Long-lived Vortices Research Articles

A budget analysis of a long-lived tropical mesoscale vortex over Hainan in October 2010

The vorticity, eddy kinetic energy, and helicity budgets were calculated to study the variations of a long-lived tropical mesoscale vortex that occurred over Hainan during the period 05–09 October 2010. The main results are as follows: the vortex was mainly located at middle to lower levels of the troposphere, and among different levels, the dominant factors responsible for the variations of the vortex were different. Intense convergence at the lower troposphere dominated the formation and longevity of the vortex. The vertical transport of positive vorticity which was closely related to the convective activities was conducive to the formation and maintenance of the vortex. The barotropic energy conversion was favorable for the formation of the vortex, while the baroclinic energy conversion accelerated its attenuation. Background circulations were favorable for the longevity of the vortex, and interactions with other synoptic systems were important to its variations. The variation of helicity was closely related to the vortex, and the maintenance of positive helicity was another favorable factor for the longevity of the vortex.

The enstrophy cascade in forced two-dimensional turbulence

We carry out direct numerical simulations of two-dimensional turbulence with forcing at different wavenumbers and resolutions up to 327682 grid points. In the absence of large-scale drag, a state is reached where enstrophy is quasi-stationary while energy is growing. In the enstrophy cascade range the energy spectrum has the form E(k) = εω2/3k−3, without any logarithmic correction, where εω is the enstrophy dissipation and is of the order of unity. However, is varying between different simulations and is thus not a perfect constant. This variation can be understood as a consequence of large-scale dissipation intermittency, following the argument by Landau (Landau & Lifshitz, Fluid Mechanics, 1959, Pergamon). In the presence of a large-scale drag, we obtain a slightly steeper spectrum. When forcing is applied at a scale which is somewhat smaller than the computational domain, no vortices are formed, and the statistics remain close to Gaussian in the enstrophy cascade range. When forcing is applied at a smaller scale, long-lived coherent vortices form at larger scales than the forcing scale, and intermittency measures become very large at all scales, including the scales of the enstrophy cascade. We conclude that the enstrophy cascade with a k−3-spectrum is a robust feature of the two-dimensional Navier–Stokes equations. However, there is a complete lack of universality of higher-order statistics of vorticity increments in the enstrophy cascade range.

Vortices as nurseries for planetesimal formation in protoplanetary discs

Turbulent, two-dimensional, hydrodynamic flows are characterized by the emergence of coherent, long-lived vortices without a need to invoke special initial conditions. Vortices have the ability to sequester particles, with typical radii from about 1 mm to 10 cm, that are slightly decoupled from the gas. A generic feature of discs with surface density and effective temperature profiles that are decreasing, power-law functions of radial distance is that four vortex zones exist for a fixed particle size. In particular, two of the zones form an annulus at intermediate radial distances within which small particles reside. Particle capture by vortices occurs on a dynamical time scale near and at the boundaries of this annulus. As the disc ages and the particles grow via coagulation, the size of the annulus shrinks. Older discs prefer to capture smaller particles because the gas surface density decreases with time, a phenomenon we term "vortex aging". More viscous, more dust-opaque and/or less massive discs can have vortices that age faster and trap a broader range of particle sizes throughout the lifetime of the disc. Thus, how efficiently a disc retains its mass in solids depends on the relative time scales between coagulation and vortex aging. If vortices form in protoplanetary discs, they are important in discs with typical masses and for particles that are likely to condense out of the protostellar nebula. Particle capture also occurs at distances relevant to planet formation. Future infrared, submillimetre and centimetre observations of grain opacity as a function of radial distance will test the hypothesis that vortices serve as nurseries for particle growth in protoplanetary discs.

From Grains to Planetesimals

This pedagogical review covers an unsolved problem in the theory of protoplanetary disks: the growth of dust grains into planetesimals, solids at least a kilometer in size. I summarize timescale constraints imposed on planetesimal formation by circumstellar disk observations, analysis of meteorites, and aerodynamic radial migration. The infall of ~meter-sized solids in a hundred years is the most stringent constraint. I review proposed mechanisms for planetesimal formation. Collisional coagulation models are informed by laboratory studies of microgravity collisions. The gravitational collapse (or Safronov-Goldreich-Ward) hypothesis involves detailed study of the interaction between solid particles and turbulent gas. I cover the basics of aerodynamic drag in protoplanetary disks, including radial drift and vertical sedimentation. I describe various mechanisms for particle concentration in gas disks -- including turbulent pressure maxima, drag instabilities and long-lived anticylonic vortices. I derive a general result for the minimum size for a vortex to trap particles in a sub-Keplerian disk. Recent numerical simulations demonstrate that particle clumping in turbulent protoplanetary disks can trigger gravitational collapse. I discuss several outstanding issues in the field.

