Showing papers on "Vortex published in 2007"

Hairpin vortex organization in wall turbulencea)

Abstract: Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.

Magnetic vortex oscillator driven by d.c. spin-polarized current

Abstract: Transfer of angular momentum from a spin-polarized current to a ferromagnet provides an efficient means to control the magnetization dynamics of nanomagnets. A peculiar consequence of this spin torque, the ability to induce persistent oscillations in a nanomagnet by applying a d.c. current, has previously been reported only for spatially uniform nanomagnets. Here, we demonstrate that a quintessentially non-uniform magnetic structure, a magnetic vortex, isolated within a nanoscale spin-valve structure, can be excited into persistent microwave-frequency oscillations by a spin-polarized d.c. current. Comparison with micromagnetic simulations leads to identification of the oscillations with a precession of the vortex core. The oscillations, which can be obtained in essentially zero magnetic field, exhibit linewidths that can be narrower than 300 kHz at ∼1.1 GHz, making these highly compact spin-torque vortex-oscillator devices potential candidates for microwave signal-processing applications, and a powerful new tool for fundamental studies of vortex dynamics in magnetic nanostructures.

Electrical switching of the vortex core in a magnetic disk

Abstract: A magnetic vortex is a curling magnetic structure realized in a ferromagnetic disk, which is a promising candidate for a memory cell for future non-volatile data-storage devices. Thus, an understanding of the stability and dynamical behaviour of the magnetic vortex is a major requirement for developing magnetic data-storage technology. Since the publication of experimental proof for the existence of a nanometre-scale core with out-of-plane magnetization in a magnetic vortex, the dynamics of vortices have been investigated intensively. However, a way to electrically control the core magnetization, which is a key for constructing a vortex-core memory, has been lacking. Here, we demonstrate the electrical switching of the core magnetization by using the current-driven resonant dynamics of the vortex; the core switching is triggered by a strong dynamic field that is produced locally by a rotational core motion at a high speed of several hundred metres per second. Efficient switching of the vortex core without magnetic-field application is achieved owing to resonance. This opens up the potentiality of a simple magnetic disk as a building block for spintronic devices such as a memory cell where the bit data is stored as the direction of the nanometre-scale core magnetization.

A turbulent jet in crossflow analysed with proper orthogonal decomposition

Abstract: Detailed instantaneous velocity fields of a jet in crossflow have been measured with stereoscopic particle image velocimetry (PIV). The jet originated from a fully developed turbulent pipe flow and entered a crossflow with a turbulent boundary layer. The Reynolds number based on crossflow velocity and pipe diameter was 2400 and the jet to crossflow velocity ratios were R=3.3 and R=1.3. The experimental data have been analysed by proper orthogonal decomposition (POD). For R=3.3, the results in several different planes indicate that the wake vortices are the dominant dynamic flow structures and that they interact strongly with the jet core. The analysis identifies jet shear-layer vortices and finds that these vortical structures are more local and thus less dominant. For R=1.3, on the other hand, jet shear-layer vortices are the most dominant, while the wake vortices are much less important. For both cases, the analysis finds that the shear-layer vortices are not coupled to the dynamics of the wake vortices. Finally, the hanging vortices are identified and their contribution to the counter-rotating vortex pair (CVP) and interaction with the newly created wake vortices are described.

Electrical switching of vortex core in a magnetic disk

Abstract: A magnetic vortex is a curling magnetic structure realized in a ferromagnetic disk, which is a promising candidate of a memory cell for future nonvolatile data storage devices. Thus, understanding of the stability and dynamical behaviour of the magnetic vortex is a major requirement for developing magnetic data storage technology. Since the experimental proof of the existence of a nanometre-scale core with out-of-plane magnetisation in the magnetic vortex, the dynamics of a vortex has been investigated intensively. However, the way to electrically control the core magnetisation, which is a key for constructing a vortex core memory, has been lacking. Here, we demonstrate the electrical switching of the core magnetisation by utilizing the current-driven resonant dynamics of the vortex; the core switching is triggered by a strong dynamic field which is produced locally by a rotational core motion at a high speed of several hundred m/s. Efficient switching of the vortex core without magnetic field application is achieved thanks to resonance. This opens up the potentiality of a simple magnetic disk as a building block for spintronic devices like a memory cell where the bit data is stored as the direction of the nanometre-scale core magnetisation.

