Primary Vortex Core Research Articles

Enhancing the Resolution of Blade Tip Vortices in Hover with High-Order WENO Scheme and Hybrid RANS–LES Methods

The accurate prediction of blade tip vortices continues to be challenging for the investigation of rotor aerodynamics. In the current work, the blade tip vortex system of a Caradonna–Tung rotor in the hovering state is simulated on account of the framework of a high-order WENO scheme and hybrid RANS/LES method progressively. With the RANS method based on a fifth-order WENO–Roe scheme, the spatial resolution of wake age and capture the accuracy of tip vortices are improved significantly. However, the unsteadiness of the vortex system fails to be distinguished. Then, the DDES and IDDES methods, coupled with a fifth-order WENO–Roe scheme, are implemented to further enhance the resolution of the spatial turbulence. Compared with RANS, the improvement of spatial resolution is reflected in both the statistical and transient results with DDES. The identifiable vortex core distributions can be predicted at older wake ages. The asymmetrical characteristic of blade tip vortices is revealed along with the release of fluctuation while the predicted distribution of velocity profiles in the vortex core is enhanced. With the application of IDDES, the secondary turbulent structures are captured around the primary vortex core of blade tip vortices while the complex behaviors of the vortices are observed. However, the statistics of the averaged flow field are similar to DDES.

Characteristics of shock tube generated compressible vortex rings at very high shock Mach numbers

Compressible vortex rings are usually formed at the open end of a shock tube. They show exciting flow phenomena during their formation, evolution, and propagation depending on the shock Mach number (Ms) and exit flow conditions. This study considers high shock tube pressure ratio (PR) cases showing hitherto unknown, spectacular flow structures. With hydrogen as a driver section gas at high PR, a supersonic compressible vortex ring having vortex ring Mach number (Mv) >1 is obtained for the first time. The formation of multiple triple points and the corresponding slipstream shear layers and, thus, multiple counter-rotating vortex rings (CRVRs) behind the primary vortex ring at different radial locations, in addition to the usual CRVRs, appears to be a unique characteristic for high Mach number vortex rings. During the formation stage, a vortex layer of reverse circulation than that of the primary vortex ring gets generated from the outer wall of the shock tube. The instability of such a vortex layer creates another series of opposite circulation vortices, which later interfere with the primary vortex core considerably. Also, a near stationary slipstream vortex and multiple fast-moving tiny vortices of opposite circulation to the slipstream vortex are observed near the central zone. Mechanisms for the formation of these complex vortical structures are identified. The implications of these phenomena on the vortex ring's geometric and kinematic characteristics, such as ring diameter, core diameter, circulation, and translational velocity, are discussed in detail, illustrating their differences with low vortex ring Mach number cases considering 0.31 < Mv < 1.08.

Synthetic jet vortex rings impinging onto a porous wall: Reynolds number effect

The interaction of synthetic jet vortex rings with a porous wall was investigated using laser-induced fluorescence (LIF) and particle image velocimetry (PIV) techniques. The synthetic jet Reynolds number (Resj) varied from 309 to 1238, where the vortex rings underwent transition from laminar to turbulent flow. For the lowest Reynolds number (Resj = 309), the flow is almost laminar; the primary vortex ring (VR1) induces and pairs with a well coherent secondary vortex ring (VR2) in the upstream side of the porous wall, leading to a conventional “rebound” and “reversal” in VR1’s trajectory. As Resj increases, the induced VR2 becomes weaker and loses coherence quickly after rolling up; even at Resj = 1238, VR2 becomes indistinguishable. During the vortex ring interacting with the porous wall, some fluid penetrates through the wall to form a transmitted vortex ring (VRT) in the downstream region. The circulation of VRT increases with the growth of Resj. In particular, for a higher Resj, the synthetic jet tends to pass through a porous wall more easily with less losses in both vortex ring circulation and jet momentum. Velocity triple decomposition shows that VRT for all tested cases has lost coherence completely before it moves out of the field of view. Moreover, for Resj = 309, the incoherence of VRT is caused by the vorticity diffusion and viscous dissipation since both the upstream and downstream flow are almost laminar. But for the high Resj (619, 928 and 1238), VRT lost coherence is mainly due to the transition, which results in a relatively large ratio of the fluctuation kinetic energy (FKE) to the total flow kinetic energy (KE). In particular, for Resj = 928 and 1238, it is observed that some small-scale Kelvin-Helmholtz vortices are formed in the trailing jet, and entrained into the primary vortex core, which accelerates the loss of coherence for the primary vortex ring. This observation can explain why the vortex ring at high Reynolds number is less coherent.

