Long-lived Vortices Research Articles

Long-lived Equilibria in Kinetic Astrophysical Plasma Turbulence

Turbulence in classical fluids is characterized by persistent structures that emerge from the chaotic landscape. We investigate the analogous process in fully kinetic plasma turbulence by using high-resolution, direct numerical simulations in two spatial dimensions. We observe the formation of long-lived vortices with a profile typical of macroscopic, magnetically dominated force-free states. Inspired by the Harris pinch model for inhomogeneous equilibria, we describe these metastable solutions with a self-consistent kinetic model in a cylindrical coordinate system centered on a representative vortex, starting from an explicit form of the particle velocity distribution function. Such new equilibria can be simplified to a Gold–Hoyle solution of the modified force-free state. Turbulence is mediated by the long-lived structures, accompanied by transients in which such vortices merge and form self-similarly new metastable equilibria. This process can be relevant to the comprehension of various astrophysical phenomena, going from the formation of plasmoids in the vicinity of massive compact objects to the emergence of coherent structures in the heliosphere.

Neutron Star Atmosphere–Ocean Dynamics

We analyze the structure and dynamics of the plasma atmospheres and Coulomb-liquid oceans on neutron stars. Salient dynamical parameters are identified and their values estimated for the governing set of magnetohydrodynamics equations. Neutron star atmospheres and oceans are strongly stratified and, depending on the rotation period, contain a multitude of long-lived vortices (spots) and/or narrow zonal jets (free-shear zones) in the large plasma-beta regime—i.e., β p ≫ 1 (hydrodynamic regime). In contrast, when β p ≲ 1 (magnetohydrodynamic regime), the flow is dominated by a global lattice of effectively fixed magnetic islands (plasmoids) without any jets. Understanding the spatiotemporal variability of dynamic atmospheres and oceans on neutron stars is crucial for interpreting observations of their X-ray emissions.

Convective Overstability in Radially Global Protoplanetary Disks. I. Pure Gas Dynamics

Protoplanetary disks are prone to several hydrodynamic instabilities. One candidate, convective overstability (COS), can drive radial semiconvection that may influence dust dynamics and planetesimal formation. However, the COS has primarily been studied in local models. This paper investigates the COS near the midplane of radially global disk models. We first conduct a global linear stability analysis, which shows that linear COS modes exist only radially inward of their Lindblad resonance (LR). The fastest-growing modes have LRs near the inner radial domain boundary with effective radial wavelengths that can be a substantial fraction of the disk radius. We then perform axisymmetric global simulations and find that the COS’s nonlinear saturation is similar to previous incompressible shearing box simulations. In particular, we observe the onset of persistent zonal and elevator flows for sufficiently steep radial entropy gradients. In full 3D, nonaxisymmetric global simulations, we find the COS produces large-scale, long-lived vortices, which induce the outward radial transport of angular momentum via the excitation of spiral density waves. The corresponding α-viscosity values of order 10−3 agree well with those found in previous 3D compressible shearing box simulations. However, in global disks, significant modifications to their radial structure are found, including the formation of pressure bumps. Interestingly, the COS typically generates an outward radial mass transport, i.e., decretion. We briefly discuss the possible implications of our results for planetesimal formation and for interpreting dust rings and asymmetries observed in protoplanetary disks.

Relationship between vorticity near the surface and a long-lived vortex raised above it

The ability to predict the behavior of vortices is valuable for solving various scientific problems. One such problem is the evolution of tornado-like vortices near the surface and their connection with the original vortex located at a certain height above the surface. This article considers a two-dimensional axisymmetric hydrodynamic model in which the initial vorticity is maintained by an external force. Using the model, the influence of external force and temperature field on the evolution of vorticity near the surface is studied. It is shown that at relatively short times, the behavior of the resulting tornado-like vortices near the surface is universal and weakly depends on the external force and temperature field. However, over time, this influence becomes significant. It is shown that, depending on the presence of an anomaly in the temperature distribution, the vortex formed at the surface can exist for a long time.