Flapping dynamics of a flag in a uniform stream

Abstract: We consider the flapping stability and response of a thin two-dimensional flag of high extensional rigidity and low bending rigidity. The three relevant non-dimensional parameters governing the problem are the structure-to-fluid mass ratio, μ = ρ s h /(ρ f L); the Reynolds number, Re=VL/ν; and the non-dimensional bending rigidity, K B = EI / (ρfV 2 L 3 ). The soft cloth of a flag is represented by very low bending rigidity and the subsequent dominance of flow-induced tension as the main structural restoring force. We first perform linear analysis to help understand the relevant mechanisms of the problem and guide the computational investigation. To study the nonlinear stability and response, we develop a fluid-structure direct simulation (FSDS) capability, coupling a direct numerical simulation of the Navier-Stokes equations to a solver for thin-membrane dynamics of arbitrarily large motion. With the flow grid fitted to the structural boundary, external forcing to the structure is calculated from the boundary fluid dynamics. Using a systematic series of FSDS runs, we pursue a detailed analysis of the response as a function of mass ratio for the case of very low bending rigidity (K B = to-4) and relatively high Reynolds number (Re=10 3 ). We discover three distinct regimes of response as a function of mass ratio μ: (I) a small μ regime of fixed-point stability; (II) an intermediate μ regime of period-one limit-cycle flapping with amplitude increasing with increasing μ; and (III) a large μ regime of chaotic flapping. Parametric stability dependencies predicted by the linear analysis are confirmed by the nonlinear FSDS, and hysteresis in stability is explained with a nonlinear softening spring model. The chaotic flapping response shows up as a breaking of the limit cycle by inclusion of the 3/2 superharmonic. This occurs as the increased flapping amplitude yields a flapping Strouhal number (St=2Af/V) in the neighbourhood of the natural vortex wake Strouhal number, St ≃ 0.2. The limit-cycle von Karman vortex wake transitions in chaos to a wake with clusters of higher intensity vortices. For the largest mass ratios, strong vortex pairs are distributed away from the wake centreline during intermittent violent snapping events, characterized by rapid changes in tension and dynamic buckling.

Detection of Lagrangian coherent structures in three-dimensional turbulence

Abstract: We use direct Lyapunov exponents (DLE) to identify Lagrangian coherent structures in two different three-dimensional flows, including a single isolated hairpin vortex, and a fully developed turbulent flow. These results are compared with commonly used Eulerian criteria for coherent vortices. We find that despite additional computational cost, the DLE method has several advantages over Eulerian methods, including greater detail and the ability to define structure boundaries without relying on a preselected threshold. As a further advantage, the DLE method requires no velocity derivatives, which are often too noisy to be useful in the study of a turbulent flow. We study the evolution of a single hairpin vortex into a packet of similar structures, and show that the birth of a secondary vortex corresponds to a loss of hyperbolicity of the Lagrangian coherent structures.

Ultrafast nanomagnetic toggle switching of vortex cores.

Abstract: We present an ultrafast route for a controlled, toggle switching of magnetic vortex cores with ultrashort unipolar magnetic field pulses. The switching process is found to be largely insensitive to extrinsic parameters, like sample size and shape, and it is faster than any field-driven magnetization reversal process previously known from micromagnetic theory. Micromagnetic simulations demonstrate that the vortex core reversal is mediated by a rapid sequence of vortex-antivortex pair creation and annihilation subprocesses. Specific combinations of field-pulse strength and duration are required to obtain a controlled vortex core reversal. The operational range of this reversal mechanism is summarized in a switching diagram for a 200 nm Permalloy disk.

Tropical Cyclone Intensification from Asymmetric Convection: Energetics and Efficiency

Abstract: Prior studies of the linear response to asymmetric heating of a balanced vortex showed that the resulting intensity change could be very closely approximated by computing the purely symmetric response to the azimuthally averaged heating. The symmetric response to the purely asymmetric part of the heating was found to have a very small and most often negative impact on the intensity of the vortex. This result stands in contrast to many previous studies that used asymmetric vorticity perturbations, which suggested that purely asymmetric forcing could lead to vortex intensification. The issue is revisited with an improved model and some new methods of analysis. The model equations have been changed to be more consistent with the anelastic approximation, but valid for a radially varying reference state. Expressions for kinetic and available potential energies are presented for both asymmetric and symmetric motions, and these are used to quantify the flow of energy from localized, asymmetric heat sour...

