The interaction of two co-rotating quasi-geostrophic vortices in the vicinity of a surface buoyancy filament

In this paper, we investigate the interaction between two like-signed quasi-geostrophic uniform potential vorticity internal vortices in the vicinity of a surface buoyancy anomaly filament in a three dimensional, stably stratified and rapidly rotating fluid. The surface buoyancy distribution locally modifies the pressure fields and generates a shear flow. We start the study by first considering the effects of a uniform linear horizontal shear on the binary vortex interaction. We confirm that a cooperative shear facilitates the merger of a pair of vortices while an adverse shear has the opposite effect. We next investigate the binary vortex interaction in the vicinity of the surface buoyancy filament explicitly. Here, not only the filament generates a shear flow, but it also responds dynamically to the forcing by the vortex pair. The filament destabilises and forms buoyancy billows at the surface. These billows interact with the internal vortices. In particular, a surface billow may pair with one of the internal vortices. In such cases, the like-signed internal vortex pair may separate if they are initially moderately distant from each other.     

Vortex merger in surface quasi-geostrophy

The merger of two identical surface temperature vortices is studied in the surface quasi-geostrophic model. The motivation for this study is the observation of the merger of submesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finite-area, constant-temperature, vortices. Such states are less deformed than their counterparts in two-dimensional incompressible flows. Finally, numerical simulations of the nonlinear surface quasi-geostrophic equations are used to investigate the finite-time evolution of initially identical and symmetric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vortex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.     

On the merger of subsurface isolated vortices

Vortex merger is a phenomenon characterizing the whole class of geophysical vortices, from atmospheric storms and large oceanic eddies up to small scale turbulence. Here we focus on the merger of subsurface oceanic anticyclones in an idealized primitive equations model. This study has been motivated by past and recent observations of colliding lens-like anticyclones off of Gibraltar Strait. The critical conditions for merger (critical merger distance and time needed for merger) are determined. We will show that the predictions of classical two-dimensional merger are not verified for subsurface isolated vortices. For instance, critical merger distances will be reduced because of the vortex potential vorticity (PV) structure. The post-merger characteristics of the vortex (radius, extension and PV), are also determined. Merger-related effects, like production of peripheral filaments and small-scale eddies are also investigated and suggest the contribution of merger in both direct and inverse energy cascades.     

Dynamics of intrathermocline vortices in a gyre flow over a seamount chain

The interaction of meddies with a complex distribution of seamounts is studied in a three-layer quasi-geostrophic model on the f-plane. This study aims at understanding if and how this seamount chain can represent a barrier to the propagation of these eddies and how it can be involved in their decay. The eddies are idealized as vortex patches in the middle layer, interacting with a regional cyclonic current and with ten idealized seamounts. The numerical code is based on the contour surgery technique. The initial position, radius, shape, number and polarity of the eddies are varied. The main results are the following: (1) Though they do not describe the unsteady flow, the streamlines of the regional and topographic flow provide a useful estimate of the vortex trajectories, in particular towards the major seamounts, where stronger velocity shears are expected. (2) The tallest and widest seamounts which have the largest vorticity reservoir are able to considerably erode the vortices, but also to draw anticyclones towards the seamount top. The ability of narrower seamounts to erode vortices is related to their multiplicity. (3) Only 1/3 of the anticyclones with about 30-km radius reach the southern boundary of the seamount chain, and their erosion is larger than 50 %. The other anticyclones are either completely eroded or trapped over a wide seamount top. Cyclones are less affected by seamounts because they oppose the topographic draft towards the seamount top and they drift along the side of the seamount. (4) Large vortices resist topographic erosion more efficiently. The rate of erosion grows from a few percent to about 35–50 % as the vortex radius decreases from about 60 to 30 km. Small cyclones are not eroded, contrary to small anticyclones (which completely decay), in relation with the different trajectories of these eddies in the vicinity of the seamounts. (5) The detailed vortex shape does not appear critical for their evolution, if they are close enough to the seamount chain initially. The interaction between a group of vortices initially north of the seamount chain can modify their trajectory to such an extent that they finally avoid collision with seamounts. (6) Finally, meddy trajectories across the Horseshoe Seamounts (data from the AMUSE experiment) show qualitative similarity with the vortex paths in the model. Several events of vortex decay also occur at comparable locations (in particular over the wide and tall seamounts) in the model and observations.     

Interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex

This paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin–Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective “self”-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs – termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.     