On the stability of elliptical vortices in accretion discs

<i>Context. <i/>The existence of large-scale and long-lived 2D vortices in accretion discs has been debated for more than a decade. They appear spontaneously in several 2D disc simulations and they are known to accelerate planetesimal formation through a dust trapping process. In some cases, these vortices may even lead to an efficient way to transport angular momentum in protoplanetary discs when MHD instabilities are inoperative. However, the issue of the stability of these structures to the imposition of 3D disturbances is still not fully understood, and it casts doubts on their long term survival<i>Aims. <i/>We present new results on the 3D stability of elliptical vortices embedded in accretion discs, based on a linear analysis and several non-linear simulations.<i>Methods. <i/>We introduce a simple steady 2D vortex model which is a non-linear solution of the equations of motion, and we show that its core is made of elliptical streamlines. We then derive the linearised equations governing the 3D perturbations in the core of this vortex, and we show that they can be reduced to a Floquet problem. We solve this problem numerically in the astrophysical regime, including a simplified model to take into account vertical stratification effects. We present several analytical limits for which the mechanism responsible for instability can be explained. Finally, we compare the results of the linear analysis to some high resolution numerical simulations obtained with spectral and finite difference methods. A discussion is provided, emphasising the astrophysical consequences of our findings for the dynamics of vortices.<i>Results. <i/>We show that most anticyclonic vortices are unstable due to a resonance between the turnover time and the local epicyclic oscillation period. A small linearly stable domain is found for vortex cores with an aspect-ratio of around 5. However, our simulations show that it is only the vortex core that is stable, with the instability still appearing on the vortex boundary. In addition, we find numerically that results obtained under the assumption of incompressibility are not affected by the introduction of a moderate compressibility. Finally, we show that a strong vertical stratification does not create any additional stable domain of aspect ratio, but it significantly reduces growth rates for relatively weak (and therefore elongated) vortices.<i>Conclusions. <i/>Elliptical vortices are always unstable, whatever the horizontal or vertical aspect-ratio is. The instability can however be weak and is often found at small scales, making it difficult to detect in low-order finite-difference simulations.

Peculiarity of current–voltage characteristics of transferred arc burning in a limited volume

Current–voltage characteristics (CVCs) of a transferred arc in a limited volume are reported. Experiments were carried out with a setup developed to reproduce the conditions which occur in a tundish equipped with a plasma system to keep the steel temperature at a predefined level. The experimental setup consists of a test chamber in which a plasma torch with a transferred arc is inserted on the top of the chamber cover and the anode is attached at the bottom. A ‘hysteresis’ of the CVC curves was observed during an increase and a decrease in the arc current. This phenomenon is explained by a long-lived ring-shaped vortex flow in the chamber, which is powered by the forces that at high currents act as an electromagnetic pump accelerating plasma in the direction of current expansion.

Saturn's south polar vortex compared to other large vortices in the Solar System

Observations made by the Imaging Science Subsystem (ISS), Visible and Infrared Mapping Spectrometer (VIMS) and the long-wavelength Composite Infrared Spectrometer (CIRS) aboard the Cassini spacecraft reveal that the large, long-lived cyclonic vortex at Saturn's south pole has a 4200-km-diameter cloud-free nearly circular region. This region has a 4 K warm core extending from the troposphere into the stratosphere, concentric cloud walls extending 20–70 km above the internal clouds, and numerous external clouds whose anticyclonic vorticity suggests a convective origin. The rotation speeds of the vortex reach 150±20 ms−1. The Saturn polar vortex has features in common with terrestrial hurricanes and with the Venus polar vortex. Neptune and other giant planets may also have strong polar vortices.