Structure of turbulent flow over regular arrays of cubical roughness

Abstract: The structure of turbulent flow over large roughness consisting of regular arrays of cubical obstacles is investigated numerically under constant pressure gradient conditions. Results are analysed in terms of first- and second-order statistics, by visualization of instantaneous flow fields and by conditional averaging. The accuracy of the simulations is established by detailed comparisons of first- and second-order statistics with wind-tunnel measurements. Coherent structures in the log region are investigated. Structure angles are computed from two-point correlations, and quadrant analysis is performed to determine the relative importance of Q2 and Q4 events (ejections and sweeps) as a function of height above the roughness. Flow visualization shows the existence of low-momentum regions (LMRs) as well as vortical structures throughout the log layer. Filtering techniques are used to reveal instantaneous examples of the association of the vortices with the LMRs, and linear stochastic estimation and conditional averaging are employed to deduce their statistical properties. The conditional averaging results reveal the presence of LMRs and regions of Q2 and Q4 events that appear to be associated with hairpin-like vortices, but a quantitative correspondence between the sizes of the vortices and those of the LMRs is difficult to establish; a simple estimate of the ratio of the vortex width to the LMR width gives a value that is several times larger than the corresponding ratio over smooth walls. The shape and inclination of the vortices and their spatial organization are compared to recent findings over smooth walls. Characteristic length scales are shown to scale linearly with height in the log region. Whilst there are striking qualitative similarities with smooth walls, there are also important differences in detail regarding: (i) structure angles and sizes and their dependence on distance from the rough surface; (ii) the flow structure close to the roughness; (iii) the roles of inflows into and outflows from cavities within the roughness; (iv) larger vortices on the rough wall compared to the smooth wall; (v) the effect of the different generation mechanism at the wall in setting the scales of structures.

Shear instability and coherent structures in shallow flow adjacent to a porous layer

Abstract: Results are presented from an experimental study of shallow flow in a channel partially obstructed by an array of circular cylinders. The cylinder array is a model for emergent vegetation in an open channel, but also represents a simple sparse porous medium. A shear layer with regular vortex structures forms at the edge of the array, evolving downstream to an equilibrium width and vortex size. The vortices induce nearly periodic oscillations with a frequency that matches the most unstable linear mode for a parallel shear flow. The shear layer is asymmetric about the array interface and has a two-layer structure. An inner region of maximum shear near the interface contains a velocity inflection point and establishes the penetration of momentum into the array. An outer region, resembling a boundary layer, forms in the main channel, and establishes the scale of the vortices. The vortex structure, educed by conditional sampling, shows strong crossflows with sweeps from the main channel and ejections from the array, which create significant momentum and mass fluxes across the interface. The sweeps maintain the coherent structures by enhancing shear and energy production at the interface. A linear stability analysis is consistent with the experimental results and demonstrates that the instability is excited by the differential drag between the channel and the array.

Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers

Abstract: The wind-driven stably stratified mid-latitude oceanic surface turbulent boundary layer is computationally simulated in the presence of a specified surface gravity-wave field. The gravity waves have broad wavenumber and frequency spectra typical of measured conditions in near-equilibrium with the mean wind speed. The simulation model is based on (i) an asymptotic theory for the conservative dynamical effects of waves on the wave-averaged boundary-layer currents and (ii) a boundary-layer forcing by a stochastic representation of the impulses and energy fluxes in a field of breaking waves. The wave influences are shown to be profound on both the mean current profile and turbulent statistics compared to a simulation without these wave influences and forced by an equivalent mean surface stress. As expected from previous studies with partial combinations of these wave influences, Langmuir circulations due to the wave-averaged vortex force make vertical eddy fluxes of momentum and material concentration much more efficient and non-local (i.e. with negative eddy viscosity near the surface), and they combine with the breakers to increase the turbulent energy and dissipation rate. They also combine in an unexpected positive feedback in which breaker-generated vorticity seeds the creation of a new Langmuir circulation and instigates a deep strong intermittent downwelling jet that penetrates through the boundary layer and increases the material entrainment rate at the base of the layer. These wave effects on the boundary layer are greater for smaller wave ages and higher mean wind speeds.