Characteristics of Accelerations and Pressure Gradient during Run-Down of Solitary Wave over Very Steep Beach: A Case Study

An experimental investigation is performed to elucidate the variations of accelerations and pressure gradients in the external stream of retreating flow during the run-down phase of a non-breaking solitary wave, propagating over a 1:3 sloping beach. Two solitary waves that have the incident wave heights (H0) of 2.9 and 5.8 cm, with respective still water depths (h0) of 8.0 and 16.0 cm (Cases A and B), were generated in a wave flume, resulting in the incident wave-height to water-depth ratios (H0/h0) being identically equal to 0.363. The latter case was only used to highlight the non-dimensional features of the wave celerity, the time history of horizontal velocity and the breaker type, which all exhibit similarity to those of the former. Two flow visualization techniques such as particle trajectory method and fluorescent dye strip and a high-speed particle image velocimetry (HSPIV) were utilized to provide the flow images and velocity fields. Based on the ensemble-averaged velocity fields and profiles, the partially depth-averaged (i.e., excluding the part in the boundary layer) values of accelerations and pressure gradient at a specified measuring section are then smoothed by a symmetric five-point smoothing scheme. Eventually, the smoothed values of the accelerations and pressure gradient are used to highlight the dynamic features of the external stream of retreating flow. It is found that, at the section of the incipient flow separation, the non-dimensional local acceleration (with respect to the gravity acceleration) in the offshore direction keeps increasing from the moment at which the run-up motion ends to the counterpart at which the incipient flow separation occurs. Afterwards, growth of the primary vortex develops with its core translating offshore. The corresponding non-dimensional local acceleration at the (moving) core section increases to a maximum of around 1.0 at the instant for occurrence of the hydraulic jump with abrupt rise of the free surface; and then decreases to zero at time for transformation of the curling jet into the projecting jet. The results exhibit that the external stream of retreating flow is accelerated temporally in the offshore direction for the interval between the time for the end of run-up motion and that for the formation of projecting jet. However, for later time interval up to generation of the two-phase flow field, the non-dimensional local acceleration in the offshore direction varies from zero to a negative maximum of −2.117 at the moment for the projecting jet heading downward before the impingement. It then decreases in magnitude continuously. The trend reveals that the external stream is decelerated temporally in the offshore direction for this later time interval. Further, at the section of the incipient flow separation, the non-dimensional pressure gradient (also with reference to the gravity acceleration) in the offshore direction increases from 0.225 for the time at which the run-up motion ends to 0.721 for the instant at which the incipient flow separation takes place. The trend highlights the external stream being under increasing adverse pressure gradient and more decelerated spatially with the increasing time, thus resulting in occurrence of the incipient flow separation. Afterwards, the value of the non-dimensional pressure gradient keeps increasing and eventually reaches a positive maximum of 2.011 and then decreases consecutively until the two-phase flow field is generated. In addition, due to the influence of acceleration of the external stream in the offshore direction, the non-dimensional vorticity of primary vortex core increases with increasing time up to the moment for occurrence of the projecting jet. Nevertheless, the non-dimensional vorticity of primary vortex core keeps decreasing with increasing time T for the later time interval due to the influence of deceleration of the external stream in the offshore direction. Finally, considerably large magnitudes of the non-dimensional accelerations and pressure gradient greater than 1.5 taking place at two non-dimensional times are worthy of noting. The negative maximum value of the non-dimensional convective acceleration equal to −2.005 appears at the instant for the occurrence of hydraulic jump. In addition, the negative maximum values of the non-dimensional local acceleration, total acceleration and pressure gradient unexpectedly as high as −2.117, −1.694 and 2.011, respectively, appear simultaneously at time for the projecting jet heading towards the retreating free surface. Under such a situation, the external stream of retreating flow is highly decelerated in the offshore direction under the fairly large adverse pressure gradient, thus forcing the retreating flow to move upwards rapidly. Meanwhile, the non-dimensional local acceleration in the vertical direction is surprisingly found to be 3.37. The result strongly reconfirms the evident rise of the free surface in the vicinity of the core section and reveals very rapid change from negative, via nearly zero, to positive vertical velocity.