Stable three-dimensional vortex families consistent with Jovian observations including the Great Red Spot

Detailed observations of the velocities of Jovian vortices exist at only one height in the atmosphere, so their vertical structures are poorly understood. This motivates this study that computes stable three-dimensional, long-lived planetary vortices that satisfy the equations of motion. We solve the anelastic equations with a high-resolution pseudo-spectral method using the observed Jovian atmospheric temperatures and zonal flow. We examine several families of vortices and find that constant-vorticity vortices, which have nearly uniform vorticity as a function of height, and horizontal areas that go to zero at their tops and bottoms, converge to stable vortices that look like the Great Red Spot (GRS) and other Jovian anticyclones. In contrast, the constant-area vortices proposed in previous studies, which have nearly uniform areas as a function of height, and vertical vorticities that go to zero at their tops and bottoms, are far from equilibrium, break apart, and converge to constant-vorticity vortices. Our late-time vortices show unexpected properties. Vortices that are initially non-hollow become hollow (i.e. have local minima of vertical vorticity at their centres), which is a feature of the GRS that cannot be explained with two-dimensional simulations. The central axes of the final vortices align with the planetary spin axis even if they align initially with the local direction of gravity. We present scaling laws for how vortex properties change with the Rossby number and other non-dimensional parameters. We prove analytically that the horizontal mid-plane of a stable vortex must lie at a height above the top of the convective zone.

Mechanisms Accounting for the Formation of the Strong Winds that Caused the Tripping Incident of Transmission Line in Eastern Inner Mongolia

Meteorological disasters pose a serious threat to the State Grid Corporation of China, which covers ~ 88% of Chinese national territory. Of these, strong winds deserve a special attention, as they often induce windage yaw discharge of transmission lines and even toppling of transmission towers, resulting in serious economic losses. On 28 June 2023, a severe tripping incident of transmission line appears in Eastern Inner Mongolia due to strong winds. In this study, we conduct comprehensive analyses to clarify the favorable background conditions and governing mechanisms for producing the strong winds. Main results are shown as follows. Synoptic analysis indicates that, the favorable background environments for the event are characterized by a strong upper-level jet associated upper tropospheric divergence; an intense middle-level warm advection ahead of a shortwave trough; and a long-lived lower-tropospheric mesoscale vortex. The strong winds that cause the tripping incident mainly occur in the southeastern quadrant of the vortex. Vorticity budget presents that the period from the mesoscale-vortex’s formation to 4 h before is crucial to the mesoscale vortex, as cyclonic vorticity increases rapidly mainly due to the lower-level convergence-related vertical stretching. In contrast, the horizontal transport mainly results in a net export of cyclonic vorticity, which is the most detrimental factor. Kinetic energy (KE) budget shows that, after the mesoscale vortex forms, the strong winds within its southeastern quadrant enhance rapidly. Overall, the positive work done by the pressure gradient force associated with the mesoscale vortex dominates the enhancement of strong winds; the horizontal transport of KE is the second dominant factor, and the vertical transport of KE (i.e., the downward momentum transportation) shows the least contribution.

Simulation and Analysis of the Mesoscale Vortex Affecting the “21·7” Extreme Rainstorm in Henan

From 17 to 22 July 2021, the “21·7” extreme rainfall event (“21·7” ERE) hit Henan Province, breaking the record for mainland China with a maximum hourly rainfall of 201.9 mm at the Zhengzhou station. The long-lived (20 h) mesoscale Huang-Huai vortex (HHV) was an important system that directly affected the major rainfall stage, including the extreme hourly rainfall. This study investigates the formation and development mechanism of the HHV, as well as its association with the simulation of extreme hourly rainfall through numerical simulations. The simulated rainfall and radar composite reflectivity were in good agreement with the observations, thus effectively reproducing the generation and developmental process of the HHV. The analysis results showed that the HHV initially formed at 850 hPa on 19 July at 1800 UTC and eventually developed to 550 hPa. The positive feedback formed by the horizontal convergence and vertical vorticity transport was the main mechanism leading to the generation and deepening of the HHV. The stretching effect (STR) term played an absolutely dominant role in the increase in the vorticity tendency, and it primarily originated from the coupling effect of boundary layer jets (BLJs) and synoptic-weather-system-related low-level jets (SLLJs). The accurate simulation of the HHV allowed the early rainfall to reasonably reproduce the surface cold pool near the Zhengzhou station, and then the cooperation of the SLLJs, the BLJs, and the cold pool made the simulated extreme hourly rainfall exactly close to the Zhengzhou station, but with a weaker intensity, due to the fact that the HHV moved northeastward after its formation, resulting in a narrow range of southerly flow in southern Henan, which is not conducive to convective triggering in the southerly flow.