Baroclinic Transition of a Long-Lived Mesoscale Convective Vortex

Abstract The period 5–15 June 2003, during the field phase of the Bow Echo and Mesoscale Convective Vortex (MCV) Experiment (BAMEX), was noteworthy for the wide variety of mesoscale convective systems (MCSs) that occurred. Of particular interest was a long-lived MCV that formed in the trailing stratiform region of an MCS over west Texas at 0600 UTC 10 June. This MCV was noteworthy for its (i) longevity as it can be tracked from 0600 UTC 10 June to 1200 UTC 14 June, (ii) development of a surface cyclonic circulation and attendant −2- to −4-hPa sea level pressure perturbation, (iii) ability to retrigger convection and produce widespread rains over several diurnal heating cycles, and (iv) transition into a baroclinic surface cyclone with distinct frontal features. Baroclinic transition, defined here as the acquisition of surface fronts, occurred as the MCV interacted with a remnant cold front, left behind by a predecessor extratropical cyclone, over the Great Lakes region. Although the MCV developed well-defined frontal structure, which helped to focus heavy precipitation, weakening occurred throughout the baroclinic transition process. Energetics calculations indicated that weakening occurred as the diabatic and baroclinic energy conversion terms approached zero just prior and during baroclinic transition. This weakening can be attributed to (i) an increase in environmental wind shear, (ii) the development of a downshear tilt and associated anticyclonic vorticity advection over the surface low center, and (iii) the eastward relative movement of organized convection away from the MCV center.

Dynamo action in complex flows: the quick and the fast

We consider the kinematic dynamo problem for a velocity field consisting of a mixture of turbulence and coherent structures. For these flows the dynamo growth rate is determined by a competition between the large flow structures that have large magnetic Reynolds number but long turnover times and the small ones that have low magnetic Reynolds number but short turnover times. We introduce the concept of a quick dynamo as one that reaches its maximum growth rate in some (small) neighbourhood of its critical magnetic Reynolds number. We argue that if the coherent structures are quick dynamos, the overall dynamo growth rate can be predicted by looking at those flow structures that have spatial and temporal scales such that their magnetic Reynolds number is just above critical. We test this idea numerically by studying 2.5-dimensional dynamo action which allows extreme parameter values to be considered. The required velocities, consisting of a mixture of turbulence with a given spectrum and long-lived vortices (coherent structures), are obtained by solving the active scalar equations. By using spectral filtering we demonstrate that the scales responsible for dynamo action are consistent with those predicted by the theory.

Vertical structure of Jupiter's troposphere from nonlinear simulations of long-lived vortices

Numerical simulations of jovian vortices at tropical and temperate latitudes, under different atmospheric conditions, have been performed using the EPIC code [Dowling, T.E., Fisher, A.S., Gierasch, P.J., Harrington, J., LeBeau, R.P., Santori, C.M., 1998. Icarus 132, 221–238] to simulate the high-resolution observations of motions and of the lifetimes presented in a previous work [Legarreta, J., Sánchez-Lavega, A., 2005. Icarus 174, 178–191] and infer the vertical structure of Jupiter's troposphere. We first find that in order to reproduce the longevity and drift rate of the vortices, the Brunt–Väisälä frequency of the atmosphere in the upper troposphere (pressures P∼1 to 7 bar) should have a lower limit value of 5×10−3 s−1, increasing upward up to 1.25×10−2 s−1 at pressures P∼0.5 bar (latitudes between 15° and 45° in both hemispheres). Second, the vortices drift also depend on the vertical structure of the zonal wind speed in the same range of altitudes. Simulations of the slowly drifting Southern hemisphere vortices (GRS, White Ovals and anticyclones at 40° S) require a vertically-constant zonal-wind with depth, but Northern hemisphere vortices (cyclonic “barges” and anticyclones at 19, 41 and 45° N) require decreasing winds at a rate of ∼5 m s−1 per scale height. However vortices drifting at a high speed, close to or in the peak of East or West jets and in both hemispheres, require the wind speed slightly increasing with depth, as is the case for the anticyclones at 20° S and at 34° N. We deduce that the maximum absolute vertical shear of the zonal wind from P∼1 bar up to P∼7 bar in these jets is ∼15 m s−1 per scale height. Intense vortices with tangential velocity at their periphery ∼100 m s−1 tend to decay asymptotically to velocities ∼40 to 60 m s−1 with a characteristic time that depends on the vortex intensity and static stability of the atmosphere. The vortices adjust their tangential velocity to the averaged peak to peak velocity of the opposed eastward and westward jets at their boundary. We show through our simulations that large-scale and long-lived vortices whose maximum tangential velocity is ∼100 m s−1 can survive by absorbing smaller intense vortices.