Radiating Vortices in Geophysical Fluid Dynamics

The dynamics of a single vortex on a beta-plane is discussed in this paper. A barotropic, an equivalent barotropic, one-and-a half and two-layer models are considered. The momentum and energy balances are used to describe the evolution of a vortex. A quasi-stationary balance of the Rossby, Zhukovsky-Kutta forces and the force induced by Rossby-wave radiation, describes the dynamics of the barotropic vortex. A net Coriolis force occurs if the fluid is stratified. The difference between the dynamics of cyclones and anticyclones results directly from the Coriolis force acting on a single vortex in a stratified fluid.All vortices radiate Rossby waves in the quasigeostrophic approximation but intense anticyclones propagate steadily in a one-and-a half layer model. A critical amplitude that bounds radiating and steadily propagating anticyclones is found. Steady propagation of anticyclones in general is impossible in a two-layer fluid due to the radiation of a barotropic Rossby-wave. Some solutions of solitary wave type which are known for a two-layer model, survive owing to wave interference.A single vortex can extract energy from a Rossby wave if synchronism conditions are satisfied. The wave interference again plays a crucial role in this case. The wave interference also determines the energy exchange of vortices located at larger distances. If the distance between the vortices is shorter than the length of the radiated waves, modon may be formed due to a small energy loss.The unbounded monotonic variation of the planetary vorticity is a characteristic feature of a beta-plane approximation. As a result, a single vortex propagates up to a 'rest latitude' where it disappears. The evolution of a single barotropic vortex over bottom topography provides another example of a background vorticity distribution with a local extremum above hills (valleys) or ridges (troughs). Physics of its movement differs from a beta-plane case, but if a vortex lies over broad topography, equations are similar and the evolution of a vortex manifests the same typical features. Particularly, a cyclonic vortex tends to drift to the top of a hill or a ridge. An anticyclonic vortex, on the contrary, slides to the bottom of a valley or a trough.An interaction of a barotropic vortex with a broad mean flow is tractable qualitatively on the basis of previous results. Numerical examples illustrating absorption of a small vortex by a larger one and a vortex movement across the flow, are direct analogies of the vortex evolution over a hill and a ridge, respectively. At the same time, strong influence of strain drastically changes the vortex structure.     

On the Structures Observed in Thin Rotating Layers of a Conductive Fluid and the Anomalies of the Geomagnetic Field

The results of the laboratory and numerical experiments in circular rotating trays with thin layers of a conductive fluid under the MHD generation of small-scale velocity fields are presented. The configurations of constant magnets for MHD generation were determined based on the numerical calculations with shallow water equations. Both the laboratory and numerical experiments with rotating trays demonstrate the emergence of nonaxisymmetric structures and large-scale near-circular vortices caused by the energy transfer from the system of the externally generated small-scale vortices to the large-scale velocity fields under the action of the Coriolis force. The near-circular vortex has areas with differential rotation when the angular velocity of rotation decreases with the radius. The single large-scale vortices and wide jet flows arise in the regimes of subrotation and superrotation relative to the external rotation depending on its angular velocity. The emergence of the flow structures with the azimuthal wave number m = 2 is demonstrated, and their probable relation to the anomalies of the geomagnetic field observed on the Earth’s surface is considered.     

Hydrodynamical Modeling Of Oceanic Vortices

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, -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 enstrophy between scales, and are essential in two-dimensional and in geostrophic turbulence. Finally, in relation with the observations, we describe a few mechanisms of vortex generation.     

Characterization of horseshoe vortex in a developing scour hole at a cylindrical bridge pier

Since local scour at bridge piers in rivers and estuaries is a major cause of bridge failure, estimation of the maximum local scour depth is of great importance to hydraulic and coastal engineers. Although numerous studies that focus on scour-depth prediction have been done and published, understanding of the flow and turbulence characteristics of the horseshoe vortex that drives the scour mechanism in a developing scour hole still is immature. This study aims to quantify the detailed turbulent flow field in a developing clear-water scour hole at a circular pier using Particle Image Velocimetry (PIV). The distributions of velocity fields, turbulence intensities, and Reynolds shear stresses of the horseshoe vortex that form in front of the pier at different scour stages (t=0, 0.5, 1, 12, 24, and 48 h) are presented in this paper. During scour development, the horseshoe vortex system was found to evolve from one initially small vortex to three vortices. The strength and size of the main vortex are found to increase with increasing scour depth. The regions of both the maximum turbulence intensity and Reynolds shear stress are found to form at a location upstream of the main vortex, where the large turbulent eddies have the highest possibility of occurrence. Results from this study not only provide new insight into the complex flow-sediment interaction at bridge piers, but also provide valuable experimental databases for advanced numerical simulations.     