Review of studies on the distribution of Antarctic krill accumulations in the Scotia Sea and analysis of mesoscale dynamics of its habitat

This article studies the mesoscale dynamics of the waters of the Scotia Sea, located at the northern tip of the Southern Ocean on its border with the Southern Atlantic Ocean. The Scotia Sea is one of the most promising fishing areas where the industrial catch of Antarctic krill (Euphausia superba) is produced. Since the distribution of commercial krill accumulations is largely determined by oceanological conditions, this paper analyzes mesoscale vortex dynamics, frontal zones, and topography in the Scotia Sea, affecting the creation of favorable oceanological conditions for the formation of commercial krill accumulations. The study is conducted using satellite and model data. It is shown that the distribution of sea level according to the GLORYS12v1 reanalysis data in the Scotia Sea has a zonal character. In winter and spring, sea level anomalies are positive (up to 20 cm), and in summer and autumn, they are negative (up to -180 cm). In the northwestern part of the Scotia Sea, according to the data of the GLORYS12v1 reanalysis for 1993-2020, thermal frontal zones with high repeatability (> 80%) are distinguished. Dynamic frontal zones are also distinguished in the northwestern part of the water area and have a repeatability reaching 100%. This area in the Scotia Sea is the most dynamically active: increased kinetic energy values are observed here. The increased dynamic activity in the northwestern part of the Scotia Sea, considered above by the average and average seasonal distributions of characteristics, is also confirmed in the synoptic range of periods. Spatial distributions of long-lived mesoscale vortices according to META 3.2 data for 1993-2021 show the localization areas of these vortices, with cyclones forming significantly more than anticyclones. Analysis of the trajectories of these vortices showed that the direction of their propagation is mainly eastern. The intense vortex dynamics in the Scotia Sea is also confirmed by reconstructed altimetric data for 1970-1992.

The Importance of Being Asymmetric for Geophysical Vortices

Several types of spatial symmetry in vortex structures within rotating stratified fluids are examined by looking at self-propagating configurations in the quasigeostrophic model. The role of symmetry breaking in the dynamics of geophysical waves, vortices and instabilities is highlighted. In particular, the energy exchange of the large-scale vertical shear with monopolar and dipolar vortices is analyzed. Various coupled vortex-wave structures are described in terms of wavy and evanescent modes. The Rossby wave radiation is shown to induce a zonal asymmetry, which is needed for the energy support and self-amplification of vortices in large-scale flow. The consequences for the evolution of the most long-lived vortices in the subtropical westward flows are discussed.

Vortex dynamics in rotating Rayleigh–Bénard convection

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh–Bénard convection in a reduced Rayleigh number range $1.3\le Ra/Ra_{c}\le 83.1$ . Under slow rotations ( $Ra\approx 80\,Ra_{c}$ ), the vortices are distributed randomly, which is manifested by the size distribution of the Voronoi cells of the vortex centres being a standard $\varGamma$ distribution. The vortices exhibit Brownian-type horizontal motion in the parameter range $Ra\gtrsim 10\,Ra_{c}$ . The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ( $4\,Ra_{c}\le Ra\lesssim 10\,Ra_{c}$ ), the centrifugal force leads to radial vortex motions, i.e. warm cyclones (cold anticyclones) moving towards (outwards from) the rotation axis. The horizontal scale of the vortices decreases with decreasing $Ra/Ra_c$ , and the size distribution of their Voronoi cells deviates from the $\varGamma$ distribution. In the rapidly rotating regime ( $1.6\,Ra_{c}\le Ra\le 4\,Ra_{c}$ ), the vortices are densely distributed. The hydrodynamic interaction of neighbouring vortices results in the formation of vortex clusters. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the outward motion of the strong anticyclones, and the radial velocity of the anticyclones is enhanced. The radial mobility of isolated vortices, scaled by their vorticity strength, is shown to be a simple power function of the Froude number. For all flow regimes studied, we show that the number of vortices with a lifespan greater than $t$ decreases exponentially as $\exp ({-t/{\tau }})$ for large time, where $\tau$ represents the characteristic lifetime of long-lived vortices.

