Vertical Shear Instability Research Articles

Vertical Shear Instability with Partially Reflecting Boundary Conditions

Abstract The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary disks. Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disk surfaces. VSI depends critically on the boundary behaviors of waves at the disk surfaces. We extend earlier studies by performing a comprehensive numerical analysis of VSI with partially reflecting BCs for both the axisymmetric and non-axisymmetric unstable VSI modes. We find that the growth rates of the unstable modes diminish when the outgoing component of the flow is greater than the incoming one for high-order body modes. When the outgoing wave component dominates, the growth of VSI is notably suppressed. We find that the non-axisymmetric modes are unstable and they grow at a rate that decreases with the azimuthal wavenumber. The different BCs at the lower and upper disk surfaces naturally lead to non-symmetric modes relative to the disk midplane. The potential implications of our studies for further understanding planetary formation and evolution in protoplanetary disks (PPDs) are also briefly discussed.

Vertical shear instability with dust evolution and consistent cooling times

Context. Gas in protoplanetary disks mostly cools via thermal accommodation with dust particles. Thermal relaxation is thus highly sensitive to the local dust size distributions and the spatial distribution of the grains. So far, the interplay between thermal relaxation and gas turbulence has not been dynamically modeled in hydrodynamic simulations of protoplanetary disks with dust. Aims. We aim to study the effects of the vertical shear instability (VSI) on the thermal relaxation times, and vice versa. We are particularly interested in the influence of the initial dust grain size on the VSI and whether the emerging turbulence is sustained over long timescales. Methods. We ran three axisymmetric hydrodynamic simulations of a protoplanetary disk including four dust fluids that initially resemble MRN size distributions of different initial grain sizes. From the local dust densities, we calculated the thermal accommodation timescale of dust and gas and used the result as the thermal relaxation time of the gas in our simulation. We included the effect of dust growth by applying the monodisperse dust growth rate and the typical growth limits. Results. We find that the emergence of the VSI is strongly dependent on the initial dust grain size. Coagulation also counteracts the emergence of hydrodynamic turbulence in our simulations, as shown by others before. Starting a simulation with larger grains (100 μm) generally leads to a less turbulent outcome. While the inner disk regions (within ∼70 au) develop turbulence in all three simulations, we find that the simulations with larger particles do not develop VSI in the outer disk. Conclusions. Our simulations with dynamically calculated thermal accommodation times based on the drifting and settling dust distribution show that the VSI, once developed in a disk, can be sustained over long timescales, even if grain growth is occurring. The VSI corrugates the dust layer and even diffuses the smaller grains into the upper atmosphere, where they can cool the gas. Whether the instability can emerge for a specific stratification depends on the initial dust grain sizes and the initial dust scale height. If the grains are initially ≳100 μm and if the level of turbulence is initially assumed to be low, we find no VSI turbulence in the outer disk regions.

Thermal Structure Determines Kinematics: Vertical Shear Instability in Stellar Irradiated Protoplanetary Disks

Turbulence is crucial for protoplanetary disk dynamics, and vertical shear instability (VSI) is a promising mechanism in outer disk regions to generate turbulence. We use the Athena++ radiation module to study VSI in full and transition disks, accounting for radiation transport and stellar irradiation. We find that the thermal structure and cooling timescale significantly influence VSI behavior. The inner rim location and radial optical depth affect disk kinematics. Compared with previous vertically isothermal simulations, our full disk and transition disks with small cavities have a superheated atmosphere and cool midplane with long cooling timescales, which suppresses the corrugation mode and the associated meridional circulation. This temperature structure also produces a strong vertical shear at τ * = 1, producing an outgoing flow layer at τ * < 1 on top of an ingoing flow layer at τ * ∼ 1. The midplane becomes less turbulent, while the surface becomes more turbulent with effective α reaching ∼10−2 at τ * ≲ 1. This large surface stress drives significant surface accretion, producing substructures. Using temperature and cooling time measured/estimated from radiation-hydro simulations, we demonstrate that less computationally intensive simulations incorporating simple orbital cooling can almost reproduce radiation-hydro results. By generating synthetic images, we find that substructures are more pronounced in disks with larger cavities. The higher velocity dispersion at the gap edge could also slow particle settling. Both properties are consistent with recent near-IR and Atacama Large Millimeter/submillimeter Array (ALMA) observations. Our simulations predict that regions with significant temperature changes are accompanied by significant velocity changes, which can be tested by ALMA kinematics/chemistry observations.