Spontaneous Emission of Gravity Waves by Interacting Vortex Dipoles in a Stratified Fluid: Laboratory Experiments

Results from a new series of experiments on the geophysically important issue of spontaneous emission of internal gravity waves during unsteady interactions of vortical structures are presented. Vortex dipoles are a common element of a quasi-two-dimensional turbulent flow. Vortex dipoles perform translational motion and can collide with other vortices. During collision events the flow is unsteady and unbalanced and a further adjustment process associated with these events can therefore result in the spontaneous emission of gravity waves. Our laboratory experiments demonstrate that gravity waves are emitted when two translating vortex dipoles interact (collide) in a layered fluid, in accord with the current theoretical results. The emission was evident both in a two-layer system and in a fluid with a linear distribution of density with depth. The waves were generated during the period of deceleration of the secondary dipoles which constitute a vortex quadrupole emerging immediately after the collision of the primary dipoles.     

The formation of new quasi-stationary vortex patterns from the interaction of two identical vortices in a rotating fluid

Within the framework of the quasi-geostrophic approximation, the interactions of two identical initially circular vortex patches are studied using the contour dynamics/surgery method. The cases of barotropic vortices and of vortices in the upper layer of a two-layer fluid are considered. Diagrams showing the end states of vortex interactions and, in particular, the new regime of vortex triplet formation are constructed for a wide range of external parameters. This paper shows that, in the nonlinear evolution of two such (like-signed) vortices, the filaments and vorticity fragments surrounding the merged vortex often collapse into satellite vortices. Therefore, the conditions for the formation and the quasi-steady motions of a new type of triplet-shaped vortex structure are obtained.     

Modelling exhaust plume mixing in the near field of an aircraft

A simplified approach has been applied to analyse the mixing and entrainment processes of the engine exhaust through their interaction with the vortex wake of an aircraft. Our investigation is focused on the near field, extending from the exit nozzle until about 30 s after the wake is generated, in the vortex phase. This study was performed by using an integral model and a numerical simulation for two large civil aircraft: a two-engine Airbus 330 and a four-engine Boeing 747. The influence of the wing-tip vortices on the dilution ratio (defined as a tracer concentration) shown. The mixing process is also affected by the buoyancy effect, but only after the jet regime, when the trapping in the vortex core has occurred. In the early wake, the engine jet location (i.e. inboard or outboard engine jet) has an important influence on the mixing rate. The plume streamlines inside the vortices are subject to distortion and stretching, and the role of the descent of the vortices on the maximum tracer concentration is discussed. Qualitative comparison with contrail photograph shows similar features. Finally, tracer concentration of inboard engine centreline of B-747 are compared with other theoretical analyses and measured data.     

Two possible mechanisms for vortex self-organization

Since the 21st century, the self-organization phe-nomenon has drawn a wide attention of Chinese sci-ence and technology researchers, and the study fields involve silicate chemistry[1, 2], the classification of re-mote sensing data[3], nanometer material[4―6], medium resistance to discharges[7], forest fires[8], mud-rock flow[9], sandpile formation[10, 11], urban geography[12], economic geography[13], intense storms over the Loess Plateau[14] and vortices over the Tibetan Plateau[15], etc. Re…     

Submesoscale vortex structures at the entrance of the Gulf of Lions in the Northwestern Mediterranean Sea

The meanders of a baroclinic coastal current in the Northwestern Mediterranean Sea have already been reported in the literature. These meanders can be surrounded by vortices. Such vortices have been observed in the western part of the Gulf of Lions but the location and the mechanism of their formation are poorly documented. In this paper, we use the current measurements of a one-year experiment, which was conducted in the eastern part of the Gulf of Lions to detect and characterize the vortex activity. A vortex detection algorithm based on few velocity data was developed. Current measurements were available at the sea surface (HF radars) and in the water column from 50 to 140 m depth (four current meter moorings). SST images and hydrologic data were also used. Results focus on observations that are coherent 50 m and at the surface. Vortices are anticyclonic, of submesoscale size and present maximal velocities of 30–50 cm/s. The drift speed of the vortices is comparable to but less than the velocity of the Northern Current. These observations enable to estimate the minimum vortex occurrence in this area. The presence of vortex structures is strongly correlated with a specific sequence of wind patterns.     