Shock-bubble interactions: Features of divergent shock-refraction geometry observed in experiments and simulations

The interaction of a planar shock wave with a spherical bubble in divergent shock-refraction geometry is studied here using shock tube experiments and numerical simulations. The particular case of a helium bubble in ambient air or nitrogen (A≈−0.8) is considered, for 1.4&amp;lt;M&amp;lt;3.0. Experimental planar laser diagnostics and three-dimensional multifluid Eulerian simulations clearly resolve features arising as a consequence of divergent shock refraction, including the formation of a long-lived primary vortex ring, as well as counter-rotating secondary and tertiary upstream vortex rings that appear at late times for M⩾2. Remarkable correspondence between experimental and numerical results is observed, which improves with increasing M, and three-dimensional effects are found to be relatively insignificant. Shocked-bubble velocities, length scales, and circulations extracted from simulations and experiments are used successfully to evaluate the usefulness of various analytical models, and characteristic dimensionless time scales are developed that collapse temporal trends in these quantities. Those linked directly to baroclinicity tend to follow time scales based on shock wave speeds, while those linked to interface deformation and vortex- or shear-induced motion tend to follow a time scale based on the postshock flow speed, though no single time scale is found to be universally successful.

Hydrodynamic Simulations of Unevenly Irradiated Jovian Planets

We employ a two-dimensional grid-based hydrodynamic model to simulate upper atmospheric dynamics on extrasolar giant planets. Our model is well-suited to simulate the dynamics of the atmospheres of planets with high orbital eccentricity that are subject to widely-varying irradiation conditions. We identify six such planets, with eccentricities between $e=0.28$ and $e=0.93$ and semimajor axes ranging from $a=0.0508$ A.U. to $a=0.432$ A.U., as particularly interesting objects for study. For each of these planets, we determine the temperature profile and resulting infrared light curves in the 8-$\mu$m Spitzer bands. Especially notable are the results for HD 80606b, which has the largest eccentricity ($e=0.9321$) of any known planet, and HAT-P-2b, which transits its parent star, so that its physical properties are well-constrained. Despite the variety of orbital parameters, the atmospheric dynamics of these eccentric planets display a number of interesting common properties. In all cases, the atmospheric response is primarily driven by the intense irradiation at periastron. The resulting expansion of heated air produces high-velocity turbulent flow, including long-lived circumpolar vortices. Additionally, a superrotating acoustic front develops on some planets; the strength of this disturbance depends on both the eccentricity and the temperature gradient resulting from uneven heating. The specifics of the resulting infrared light curves depend strongly on the orbital geometry. We show, however, that the variations on HD 80606 b and HAT-P-2b should be readily detectable at 4.5 and 8 $\mu$m using the Spitzer Space Telescope. Indeed, these two objects present the most attractive observational targets of all known high-$e$ exoplanets.

Numerical models of Saturn's long-lived anticyclones

New measurements of the dynamical properties of the long-lived Saturn's anticyclonic vortex known as “Brown Spot” (BS), discovered during the Voyager 1 and 2 flybys in 1980–1981 at latitude 43.1° N, and model simulations using the EPIC code, have allowed us to constrain the vertical wind shear and static stability in Saturn's atmosphere (vertically from pressure levels from 10 mbar to 10 bars) at this latitude. BS dynamical parameters from Voyager images include its size as derived from cloud albedo gradient (6100 km East–West times 4300 km North–South), mean tangential velocity ( 45 ± 11 m s −1 at 2400 km from center) and mean vorticity ( 4.0 ± 1.5 × 10 −5 s −1 ) , lifetime >1 year, drift velocity ( 5.3 ± 0.1 m s −1 ) relative to Voyager's System III rotation rate, mean meridional atmospheric wind profile at cloud level at its latitude and interactions with nearby vortices (pair orbiting and merging). An extensive set of numerical experiments have been performed to try to reproduce this single vortex properties and its observed mergers with smaller anticyclones by varying the vertical structure of the zonal wind and adjusting the static stability of the lower stratosphere and upper troposphere. Within the context of the EPIC model atmosphere, our simulations indicate that BS's drift velocity, longevity and merging behavior are very sensitive to these two atmospheric properties. The best results at the BS latitude occur for static stability conditions that use a Brunt–Väisäla frequency constant in the upper troposphere (from 0.5 to 10 bar) above 3.2 × 10 −3 s −1 and suggest that the wind speed slightly decays below the visible cloud deck from ∼0.5 to 10 bar at a rate ∂ u / ∂ z ∼ 2 – 6 m s −1 per scale height. Changing the vortex latitude within the band domain introduces latitude oscillations in the vortex but not a significant meridional migration. Simulated mergers always showed orbiting movements with a typical merging time of about three days, very close to the time-span observed in the interaction of real vortices. Although these results are not unique in view of the unknowns of Saturn's deep atmosphere, they serve to constrain realistically its structure for ongoing Cassini observations.