MATRICS: The implicit matrix-free Eulerian hydrodynamics solver

Context. There exists a zoo of different astrophysical fluid dynamics solvers, most of which are based on an explicit formulation and hence stability-limited to small time steps dictated by the Courant number expressing the local speed of sound. With this limitation, the modeling of low-Mach-number flows requires small time steps that introduce significant numerical diffusion, and a large amount of computational resources are needed. On the other hand, implicit methods are often developed to exclusively model the fully incompressible or 1D case since they require the construction and solution of one or more large (non)linear systems per time step, for which direct matrix inversion procedures become unacceptably slow in two or more dimensions. Aims. In this work, we present a globally implicit 3D axisymmetric Eulerian solver for the compressible Navier–Stokes equations including the energy equation using conservative formulation and a fully simultaneous approach. We use the second-order-in-time backward differentiation formula for temporal discretization as well as the κ scheme for spatial discretization. We implement different limiter functions to prohibit the occurrence of spurious oscillations in the vicinity of discontinuities. Our method resembles the well-known monotone upwind scheme for conservation laws (MUSCL). We briefly present efficient solution methods for the arising sparse and nonlinear system of equations. Methods. To deal with the nonlinearity of the Navier–Stokes equations we used a Newton iteration procedure in which the required Jacobian matrix-vector product was reconstructed with a first-order finite difference approximation to machine precision in a matrix-free way. The resulting linear system was solved either completely matrix-free with a combination of a sufficient Krylov solver and an approximate Jacobian preconditioner or semi-matrix-free with the incomplete lower upper factorization technique as a preconditioner. The latter was dependent on a standalone approximation of the Jacobian matrix, which was optionally calculated and needed solely for the purpose of preconditioning. Results. We show our method to be capable of damping sound waves and resolving shocks even at Courant numbers larger than one. Furthermore, we prove the method’s ability to solve boundary value problems like the cylindrical Taylor-Couette flow (TC), including viscosity, and to model transition flows. To show the latter, we recover predicted growth rates for the vertical shear instability, while choosing a time step orders of magnitude larger than the explicit one. Finally, we verify that our method is second order in space by simulating a simplistic, stationary solar wind.

Energy Partition between Submesoscale Internal Waves and Quasigeostrophic Vortical Motion in the Pycnocline

Abstract Shipboard ADCP velocity and towed CTD chain density measurements from the eastern North Pacific pycnocline are used to segregate energy between linear internal waves (IW) and linear vortical motion [quasigeostrophy (QG)] in 2D wavenumber space spanning submesoscale horizontal wavelengths λx ∼ 1–50 km and finescale vertical wavelengths λz ∼ 7–100 m. Helmholtz decomposition and a new Burger number (Bu) decomposition yield similar results despite different methodologies. While these wavelengths are conventionally attributed to internal waves, both QG and IW contribute significantly at all measured scales. Partition between IW and QG total energies depends on Bu. For Bu &lt; 0.01, available potential energy EP exceeds horizontal kinetic energy EK and is contributed mostly by QG. In contrast, energy is nearly equipartitioned between QG and IW for Bu ≫ 1. For Bu &lt; 2, EK is contributed mainly by IW, and EP by QG, while, for Bu &gt; 2, contributions are reversed. Finescale near-inertial IW dominate vertical shear variance, implying negligible QG contribution to vertical shear instability. In contrast, both QG and IW at the smallest λx ∼ 1 km contribute large horizontal shear variance, so that both may lead to horizontal shear instability, while QG, with its longer time scales, likely dominates isopycnal stirring. Both QG and IW contribute to vortex stretching at small vertical scales. For QG, the relative vorticity contribution to linear potential vorticity anomaly increases with decreasing horizontal and increasing vertical scales.