LES study of transient behaviour and turbulent characteristics of free-surface and floor-attached vortices in pump sump

ABSTRACTIn this work, large eddy simulation combined with volume of fluid method is performed to simulate the flow and the associated vortices in a pump sump. The numerical results are compared with experimental data. Particular interest is paid to discovering the temporal evolution of the free-surface and floor-attached vortices. Both vortices undergo periodic enhancement and attenuation due to the advection and stretching/tilting effects generated by the background flow. The primary vortex core is accompanied by spirally wrapped secondary vortex tubes, resulting in anisotropic turbulence structure around the vortex core regions. The findings provide a deep insight into the application of large eddy simulation in pump sump and the underlying mechanism of vortex formation and evolution in the sump.

Successive bifurcations in a fully three-dimensional open cavity flow

The transition to unsteadiness of a three-dimensional open cavity flow is investigated using the joint application of direct numerical simulations and fully three-dimensional linear stability analyses, providing a clear understanding of the first two bifurcations occurring in the flow. The first bifurcation is characterized by the emergence of Taylor–Görtler-like vortices resulting from a centrifugal instability of the primary vortex core. Further increasing the Reynolds number eventually triggers self-sustained periodic oscillations of the flow in the vicinity of the spanwise end walls of the cavity. This secondary instability causes the emergence of a new set of Taylor–Görtler vortices experiencing a spanwise drift directed toward the spanwise end walls of the cavity. While a two-dimensional stability analysis would fail to capture this secondary instability due to the neglect of the lateral walls, it is the first time to our knowledge that this drifting of the vortices can be entirely characterized by a three-dimensional linear stability analysis of the flow. Good agreements with experimental observations and measurements strongly support our claim that the initial stages of the transition to turbulence of three-dimensional open cavity flows are solely governed by modal instabilities.

Numerical investigation on the three-dimensional flow characteristics of unsteady subsonic elliptic jet

Based on large eddy simulation (LES), combined with high order tuned centered-difference (TCD) scheme, the initial flow characteristics of the unsteady subsonic elliptic jet was investigated numerically. The numerical results illustrate the formation, variation and development of the subsonic elliptic jets’ initial flow structures. Moreover, the self-induced deformation of the noncircular vortex loops and the distribution of the streamwise vorticity field have been completely clear using the three-dimensional (3D) view. The vorticity field of the results qualitatively shows that the self-induced Biot-Savart deformation of primary vortex loop (PVL) leads to the streamwise vortices generation in the flow, and the streamwise vortex pairs enlarge along the primary vortex core and augment the deformation of PVL. These two mechanisms govern the phenomenon of axis switching. Subsequently, the coherent structures present in the major and minor axis planes of the elliptic vortex loop and jet shear layer are identified with proper orthogonal decomposition (POD) method. Moreover, the mechanisms of vortex dynamics and the entrainment features of various noncircular jets have also been described in detail.

Intermittency and transition to chaos in the cubical lid-driven cavity flow

Transition from steady state to intermittent chaos in the cubical lid-driven cavity flow is investigated numerically. Fully three-dimensional stability analyses have revealed that the flow experiences an Andronov–Poincaré–Hopf bifurcation at a critical Reynolds number Rec = 1914. As for the 2D-periodic lid-driven cavity flows, the unstable mode originates from a centrifugal instability of the primary vortex core. A Reynolds–Orr analysis reveals that the unstable perturbation relies on a combination of the lift-up and anti lift-up mechanisms to extract its energy from the base flow. Once linearly unstable, direct numerical simulations show that the flow is driven toward a primary limit cycle before eventually exhibiting intermittent chaotic dynamics. Though only one eigenpair of the linearized Navier–Stokes operator is unstable, the dynamics during the intermittencies are surprisingly well characterized by one of the stable eigenpairs.