Vortex Street Dynamics: The Selection Mechanism for the Areas and Locations of Jupiter’s Vortices

Abstract With the exception of the Great Red Spot, Jupiter’s long-lived vortices are not isolated, but occur in east–west rows. Each row is centered about a westward-going jet stream with anticyclones on the poleward side and cyclones on the equatorial. Vortices are staggered so that like-signed vortices are never longitudinally adjacent. These double rows of vortices, called here Jovian vortex streets (JVSs) are robust. Calculations with no forcing and no dissipation (i.e., Hamiltonian dynamics) allow a continuum of JVS solutions, so they cannot be used to determine the physics that selects the observed values of the areas, circulations, and locations of Jupiter’s vortices. Constraints imposed by stability put few bounds on these values. When small amounts of dissipation and forcing are added to the governing equations, there is no longer a continuum of solutions; an initial JVS that was a solution of the Hamiltonian equations is now out of equilibrium and evolves to an attractor. For fixed forcing, all initial JVS evolve to the same attractor, so that the area of the vortices in the late-time JVS is selected uniquely as is the separation width in latitude between the row of cyclones and row of anticyclones. The separation width of the attracting JVS is nearly independent of the forcing, but the areas of the vortices in the attracting JVS depend strongly on the strength of the forcing, which is a measure of the ambient Jovian turbulence. Results are compared with observations.

Three‐dimensional Compressible Hydrodynamic Simulations of Vortices in Disks

We carry out three-dimensional, high resolution (up to $1024^2\times 256$) hydrodynamic simulations of the evolution of vortices in vertically unstratified Keplerian disks using the shearing sheet approximation. The transient amplification of incompressible, linear amplitude leading waves (which has been proposed as a possible route to nonlinear hydrodynamical turbulence in disks) is used as one test of our algorithms; our methods accurately capture the predicted amplification, converges at second-order, and is free from aliasing. Waves expected to reach nonlinear amplitude at peak amplification become unstable to Kelvin-Helmholtz modes when $\mid W_{\rm max}\mid\gtrsim \Omega$ (where $W_{\rm max}$ is the local maximum of vorticity and $\Omega$ the angular velocity). We study the evolution of a power-law distribution of vorticity consistent with Kolmogorov turbulence; in two-dimensions long-lived vortices emerge and decay slowly, similar to previous studies. In three-dimensions, however, vortices are unstable to bending modes, leading to rapid decay. Only vortices with a length to width ratio smaller than one survive; in three-dimensions the residual kinetic energy and shear stress is at least one order of magnitude smaller than in two-dimensions. No evidence for sustained hydrodynamical turbulence and transport is observed in three-dimensions. Instead, at late times the residual transport is determined by the amplitude of slowly decaying, large-scale vortices (with horizontal extent comparable to the scale height of the disk), with additional contributions from nearly incompressible inertial waves possible. Evaluating the role that large-scale vortices play in astrophysical accretion disks will require understanding the mechanisms that generate and destroy them.