Mechanisms Governing the Formation and Long-Term Sustainment of a Northeastward Moving Southwest Vortex

From 10 July to 12 July 2021, a long-lived (~66 h) southwest vortex (SWV), moved from Southwest China to Northeast China and caused a series of heavy rainfall events. This SWV case was rarely seen, as its lifespan was much longer than the SWVs’ mean lifespan, and the vast majority of SWVs showed a quasi-stationary behavior. It was found that the SWV formed and sustained in favorable background environments, which were characterized by a strong upper-level divergence (related to the South Asia High), a notable middle-tropospheric warm advection (related to a shortwave trough), and a vigorous low-level jet. The SWV showed remarkable interactions with a middle-tropospheric mesoscale vortex. The strong southwesterly wind in the eastern section of a deep shortwave trough east of the Tibetan Plateau acted as the steering flow for the northeastward movement of both vortices. Vorticity budget showed that the convergence-related vertical stretching dominated the SWV’s formation and development; the convection-related upward transport of cyclonic vorticity was the most favorable factor for the SWV’s sustainment, whereas, during the decaying stage, the SWV dissipated mainly due to the tilting effects and the net export transport of cyclonic vorticity. Backward trajectory analyses showed that most of the air particles that formed the SWV (at its formation time) were sourced from the lower troposphere. These air particles mainly ascended and experienced a rapid increase in cyclonic vorticity during the SWV’s formation stage. The topography of the Yunnan–Guizhou Plateau was crucial for the SWV’s formation, as around a half of the air particles (that formed the SWV) came from this region. Most of these air particles enhanced in their cyclonic vorticity and convergence when they descended along the topography of the plateau.

Friction-enhanced lifetime of bundled quantum vortices

Experiments in the early 1980s have shown that a compact bundle of quantum vortex rings in superfluid helium remains coherent and travels a significant distance compared to its size. This is surprising because a single vortex ring, under the effect of friction with the background of thermal excitations (the so-called normal fluid), would quickly lose energy and decay. The observation of these long-lived vortex structures has remained an unsettled question since their experimental detection. In this work, by taking into account the fully coupled dynamics of superfluid vortices and the normal fluid, we show that the motion of the superfluid bundle generates a large-scale wake in the normal fluid which reduces the overall friction experienced by the bundle, enhancing its lifetime. This collective effect is similar to the drag reduction observed in systems of active, hydrodynamically cooperative agents such as bacteria in aqueous suspensions, fungal spores in the atmosphere and cyclists in pelotons.

Statistics of clustered vortices in the inverse energy cascade of two-dimensional turbulence

Strong, long-lived vortices play a prominent role in two-dimensional (2D) turbulent flows, and understanding their statistics is key to unravelling 2D turbulence. Here it is shown that clustered same-sign vortices in forced 2D turbulence have a scale-invariant distribution of areas and are described by a mean-field theory. Larger clusters come apart more quickly, and the flow surrounding the remaining clusters becomes progressively more randomized and neutral, while vortex merger concentrates coherent enstrophy into a smaller and smaller fraction of the domain.

Large Eddy Simulation of a sediment particle under entrainment conditions

A Large Eddy Simulation of a fully developed turbulent open-channel flow with a Reynolds number of was performed to study dynamics of coherent structures in the vicinity of a stationary sediment particle. The sediment particle was positioned at the bottom on a smooth channel bed. The impulse concept was employed by computing three-dimensional hydrodynamic forces acting on the sediment particle in order to predict the onset of particle motion. Results of quadrant analyses at high impulse events yielded mostly outward and sweep events. Auto- and cross-correlation of the hydrodynamic forces and the flow field were studied and discussed. An identification of coherent structures at high impulse events showed that large-scale, long-lived hairpin-like vortices whose bed-normal lengths are larger than viscous units were resulting in an increase of lift and drag forces simultaneously, facilitating initiation of particle motion.

Substructures in Protoplanetary Disks Imprinted by Compact Planetary Systems

The substructures observed in protoplanetary disks may be the signposts of embedded planets carving gaps or creating vortices. The inferred masses of these planets often fall in the Jovian regime despite their low abundance compared to lower-mass planets, partly because previous works often assume that a single substructure (a gap or vortex) is caused by a single planet. In this work, we study the possible imprints of compact systems composed of Neptune-like planets (∼10–30 M ⊕) and show that long-standing vortices are a prevalent outcome when their interplanetary separation (Δa) falls below ∼8 times H p—the average disk’s scale height at the planet’s locations. In simulations where a single planet is unable to produce long-lived vortices, two-planet systems can preserve them for at least 5000 orbits in two regimes: (i) fully shared density gaps with elongated vortices around the stable Lagrange points L 4 and L 5 for the most compact planet pairs (Δa ≲ 4.6 H p), and (ii) partially shared gaps for more widely spaced planets (Δa ∼ 4.6–8 H p) forming vortices in a density ring between the planets through the Rossby wave instability. The latter case can produce vortices with a wide range of aspect ratios down to ∼3 and can occur for planets captured into the 3:2 (2:1) mean-motion resonances for disks’ aspects ratios of h ≳ 0.033 (h ≳ 0.057). We suggest that their long lifetimes are sustained by the interaction of spiral density waves launched by the neighboring planets. Overall, our results show that the distinguishing imprint of compact systems with Neptune-mass planets are long-lived vortices inside the density gaps, which in turn are shallower than single-planet gaps for a fixed gap width.