On the front velocity of gravity currents

Abstract: Highly resolved three-dimensional and two-dimensional simulations of gravity currents in planar and cylindrical configurations are presented. The volume of release of the heavy fluid is varied and the different phases of spreading, namely acceleration, slumping, inertial and viscous phases, are studied. The incompressible Navier–Stokes equations are solved assuming that the Boussinesq approximation is valid for small density difference. The simulations are performed for three different Reynolds numbers (Re): 895, 3450 and 8950 (this particular choice corresponds to values of Grashof number: 10 5 ,1 .5×10 6 and 10 7 , respectively). Following their sudden release, the gravity currents are observed to go through an acceleration phase in which the maximum front velocity is reached. As the interface of the current rolls up, the front velocity slightly decreases from the maximum and levels off to a nearly constant value. At higher Re, three-dimensional disturbances grow rapidly and the currents become strongly turbulent. In contrast, in two-dimensional simulations, the rolled-up vortices remain coherent and very strong. Depending on the initial Re of the flow and on the size of the release, the current may transition from the slumping to the inertial phase, or directly to the viscous phase without an inertial phase. New criteria for the critical Re are introduced for the development of the inertial phase. Once the flow transitions to the inertial or viscous phase, it becomes fully three-dimensional. During these phases of spreading, two-dimensional approximations underpredict the front location and velocity. The enhanced vortex coherence of the two-dimensional simulations leads to strong vortex interaction and results in spurious strong time variations of the front velocity. The structure and dynamics of the three-dimensional currents are in good agreement with previously reported numerical and experimental observations.

Bat Flight Generates Complex Aerodynamic Tracks

Abstract: The flapping flight of animals generates an aerodynamic footprint as a time-varying vortex wake in which the rate of momentum change represents the aerodynamic force. We showed that the wakes of a small bat species differ from those of birds in some important respects. In our bats, each wing generated its own vortex loop. Also, at moderate and high flight speeds, the circulation on the outer (hand) wing and the arm wing differed in sign during the upstroke, resulting in negative lift on the hand wing and positive lift on the arm wing. Our interpretations of the unsteady aerodynamic performance and function of membranous-winged, flapping flight should change modeling strategies for the study of equivalent natural and engineered flying devices.

Hydrodynamics of a biologically inspired tandem flapping foil configuration

Abstract: Numerical simulations have been used to analyze the effect that vortices, shed from one flapping foil, have on the thrust of another flapping foil placed directly downstream. The simulations attempt to model the dorsal-tail fin interaction observed in a swimming bluegill sunfish. The simulations have been carried out using a Cartesian grid method that allows us to simulate flows with complex moving boundaries on stationary Cartesian grids. The simulations indicate that vortex shedding from the upstream (dorsal) fin is indeed capable of increasing the thrust of the downstream (tail) fin significantly. Vortex structures shed by the upstream dorsal fin increase the effective angle-of-attack of the flow seen by the tail fin and initiate the formation of a strong leading edge stall vortex on the downstream fin. This stall vortex convects down the surface of the tail and the low pressure associated with this vortex increases the thrust on the downstream tail fin. However, this thrust augmentation is found to be quite sensitive to the phase relationship between the two flapping fins. The numerical simulations allows us to examine in detail, the underlying physical mechanism for this thrust augmentation.

Reversal modes in magnetic nanotubes

Abstract: The magnetic switching of ferromagnetic nanotubes is investigated as a function of their geometry. Two independent methods are used: Numerical simulations and analytical calculations. It is found that for long tubes the reversal of magnetization is achieved by two mechanisms: The propagation of a transverse domain wall or propagation of a vortex domain wall depending on the internal and external radii of the tube.