DDES study of the aerodynamic forces and flow physics of a delta wing in static ground effect

During takeoff and landing phases, the performance of an aircraft with delta wing configuration is significantly influenced by the ground effect (GE). In this paper, the static ground effect (SGE) of a 65° sweep delta wing (VFE-2) with sharp leading edge at α=20° is investigated by the Delayed Detached Eddy Simulation (DDES) grounded on Spalart–Allmaras (S–A) turbulence model. With the ride height decreasing, the lift, drag and nose-down pitching moment of the delta wing increase nonlinearly, and the majority of aerodynamic force increments in SGE are from the windward side of the delta wing. With the ride height decreasing, under the windward side, the flow is severely blocked resulting in the augmentation of static pressure, and the increasing span wise flow near the leading edge strengthens the shear layer and the leading edge vortex over the leeward side. The strengthened leading edge vortex induces lower pressure over the leeward side, and moves outside along the span wise direction. With the ride height decreasing, the jet-like flow in the primary vortex core is accelerated before the vortex breakdown, and the wake-like flow in the primary vortex core is decelerated after the vortex breakdown.

Modal analysis of confined square and rectangular cavity flows

Particle image velocimetry (PIV) and common-base proper orthogonal decomposition (CPOD) were used to quantify the velocity field within the separated region of confined square and rectangular cavities with streamwise aspect ratios of one and two, respectively. For a constant Reynolds number of 60,000, the flow structure within the entire domain of the square cavity is dominated by a nominally two-dimensional primary vortex. The flow unsteadiness here is manifested in the rms distributions, which reveal significant contributions from the pseudo-fluctuations due to the meandering of the primary vortex core and from random unsteadiness. Comparisons were made to the backward-facing step geometry, and in contrast, for the rectangular cavity and backward-facing step, large-scale unsteady flow patterns, three-dimensional in character, are present in the velocity field. The formation of these unsteady events was identified through the realization of instantaneous velocity fields. In contrast to the square cavity, the CPOD analysis reveals the presence of a “shift mode” for the rectangular cavity, which results in spanwise variation throughout the entire flow field. As a conclusion, the unsteady behavior observed for both the rectangular-cavity and backward-facing-step flows is absent for the square cavity, which can be attributed to the strong coupling effect of the two vertical cavity boundaries at low streamwise aspect ratios. Furthermore, the spatio-temporal character of the rectangular cavity is shown to be more closely related to the backward-facing step than the square cavity.

On the structure of vortex rings from inclined nozzles

AbstractWe carry out numerical simulations to investigate the vortex dynamics of laminar, impulsively driven flows through inclined nozzles in a piston–cylinder apparatus. Our simulations are motivated by the need to provide a complete description of the intricate vortical structures and governing mechanisms emerging in such flows as documented in the experiments of Webster & Longmire (Phys. Fluids, vol. 10, 1998, pp. 400–416) and Troolin & Longmire (Exp. Fluids, vol. 48, 2010, pp. 409–420). We show that the flow is dominated by the interaction of two main vortical structures: the primary inclined vortex ring at the nozzle exit and the secondary stopping ring that arises due to the entrainment of the flow into the cylinder when the piston stops moving. These two structures are connected together with pairs of vortex tubes, which evolve from the continuous vortex sheet initially connecting the primary vortex ring with the interior cylinder wall. In the exterior of the nozzle the key mechanism responsible for the breakup of the vortical structure is the interaction of the stronger inclined primary ring with the weaker stopping ring near the longest lip of the nozzle. In the interior of the nozzle the dynamics is governed by the axial stretching of the secondary ring and the ultimate impingement of this ring on the cylinder wall. Our simulations also clarify the kinematics of the azimuthal flow along the core of the primary vortex ring documented in the experiments by Lim (Phys. Fluids, vol. 10, 1998, pp. 1666–1671). We show that the azimuthal flow is characterized by a pair of two spiral saddle foci at the long and short lips of the nozzle through which ambient flow enters and exits the primary vortex core.

Dual leading-edge vortex structure for flow over a simplified butterfly model

The dye visualization experiments show that a dual leading-edge vortex (LEV) structure exists on the suction side of a simplified butterfly model of Papilio ulysses at α = 8°−12°. Furthermore, the results of particle image velocimetry (PIV) measurement indicate that the axial velocity of the primary (outer) vortex core reaches the lower extreme value while a transition from a “wake-like” to a “jet-like” axial velocity profile occurs. The work reveals for the first time the existence of dual LEV structure on the butterfly-like forward-sweep wing configuration.