Characteristics of long-track tropopause polar vortices

Abstract. Tropopause polar vortices (TPVs) are closed circulations centered on the tropopause that form and predominately reside in high latitudes. Due to their attendant flow, TPVs have been shown to influence surface weather features, and thus, a greater understanding of the dynamics of these features may improve our ability to forecast impactful weather events. In this study, we focus on the subset of TPVs that have lifetimes of longer than 2 weeks (the 95th percentile of all TPV cases between 1979 and 2018); these long-lived vortices offer a unique opportunity to study the conditions under which TPVs strengthen and analyze patterns of vortex formation and movement. Using ERA-Interim data, along with TPV tracks derived from the same reanalysis, we investigate the formation, motion, and development of these long-lived vortices. We find that these TPVs are significantly stronger, occur more often in the summer, and tend to remain more poleward than an average TPV. Similarly, these TPVs are shown to form at higher latitudes than average. Long-lived TPVs form predominately by splitting from existing vortices, but a notable minority seem to generate via dynamic processes in the absence of pre-existing TPVs. These non-likely split genesis events are found to occur in select geographic regions, driven by Rossby wave growth and breaking. Seasonal variations emerge in the life cycles of long-lived vortices; notably, winter TPVs progress more equatorward and generally grow to stronger amplitudes. These long-lived TPVs also appear as likely as any TPV to exit the Arctic and move into the mid-latitudes, doing so via two primary pathways: through Canada or Siberia.

Impact of local pressure enhancements on dust concentration in turbulent protoplanetary discs

The standard core accretion model for planetesimal formation in protoplanetary discs (PPDs) is subject to a number of challenges. One is related to the vertical settling of dust to the disc mid-plane against turbulent stirring. This is particularly relevant in the presence of the vertical shear instability (VSI), a purely hydrodynamic instability applicable to the outer parts of PPDs, which drives moderate turbulence characterized by large-scale vertical motions. We investigate the evolution of dust and gas in the vicinity of local pressure enhancements (pressure bumps) in a PPD with turbulence sustained by the VSI. Our goal is to determine the morphology of dust concentrations and if dust can concentrate sufficiently to reach conditions that can trigger the streaming instability (SI). We performed a suite of global 2D axisymmetric and 3D simulations of dust and gas for a range of values for Σd∕Σg (ratio of dust-to-gas surface mass densities or metallicity), particle Stokes numbers, τ, and pressure bump amplitude, A. Dust feedback onto the gas is included. For the first time, we use global 3D simulations to demonstrate the collection of dust in long-lived vortices induced by the VSI. These vortices, which undergo a slow radial inward drift, are the dusty analogs of large long-lived vortices found in previous dust-free simulations of the VSI. Without a pressure bump and for solar metallicity Z ≈ 0.01 and Stokes numbers τ ~ 10−2, we find that such vortices can reach dust-to-gas density ratios slightly below unity in the discs’ mid-plane, while for Z ≳ 0.05, long-lived vortices are largely absent. In the presence of a pressure bump, for Z ≈ 0.01 and τ ~ 10−2, a dusty vortex forms that reaches dust-to-gas ratios of a few times unity, such that the SI is expected to develop, before it eventually shears out into a turbulent dust ring. At intermediate metallicities, Z ~ 0.03, this occurs for τ ~ 5 × 10−3, but with a weaker and more short-lived vortex, while for larger τ, only a turbulent dust ring forms. For Z ≳ 0.03, we find that the dust ring becomes increasingly axisymmetric for increasing τ and dust-to-gas ratios reach order unity for τ ≳ 5 × 10−3. Furthermore, the vertical mass flow profile of the disc is strongly affected by dust for Z ≳ 0.03, such that gas is transported inward near the mid-plane and outward at larger heights, which is the reversed situation compared to simulations with zero or small amounts of dust. We find viscous α-values to drop moderately as ~10−3–10−4 for metallicities increasing as Z = 0–0.05. Our results suggest that the VSI can play an active role in the formation of planetesimals through the formation of vortices for plausible values of metallicity and particle size. Also, it may provide a natural explanation for the presence or absence of asymmetries of observed dust rings in PPDs, depending on the background metallicity.