Characteristics of Horseshoe Vortex in Developing Scour Holes at Piers

Abstract: The outcome of an experimental study on the turbulent horseshoe vortex flow within the developing (intermediate stages and equilibrium) scour holes at cylindrical piers measured by an acoustic Doppler velocimeter (ADV) are presented. Since the primary objective was to analyze the evolution of the turbulent flow characteristics of a horseshoe vortex within a developing scour hole, the flow zone downstream of the pier was beyond the scope of the investigation. Experiments were conducted for the approaching flow having undisturbed flow depth (=0.25 m) greater than twice the pier diameter and the depth-averaged approaching flow velocity (=0.357 m/s) about 95% of the critical velocity of the uniform bed sand that had a median diameter of 0.81 mm. The flow measurements by the ADV were taken within the intermediate (having depths of 0.25, 0.5, and 0.75 times the equilibrium scour depth) and equilibrium scour holes (frozen by spraying glue) at a circular pier of diameter 0.12 m. In order to have a comparative study, the ADV measurements within an equilibrium scour hole at a square pier (side facing the approaching flow) of sides equaling the diameter of the circular pier were also taken. The contours of the time-averaged velocities, turbulence intensities, and Reynolds stresses at different azimuthal planes (0, 45, and 90°) are presented. Vector plots of the flow field at azimuthal planes reveal the evolution of the characteristics of the horseshoe vortex flow associated with a downflow from intermediate stages to equilibrium condition of scour holes. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics of the horseshoe vortex are discussed from the point of view of the similarity with the velocity and turbulence characteristic scales. The imperative observation is that the flow and turbulence intensities in the horseshoe vortex flow in a developing scour hole are reasonably similar.

Experimental Study and Numerical Simulation of the Flindt Draft Tube Rotating Vortex

Abstract: The dynamics of the rotating vortex taking place in the discharge ring of a Francis turbine for partial flow rate operating conditions and cavitation free conditions is studied by carrying out both experimental flow survey and numerical simulations. 2D laser Doppler velocimetry, 3D particle image velocimetry, and unsteady wall pressure measurements are performs to investigate thoroughly the velocity and pressure fields in the discharge ring and to give access to the vortex dynamics. Unsteady RANS simulation are performed and compared to the experimental results. The computing flow domain includes the rotating runner and the elbow draft tube. The mesh size of 500,000 nodes for the 17 flow passages of the runner and 420,000 nodes for the draft tube is optimized to achieve reasonable CPU time for a good representation of the studied phenomena. The comparisons between the detailed experimental flow field and the CFD solution yield to a very good validation of the modeling of the draft tube rotating vortex and, then, validate the presented approach for industrial purpose applications.

Vortex formation by merging of multiple trapped Bose-Einstein condensates.

Abstract: We report observations of vortex formation by merging and interfering multiple (87)Rb Bose-Einstein condensates (BECs) in a confining potential. In this experiment, a single harmonic potential well is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either automatically merge together during their growth, or for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.

The effect of streamwise vortices on the aeroacoustics of a Mach 0.9 jet

Abstract: The role of the streamwise vortices on the aeroacoustics of a Mach 0.9 axisymmetric jet is investigated using two different devices to generate streamwise vortices: microjets and chevrons. The resultant acoustic field is mapped by sideline microphones and a microphone phased array. The flow-field characteristics within the first few diameters of the nozzle exit are obtained using stereoscopic particle image velocimetry (PIV). The flow-field measurements reveal that the counter-rotating streamwise vortex pairs generated by microjets are located primarily at the high-speed side of the initial shear layer. In contrast, the chevrons generate vortices of greater strength that reside mostly on the low-speed side. Although the magnitude of the chevron's axial vorticity is initially higher, it decays more rapidly with downstream distance. As a result, their influence is confined to a smaller region of the jet. The axial vorticity generated by both devices produces an increase in local entrainment and mixing, increasing the near-field turbulence levels. It is argued that the increase in high-frequency sound pressure levels (SPL) commonly observed in the far-field noise spectrum is due to the increase in the turbulence levels close to the jet exit on the high-speed side of the shear layer. The greater persistence and lower strength of the streamwise vortices generated by microjets appear to shift the cross-over frequencies to higher values and minimize the high-frequency lift in the far-field spectrum. The measured overall sound pressure level (OASPL) shows that microjet injection provides relatively uniform noise suppression for a wider range of sound radiation angles when compared to that of a chevron nozzle.