Observations of convection in the giant planets: results from space missions

AbstractThe giant planets are fluid objects; their solid cores occupy much less than half of their volumes. The largest planet, Jupiter, is over ten times the size of Earth. The giant planet atmospheres are powered in roughly equal parts by sunlight and by internal heat, which is left over from planetary formation. In most cases, the winds are measured by tracking clouds relative to the internal magnetic fields. Saturn is the exception, since the internal field is axisymmetric and therefore provides no evidence of rotation. In all four giant planets, the winds blow mainly in the east-west (zonal) direction, and the coloured cloud bands are aligned with the winds. The patterns are organized by rotation and not by the energy sources, since the sun at zenith moves from one pole to the other during the course of a year on Uranus, and yet the winds do not change. Although the power per unit area - the sum of absorbed sunlight and internal heat - is 20 times greater at Jupiter than at Neptune, the winds at Neptune are stronger. In fact Jupiter has the weakest winds of all the giant planets, although it is closest to the sun. Besides the zonal winds, the giant planets have long-lived vortices that have the same sign of vorticity as the latitude bands in which they sit. These large vortices exhibit a variety of behaviours, including oscillation in shape, position, and orientation, merging and splitting, and filament ejection. The anticyclones have a compact, oval shape; the cyclones are more elongated and diffuse. The cyclones contain lightning, which is a sign of moist convection. The cyclones therefore have a more disturbed appearance, since the convective storms are vigorous and chaotic. The convective storms are more frequent on Jupiter, but they are apparently more energetic on Saturn. The convective storms maintain a Reynolds stress that pumps momentum into the zonal jets in what is known as an inverse energy cascade. The depth to which the zonal winds extend is largely unknown. The winds could be confined to the outer 1 percent of the planets radii, or they could extend down into the fluid interiors, where the electrical conductivity and magnetic field become important.

Renewed acceleration of the 24° N jet on Jupiter

Jupiter's eastward jet at 24° N, which formerly had the fastest winds on the planet, has maintained a less extreme speed of ∼135 m/s since 1991, carrying a series of long-lived vortices at 125 m/s. In 2002–2003, as the albedo of the adjacent North Temperate Belt increased, the tracks of the vortices accelerated slightly, and they had disappeared by 2005. In 2005, small tracers had a mean speed of 146.4 (±0.9) m/s, significantly faster than the previous mean speed of the jet, suggesting that the jet peak itself has accelerated at cloud-top level, and that the jet is beginning to return to the super-fast state. These changes may resemble the even greater transformations occurring in the equatorial jet of Saturn.

Anomalous Hydrodynamics and Normal Fluids in Rapidly Rotating Bose-Einstein Condensates

In rapidly rotating condensed Bose systems we show that there is a regime of anomalous hydrodynamics which coincides with the mean field quantum Hall regime. A consequence is the absence of a normal fluid in any conventional sense. However, even the superfluid hydrodynamics is not described by conventional Bernoulli and continuity equations. We show that there are constraints which connect spatial variations of density and phase and that the vortex positions are not the simplest description of the dynamics. We demonstrate, inter alia, a simple relation between vortices and surface waves. We show that the surface waves can emulate a "normal fluid," allowing dissipation by energy and angular momentum absorbtion from vortex motion in the trap. The time scale is sensitive to the initial configuration, which can lead to long-lived vortex patches--perhaps related to those observed at JILA.

Vortices of the Mediterranean Sea: An Altimetric Perspective

AbstractThe presence of coherent vortices makes observed mesoscale fields of the ocean resemble two-dimensional turbulence. Using this analogy, a common definition of a coherent structure has been used to study the statistical properties of Mediterranean Sea vortices observed by satellite altimeters over a 7-yr period. A vortex has been defined as the simply connected region with values of the Okubo–Weiss parameter W &amp;lt; −0.2σW, where σW is the spatial standard deviation of W, and the same sign of vorticity. This definition is shown to be appropriate to detect and characterize, statistically, properties such as size, mean kinetic energy, and amplitude of vortices in the Mediterranean basin from sea level anomaly maps corresponding to the period from October 1992 to October 1999. The distribution of such properties for the Mediterranean vortices suggests a heuristic criterion to extract and select very coherent and long-lived vortices from the whole set of structures identified in altimetric maps. Such coherent vortices appear to be selected for amplitudes greater than 2σW, where the amplitude has been defined in terms of the Okubo–Weiss parameter rather than vorticity, and strongly correspond to those reported from observations with independent data. Systematic locating and tracking of such vortices provide, for the first time, a general picture of their preferential paths in the Mediterranean basin, which are characterized by complex but rather well defined patterns.

Vortices in Thin, Compressible, Unmagnetized Disks

We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set of long-lived vortices, each of which has a radial extent comparable to the local scale height. But we also find that the resulting velocity field has a positive shear stress, . This effect appears only at high resolution. The transport, which decays with time as t^-1/2, arises primarily because the vortices drive compressive motions. This result suggests a possible mechanism for angular momentum transport in low-ionization disks, with two important caveats: a mechanism must be found to inject vorticity into the disk, and the vortices must not decay rapidly due to three-dimensional instabilities.