Evolution of a vortex system in the vicinity of an external dihedral corner

Results of experimental investigations of the evolution of a vortex system formed in a supersonic flow past a streamwise-aligned external dihedral right angle owing to a difference in pressures on the upper and side faces of the corner are analyzed. The experiments are performed in a T-313 wind tunnel based at ITAM SB RAS at Mach numbers M∞ = 2.27, 3, and 4, and angles of attack α = −4° ÷ +20°. It is shown that the size of the vortex system influence zones is almost independent of the free-stream Mach number in the examined range of the angles of attack, and the relative values of flow rarefaction on the model surface under the primary vortex core smoothly tend to their minimum values.

Evolution of Tip Vortices Generated by Two Bladed Rotor in Hover at Early Wake Ages

In order to investigate change of vortex structures and its evolving processes, two dimensional LDV system was used for measurement of velocity vectors of tip vortex, and PIV system was also used for visualizations of tip vortex array for two bladed rotor, respectively. Experiments provided vortex locations, tangential and axial velocity components of tip vortex at six wake ages of 9.5, 10.5, 60.5, 99.5, 129.5, 169.5 and corresponded six wake ages shifted with 180 degrees per each. It was resulted that tip vortices generated by the first blade satisfy Landgrebe’s model for their vortex locations even after they were accelerated by the second blade in downstream. Tangential velocity components of tip vortices follow Vatistas’ n=2 model on both inside and outside regions of rotor slipstream without loss of vortex circulation. Axial velocity profiles revealed that there were small but significant perturbations just outside the primary vortex core which implies the second blade affects the wake substantially. It was also found that tip paths of each blade were not willing to be coincided intrinsically.

Numerical simulations of leading-edge vortex core axial velocity for flow over delta wings

Numerical simulations have been performed to investigate the characteristics of leading-edge vortex core axial velocity over two delta wings with leading edge swept angles Λ = 50° and 76°, respectively. It is obtained that Reynolds number has the most important effect on the axial velocity of the primary leading-edge vortex core. At Reynolds numbers larger than 105, the jet-like flow of the vortex core is the most common type for both the large and the moderate swept delta wings. While if Reynolds number decreases to 103–104, the core axial velocity distributions for these two delta wings present the wake-like profile for all angles of attack considered in the present investigation.

Sphere–wall collisions: vortex dynamics and stability

For moderate Reynolds numbers, a sphere colliding with a wall in the normal direction will lead to a trailing recirculating wake, threading over the sphere after impact and developing into a complex vortex-ring system as it interacts with vorticity generated at the wall. The primary vortex ring, consisting of the vorticity from the wake of the sphere prior to impact, persists and convects, relatively slowly, outwards away from the sphere owing to the motion induced from its image. The outward motion is arrested only a short distance from the axis because of the strong interaction with the secondary vorticity. In this paper, the structure and evolution of this combined vortex system, consisting of a strong compact primary vortex ring surrounded by and interacting with the secondary vorticity, is quantified through a combined experimental and numerical study. The Reynolds-number range investigated is (100 < Re < 2000). At Reynolds numbers higher than about 1000, a non-axisymmetric instability develops, leading to rapid distortion of the ring system. The growth of the instability does not continue indefinitely, because of the dissipative nature of the flow system; it appears to reach a peak when the wake vorticity first forms a clean primary vortex ring. A comparison of the wavelength, growth rate and perturbation fields predicted from both linear stability theory and direct simulations, together with theoretical predictions, indicates that the dominant physical mechanism for the observed non-axisymmetric instability is centrifugal in nature. The maximum growth occurs at the edge of the primary vortex core, where the vorticity changes sign. Notably, this is a physical mechanism different from that proposed previously to explain the development of the three-dimensional flow of an isolated vortex ring striking a wall.

Scaling and instability of a junction vortex

This paper details experiments in the region where an impulsively started moving wall slides under a stationary wall. The experiments were conducted over a Reynolds number range of ReΓ=5×102–5×105. The length scale for the Reynolds number is defined as the distance the wall has moved from rest and increases during an experiment. Experiments show that for ReΓ>103 a vortex forms close to the junction where the moving wall meets the stationary one. The data shows that while the vortical structure is small, in relation to the fixed-apparatus length scale, the size of the vortex normalized with respect to the wall speed and viscosity scales in a universal fashion with respect to ReΓ. The scaling rate is proportional to t5/6 when the Reynolds number is large. The kinematic behaviour of the vortex is related to the impulse that the moving wall applies to the fluid and results in a prediction that the transient structure should grow as t5/6 and the velocity field should scale as t−1/6. The spatial-growth prediction is in good agreement with the experimental results and the velocity scaling is moderately successful in collapsing the experimental data.For ReΓ>2×104 three-dimensional instabilities appear on the perimeter of the vortical structure and the flow transitions from an unsteady two-dimensional flow to a strongly three-dimensional vortical structure at ReΓ≃ 4 × 104. The instability mechanism is centrifugal. The formation and growth of these instability structures and their ingestion into the primary vortex core causes the three-dimensional breakdown of the primary vortex. Two movies are available with the online version of the paper.