Cavitation microstreaming patterns in single and multiple bubble systems

Abstract: Cavitation microstreaming is a well-known phenomenon; however, few flow visualizations or measurements of the velocity fields have been conducted. In this paper micro-PIV (particle image velocimetry) measurements and streak photography were used to study the flow field around a single and two oscillating bubbles resting on a solid boundary. The mode of oscillation of the bubble was also measured in terms of the variation in the radius of the bubble and the movement of the bubble's centroid so that the streaming flow field could be accurately related to the bubble's oscillatory motion. The mode of oscillation was found to vary primarily with the applied acoustic frequency. Several modes of oscillation were investigated, including translating modes where the bubble's centroid moves along either a single axis, an elliptical orbit or a circular orbit. The flow field resulting from these oscillation modes contains closed streamlines representing vortical regions in the vicinity of the bubble. The translating modes were observed to occur in sequential order with the acoustic excitation frequency, changing from a translation along a single axis, to an elliptical orbit and finally to a circular orbit, or vice versa. Following this sequence, there is a corresponding transformation of the streaming pattern from a symmetrical flow structure containing four vortices to a circular vortex centred on the bubble. Despite some inconsistencies, there is general agreement between these streaming patterns and those found in existing theoretical models. Volume and shape mode oscillations of single bubbles as well as several different cases of multiple bubbles simultaneously oscillating with the same frequency and phase were also investigated and show a rich variety of streaming patterns.

Stability of helical tip vortices in a rotor far wake

Abstract: As a means of analysing the stability of the wake behind a multi-bladed rotor the stability of a multiplicity of helical vortices embedded in an assigned flow field is addressed. In the model the tip vortices in the far wake are approximated by infinitely long helical vortices with constant pitch and radius. The work is a further development of a model developed in Okulov (J. Fluid Mech., vol. 521, p. 319) in which the linear stability of N equally azimuthally spaced helical vortices was considered. In the present work the analysis is extended to include an assigned vorticity field due to root vortices and the hub of the rotor. Thus the tip vortices are assumed to be embedded in an axisymmetric helical vortex field formed from the circulation of the inner part of the rotor blades and the hub. As examples of inner vortex fields we consider three generic axial columnar helical vortices, corresponding to Rankine, Gaussian and Scully vortices, at radial extents ranging from the core radius of a tip vortex to several rotor radii.The analysis shows that the stability of tip vortices largely depends on the radial extent of the hub vorticity as well as on the type of vorticity distribution. As part of the analysis it is shown that a model in which the vortex system is replaced by N tip vortices of strength Γ and a root vortex of strength − N/Γ is unconditionally unstable.

Direct numerical simulation of turbulent Taylor–Couette flow

Abstract: We investigate the dynamical and statistical features of turbulent Taylor–Couette flow (for a radius ratio 0.5) through three-dimensional direct numerical simulations (DNS) at Reynolds numbers ranging from 1000 to 8000. We show that in three-dimensional space the Gortler vortices are randomly distributed in banded regions on the wall, concentrating at the outflow boundaries of Taylor vortex cells, which spread over the entirecylinder surface with increasing Reynolds number. Gortler vortices cause streaky structures that form herringbone-like patterns near the wall. For the Reynolds numbers studied here, the average axial spacing of the streaks is approximately 100 viscous wall units, and the average tilting angle ranges from 16° to 20°. Simulationresults have been compared to the experimental data in the literature, and the flow dynamics and statistics are discussed in detail.

Vortex generation in protoplanetary disks with an embedded giant planet

Abstract: Context. Vortices in protoplanetary disks can capture solid particles and form planetary cores within shorter timescales than those involved in the standard core-accretion model. Aims. We investigate vortex generation in thin unmagnetized protoplanetary disks with an embedded giant planet with planet to star mass ratio 10 4 and 10 3 . Methods. Two-dimensional hydrodynamical simulations of a protoplanetary disk with a planet are performed using two di erent numerical methods. The results of the non-linear simulations are compared with a time-resolved modal analysis of the azimuthally averaged surface density profiles using linear perturbation theory. Results. Finite-di erence methods implemented in polar coordinates generate vortices moving along the gap created by Neptune- mass to Jupiter-mass planets. The modal analysis shows that unstable modes are generated with growth rate of order 0:3 K for azimuthal numbers m= 4; 5; 6, where K is the local Keplerian frequency. Shock-capturing Cartesian-grid codes do not generate very much vorticity around a giant planet in a standard protoplanetary disk. Modal calculations confirm that the obtained radial profiles of density are less susceptible to the growth of linear modes on timescales of several hundreds of orbital periods. Navier-Stokes viscosity of the order = 10 5 (in units of a 2 p) is found to have a stabilizing e ect and prevents the formation of vortices. This result holds at high resolution runs and using di erent types of boundary conditions. Conclusions. Giant protoplanets of Neptune-mass to Jupiter-mass can excite the Rossby wave instability and generate vortices in thin disks. The presence of vortices in protoplanetary disks has implications for planet formation, orbital migration, and angular momentum transport in disks.