First the dispersion relation is calculated, to find all possible values of the phase velocity of the linear waves. Then an integral relation that determines the center-of-mass velocity of localized structures must be found. The existence condition is that this velocity should be outside the region of linear phase velocities. After a presentation of the method, previous work on the plasma drift wave model and the shallow-water equations is reviewed. In both cases it is found that the center-of-mass velocity is larger than the maximum phase velocity of the linear waves if the amplitude is large enough, and steady localized vortices can therefore exist. New results are then obtained for a number of two-field models. For the coupled ion acoustic-drift modes in plasmas, it is found that the center-of-mass velocity depends on the ratio between the parallel ion velocity component and the electrostatic potential in the vortex. If this ratio is large enough, the vortex can be steady. For the drift-Alfven mode the "center-of-charge" velocity is proportional to the ratio between the parallel current and the total charge in the vortex. It can therefore be steady if this ratio satisfies the appropriate conditions. For the quasigeostrophic two-layer equations, describing stratified flow on a rotating planet, it is found that the center-of-mass velocity is determined by the ratio between the baroclinic and the barotropic components in the vortex. If a baroclinic component with an appropriate sign is added to a barotropic vortex, it propagates faster than the barotropic Rossby waves, and can be steady. Finally, the existence conditions for a vortex in an external zonal flow are examined. It is found that the center-of-mass velocity acquires an additional westward contribution in an anticyclonic shear zone in the framework of the shallow-water equations, and also that an easterly jet south of this shear zone partly shields a vortex situated in the shear zone from the dispersive influence of the fast Rossby waves on the equatorward side.     

Successes and failures of shallow-water interpretations of Voyager wind data

Studying the dynamics of Jupiter's atmosphere is a rewarding experience, in part because the planet's cloud-top circulations are easy to track from space, the jet streams flow in straight lines eastward or westward, and there is enough room for the vortices to usually keep out of each other's way. Earth, in contrast, is a planet with global circulations that are not easy to track from space, with jet streams that make wide, fluctuating arcs as they negotiate mountain ranges, and with vortices that are constantly jostling against each other in a cramped environment. But we know a great deal more about the vertical structure of Earth's atmosphere than of Jupiter's. In order to make headway on the Jovian problem, researchers have turned to the shallow-water model as a guide to interpreting the Voyager wind data. The shallow-water model matches the character of the data because it combines high-resolution horizontal dynamics with low-resolution vertical structure, but there is no guarantee that it captures the character of Jupiter's atmosphere itself. Remarkably, the model does well at reproducing the Great Red Spot, and it has revealed that Jupiter is clever about how it manages its vorticity by arranging its zonal winds to be neutrally stable with respect to Arnol'd's second stability theorem. We discuss reasons why the shallow-water model works for Jupiter and point out the limitations that are motivating researchers to develop more realistic models.     

Modulation of large-scale meandering and three-dimensional flows in turbulent slot jets

We investigate a vertically discharged shallow wall-bounded turbulent water jet both experimentally (LIF, TomoPIV) and numerically (LES). We identify the well-known meandering motion of the jet core generating large-scale planar vortices similar to the Karman vortex street. The modulation of the meandering amplitude is identified in experiments and simulations, which is attributed to the competition between sinusoidal and symmetric instability modes. TomoPIV data confirms that elongated streamwise vortices represent the smaller scale vortical structure of the jet in the near and far fields.     

Characteristic zonal winds and long-lived vortices in the atmospheres of the outer planets

The cameras on board the NASA Voyager spacecraft provided a survey of cloud systems within the atmospheres of the giant planets and allowed determination of zonal wind patterns, which constrain long-lived cloud systems. The basic atmospheric circulations are compared and long-lived cloud features are reviewed. The basic structure of the Great Red Spot is reviewed and the tendency of the spot to drift at -4 m s(-1) or -2 m s(-1) is presented.     

The laminar horseshoe vortex upstream of a short-cylinder confined in a channel formed by a pair of parallel plates

A flow visualization experiment was performed in order to characterize the laminar horseshoe vortex system that appears upstream of the junction of a short cylinder and a pair of flat parallel plates. The experiments were performed in a water tunnel and the technique used for flow visualization was laser illumination of seeded particles whose traces were captured using long exposure photography. Geometrical and flow parameters, such as Reynolds number and height-to-diameter ratio of the cylinders, are varied during the experiments and the flow regimes are analyzed as a function of these parameters. The behavior of vortex systems is reported. For low Reynolds number cases, the vortices stay in a fixed position, as the Reynolds number is increased the number of vortices grows and for larger Reynolds numbers the vortex system becomes oscillatory and for further increases it becomes periodic. As for the dimensionless height of the cylinders, the vortex system is weak for short cylinders and increases its strength and number of vortices as the cylinder height-to-diameter ratio is increased. For further increases in height the vortex system do not change, which shows that the flow becomes independent of the height-to-diameter ratio for sufficiently tall cylinders. Information of the frequency of appearance of periodic vortices is also included.     

2D-PIV analysis of loach motion and flow field

The propulsion methods of the aquatic lives are the results of optimization by evolution and are useful for the design of swimming-robot, etc. Among them, loach has unique propulsion technique both bending its long body and shaking caudal fin. Our purpose of the research is to clarify its swimming mechanism through flow field analysis. Two dimensional motion and flow around it have been experimentally visualized by particle image velocimetry (PIV). Vortices around a loach and the interactions between the loach body and surrounding water are analyzed. Generating and growing vortices by bending its body, it pushes water backward to gain repulsing force, and it seems that moves through vortices reducing the resistance force at the same time. When a vortex reaches to the caudal fin, it accelerates both sides of the vortex pushing water backward and seems gaining propulsion utilizing the caudal fin. After moving forward, loach leaves a vortex street like reverse Karman vortices, which means that loach gains propulsion.     

Creep of superconducting vortices in the limit of vanishing temperature: a fingerprint of off-equilibrium dynamics

We theoretically study the creep of vortex matter in superconductors. The low temperature experimental phenomenology, previously interpreted in terms of "quantum tunneling" of vortices, is reproduced by Monte Carlo simulations of a purely "classical" vortex model. We demonstrate that a nonzero creep rate in the limit of vanishing temperature is to be expected in systems with slow relaxations as a consequence of their off-equilibrium evolution in a complex free energy landscape.