Some interactions between small numbers of baroclinic,geostrophic vortices

Abstract

Various interactions between small numbers (two and four) of baroclinic, geostrophic point vortices in a two-layer system are studied with attention to the qualitative changes in behavior which occur as size of the deformation radius is varied.

A particularly interesting interaction, which illustrates the richness of baroclinic vortex dynamics, is a collision between two hetons. (A heton is a vortex pair in which the constituent vortices have opposite signs and are in opposite layers. The “breadth” of a heton is the distance between its constituent vortices. A translating heton transports heat.) When two hetons, which initially have different breadths, collide, the result is either an exchange of partners, or a “slip-through” collision in which the initial structures are preserved. It is shown here that the outcome is always an exchange, provided the deformation radius is sufficiently small. This strongly contrasts with a collision between pairs of classical, one-layer vortices in which no exchange occurs if the initial ratio of the breadths is sufficiently extreme.

Finally the transport of passive fluid by a translating baroclinic pair is investigated. A pair of vortices in the top layer transports no lower layer fluid if the distance between the vortices is less than 1.72 deformation radii. By contrast, the size of the region trapped by a heton increases without bound as the spacing between the vortices increases.     

A Formal Theory for Vortex Rossby Waves and Vortex Evolution

A formal theory is presented for the balanced evolution of a small-amplitude, small-scale wave field in the presence of an axisymmetric vortex initially in gradient-wind balance and the accompanying changes induced in the vortex by the azimuthally averaged wave fluxes. The theory is a multi-parameter, asymptotic perturbation expansion for the conservative, rotating, f-plane, shallow-water equations. It extends previous work on Rossby-wave dynamics in vortices and more generally provides a new perspective on wave/mean-flow interaction in finite Rossby-number regimes. Some illustrative solutions are presented for a perturbed vortex undergoing axisymmetrization.     

Influence of condensation and latent heat release upon barotropic and baroclinic instabilities of vortices in a rotating shallow water f-plane model

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 three 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 cut-off 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.     

Experiments on instability of columnar vortex pairs in rotating fluid

We present results from a new series of experiments on the geophysically important issue of the instability of anticyclonic columnar vortices in a rotating fluid in circumstances such that the Rossby number exceeds unity. The vortex pair consisting of a cyclonic and an anticyclonic vortex is induced by a rotating flap in a fluid which is itself initially in a state of solid-body rotation. The anticyclonic vortex is then subject to either centrifugal or elliptical instability, depending on whether its initial ellipticity is small or large, while the cyclone always remains stable. The experimental results demonstrate that the perturbations due to centrifugal instability have a typical form of toroidal vortices of alternating sign (rib vortices). The perturbations due to elliptical instability are of the form of sinuous deformation of the vortex filament in the plane of maximal stretching which corresponds to the plane of symmetry for the vortex pair. The initial perturbations in both cases are characterized by a definite wave number in the vertical direction. The characteristics of the unstable anticyclone are determined by the main nondimensional parameter of the flow - the Rossby number. The appearance of both centrifugal and elliptical instabilities are in accord with the predictions of theoretical criteria for these cases.     

Vortex evolution due to straining: a mechanism for dominance of strong,interior anticyclones

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).     

陆地下垫面与环境气流对锋面气旋发展过程影响的理想试验

地面摩擦和大尺度流场是影响锋面气旋结构演变的重要因子,本文使用WRF模式并采用湿物理方案,通过理想化试验,综合考虑陆面摩擦、气旋式扰动相对于急流位置和大尺度流场对锋面气旋结构变化的影响.结果表明：当仅考虑单一因子时,气旋式扰动位于急流南侧和辐合流流场有利于气旋形成Shapiro-Keyser（S-K）模型结构.当同时考虑地面摩擦和大尺度辐合时,气旋式扰动位于急流北侧的气旋发展整体向经典的挪威气旋模型转变;扰动位于急流南侧的的气旋发展则整体呈现S-K模型结构,此时辐合流场有利于S-K模型结构出现.当同时考虑地面摩擦和大尺度辐散时,扰动处于急流北侧的气旋呈现挪威气旋模型结构;由于气旋式扰动穿越急流和辐散流场同时有利于暖锋后弯发展以及冷暖锋距离加大和锋消,扰动处于急流南侧的气旋呈现典型S-K气旋模型结构.这个结果解释了在东亚大陆地区辐散场形势下出现的S-K模型结构气旋个例.