Hydrodynamics of a particle impact on a wall

The problem of a particle impacting on a wall, a common phenomenon in particle-laden flows in the minerals and process industries, is investigated computationally using a spectral-element method with the grid adjusting to the movement of the particle towards the wall. Remeshing is required at regular intervals to avoid problems associated with mesh distortion and the constantly reducing maximum time-step associated with integration of the non-linear convective terms of the Navier–Stokes equations. Accurate interpolation between meshes is achieved using the same high-order interpolation employed by the spectral-element flow solver. This approach allows the full flow evolution to be followed from the initial approach, through impact and afterwards as the flow relaxes. The method is applied to the generic two-dimensional and three-dimensional bluff body geometries, the circular cylinder and the sphere. The principal case reported here is that of a particle colliding normally with a wall and sticking. For the circular cylinder, non-normal collisions are also considered. The impacts are studied for moderate Reynolds numbers up to approximately 1200. A cylindrical body impacting on a wall produces two vortices from its wake that convect away from the cylinder along the wall before stalling while lifting induced wall vorticity into the main flow. The situation for a sphere impact is similar, except in this case a vortex ring is formed from the wake vorticity. Again, secondary vorticity from the wall and particle plays a role. At higher Reynolds number, the secondary vorticity tends to form a semi-annular structure encircling the primary vortex core. At even higher Reynolds numbers, the secondary annular structure fragments into semi-discrete structures, which again encircle and orbit the primary core. Vorticity fields and passive tracer particles are used to characterize the interaction of the vortical structures. The evolution of the pressure and viscous drag coefficients during a collision are provided for a typical sphere impact. For a Reynolds number greater than approximately 1000 for a sphere and 400 for a cylinder, the primary vortex core produced by the impacting body undergoes a short-wavelength instability in the azimuthal/spanwise direction. Experimental visualisation using dye carried out in water is presented to validate the predictions.

Development of a Tip-Leakage Flow Part 2: Comparison Between the Ducted and Un-ducted Rotor

The vortical flow in the tip region of a three-bladed rotor was examined using particle imaging velocimetry (PIV). The vortex forming at the tip of the un-ducted propeller was compared to the tip-leakage vortex of the ducted rotor. The planar flow fields were used to identify regions of concentrated vorticity and determine instantaneous vortex properties, revealing the presence of a primary tip-leakage vortex surrounded by a number of secondary vortices. Comparison between the ducted and un-ducted rotor indicated that the presence of the duct reduced the relative strength of the primary tip vortex, making its strength a smaller fraction of the overall shed circulation near the tip. The weaker tip-leakage vortex then became closer in strength to the other secondary vortices in the tip-flow region. However, for the rotor tip geometry considered here, the radius of the primary vortex core did not vary substantially between the ducted and un-ducted cases. The variability of the flow was larger for the ducted case, in terms of the primary vortex position, its identified circulation, core size, and inferred core pressure. This variability was also observed in the scaled velocity fluctuations near the core of the vortex.

Vortex dynamics associated with the collision of a sphere with a wall

For moderate Reynolds numbers, a sphere striking a wall in the normal direction leads to the trailing recirculating wake threading over the sphere and developing into a complex vortex ring system as it interacts with the wall. The primary vortex ring, which consists of vorticity from the wake, persists and convects slowly outwards away from the sphere due to the motion induced from its image. The structure and evolution of this vortex system is quantified through a combined experimental and numerical study. At higher Reynolds numbers a non-axisymmetric instability develops, which leads to rapid dispersion of the ring system. A comparison of the wavelength and growth rate, predicted from both linear stability theory and direct simulations, with idealized models indicates that the mechanism is dominated by a centrifugal instability at the edge of the primary vortex core.