Mechanisms governing the evolution of a long-lived northwest vortex that caused a series of disasters in Northwest China

The northwest vortex (NWV) is a type of mesoscale vortex that appears with a relatively high frequency in Northwest China. To further the understanding of the NWV's evolution, in this study, the moisture and circulation budgets of a long-lived NWV (∼132 h) that appeared in early August 2019 were calculated. This vortex induced a series of torrential rainfall events in Northwest China and Mongolia, which caused severe transmission line faults and urban waterlogging. Synoptic analyses indicate that the NWV was generated in a favorable background environment characterized by notable upper-level divergence and strong mid-level warm advection. The moisture budget shows that the East China Sea and Bohai Sea acted as the main moisture sources for the NWV-associated precipitation, and the water vapor was transported into the rainfall regions mainly by easterly and southeasterly winds. The circulation budget indicates that, during the developing stage, convergence-related vertical stretching was a dominant factor for the NWV's development; whereas, the vortex's displacement from regions with stronger cyclonic vorticity to those with weaker cyclonic vorticity mainly decelerated its development. In the decaying stage, divergence-related vertical shrinking and the net export of cyclonic vorticity due to the eddy flow's transport resulted in the NWV's dissipation.摘要西北涡是我国西北地区一类发生频率较高的中尺度涡旋, 其所引发灾害的强度与西南低涡, 高原涡相当, 但相关研究却远远少于前两种涡旋.为了深化对西北涡的认识, 本文利用水汽与环流收支对一次长生命史西北涡 (其在西北地区引发了一系列暴雨过程, 导致了严重的输电线路故障与城市内涝) 进行了研究, 发现, 东海与渤海是此西北涡引发暴雨的主要水汽来源, 东风与东南风则是主要的输送气流. 辐合所引起的垂直伸展是西北涡发展的主导因子, 而涡旋由较强背景涡度区向较弱背景涡度区的移动则一定程度上延缓了涡旋的发展.

Collective excitations in active fluids: Microflows and breakdown in spectral equipartition of kinetic energy.

The effect of particle activity on collective excitations in active fluids of microflyers is studied. With an in silico study, we observed an oscillating breakdown of equipartition (uniform spectral distribution) of kinetic energy in reciprocal space. The phenomenon is related to short-range velocity-velocity correlations that were realized without forming of long-lived mesoscale vortices in the system. This stands in contrast to well-known mesoscale turbulence operating in active nematic systems (bacterial or artificial) and reveals the features of collective dynamics in active fluids, which should be important for structural transitions and glassy dynamics in active matter.

The Sandwich Mode for Vertical Shear Instability in Protoplanetary Disks

Abstract Turbulence has a profound impact on the evolution of gas and dust in protoplanetary disks (PPDs), from driving the collisions and the diffusion of dust grains, to the concentration of pebbles in giant vortices, thus, facilitating planetesimal formation. The vertical shear instability (VSI) is a hydrodynamic mechanism, operating in PPDs if the local rate of thermal relaxation is high enough. Previous studies of the VSI have, however, relied on the assumption of constant cooling rates, or neglected the finite coupling time between the gas particles and the dust grains. Here, we present the results of hydrodynamic simulations of PPDs with the PLUTO code that include a more realistic thermal relaxation prescription, which enables us to study the VSI in the optically thick and optically thin parts of the disk under consideration of the thermal dust-gas coupling. We show the VSI to cause turbulence even in the optically thick inner regions of PPDs in our two- and three-dimensional simulations. The collisional decoupling of dust and gas particles in the upper atmosphere and the correspondingly inefficient thermal relaxation rates lead to the damping of the VSI turbulence. Long-lived anticyclonic vortices form in our three-dimensional simulation. These structures emerge from the turbulence in the VSI-active layer, persist over hundreds of orbits and extend vertically over the whole extent of the turbulent region. We conclude that the VSI leads to turbulence and the formation of long-lived dust traps within ±3 pressure scale heights distance from the disk midplane.