A self-consistent model for dust settling and the vertical shear instability in protoplanetary disks

Abstract The spatial distribution of dust particles in protoplanetary disks affects dust evolution and planetesimal formation processes. The vertical shear instability (VSI) is one of the candidate hydrodynamic mechanisms that can generate turbulence in the outer disk region and affect dust diffusion. Turbulence driven by the VSI has a predominant vertical motion that can prevent dust settling. On the other hand, the dust distribution controls the spatial distribution of the gas cooling rate, thereby affecting the strength of VSI-driven turbulence. Here, we present a semi-analytic model that determines the vertical dust distribution and the strength of VSI-driven turbulence in a self-consistent manner. The model uses an empirical formula for the vertical diffusion coefficient in VSI-driven turbulence obtained from our recent hydrodynamical simulations. The formula returns the vertical diffusion coefficient as a function of the vertical profile of the cooling rate, which is determined by the vertical dust distribution. We use this model to search for an equilibrium vertical dust profile where settling balances with turbulent diffusion for a given maximum grain size. We find that if the grains are sufficiently small, there exists a stable equilibrium dust distribution where VSI-driven turbulence is sustained at a level of αz ∼ 10−3, where αz is the dimensionless vertical diffusion coefficient. However, as the maximum grain size increases, the equilibrium solution vanishes because the VSI can no longer stop the settling of the grains. This runaway settling may explain highly settled dust rings found in the outer part of some protoplanetary disks.

Length and Velocity Scales in Protoplanetary Disk Turbulence

In the theory of protoplanetary disk turbulence, a widely adopted ansatz, or assumption, is that the turnover frequency of the largest turbulent eddy, Ω L , is the local Keplerian frequency Ω K . In terms of the standard dimensionless Shakura–Sunyaev α parameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by αH and αc , in which H and c are the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as vertical shear instability. Here, we explore the more general case where Ω L ≥ Ω K and show that, under these conditions, the characteristic length and velocity scales are respectively α/R′H and αR′c , where R′≡ΩL/ΩK is twice the Rossby number. It follows that α=α˜/R′ , where α˜c is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and it may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For R′>1 , the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation.

Dynamics of cold circumstellar gas in debris disks

Abstract Mounting observational evidence indicates that cold circumstellar gas is present in debris disk systems. This work focuses on various dynamical processes that debris-disk gas may undergo. We review five mechanisms that can transport angular momentum and their applications to debris disks. These include molecular viscosity, hydrodynamic turbulence, magnetohydrodynamic turbulence, magnetized disk winds, and laminar magnetic stress. We find that molecular viscosity can result in α as high as ≲ 0.1 for sufficiently low densities, while the Rossby wave instability is a possible source of hydrodynamic turbulence and structure formation. We argue that the vertical shear instability is unlikely due to the long cooling times. The onset of the magnetorotational instability (MRI) is dichotomous: for low density disks the MRI can be excited at the midplane, while for high mass disks it may only be operating at z &amp;gt; 2 − 3H, if at all. The MHD wind and laminar magnetic stress mechanisms rely on the configuration and strength of any background large-scale magnetic field, the existence of which is uncertain and possibly unlikely. We conclude that the dominant mechanism and its efficiency in transporting angular momentum varies from one system to the other, depending especially closely on the gas density. More detailed analyses shall be performed in the future focusing on representative, nearby debris disks.

Evidence for layered anisotropic stratified turbulence in a freely evolving horizontal shear flow

We present evidence for layered anisotropic stratified turbulence (LAST) and mixing produced in a freely evolving uniformly stratified shear layer where the direction of shear is orthogonal to gravity. As originally reported by Basak &amp; Sarkar (J. Fluid. Mech., vol. 568, 2006, pp. 19–54), such a flow develops a rich three-dimensional structure in the form of interlocking columnar vortices formed by horizontal shear instability that remain coherent at large scales due to the stabilising vertical stratification. Here, we modify the initial velocity field by introducing additional small-amplitude vertical perturbations designed to be representative of pre-existing horizontal layers often observed in strongly stratified ocean environments. This reveals a novel finite amplitude, non-normal mode growth mechanism through which the vertical shear between layers may be rapidly amplified by its interaction with the horizontal shear layer prior to the growth of shear instability, leading to a rapid turbulent transition instigated by the subsequent interaction of the layers with the emerging columnar vortices. Through a consideration of relevant flow statistics and associated dimensionless parameters, we demonstrate that turbulence can enter the LAST regime, thereby indicating a generic mechanism leading to the transient development of regions of strongly stratified turbulence in the ocean. We discuss the properties of mixing and the parameterisation of mixing efficiency in terms of the relationship between turbulent length scales in the flow, in particular highlighting links to models based on the classical vertical shear instability paradigm typically associated with more weakly stratified flows that produce isolated turbulent ‘patches’.

Kinematic signatures of planet–disk interactions in vertical shear instability-turbulent protoplanetary disks

Context. Planets are thought to form inside weakly ionized regions of protoplanetary disks, where turbulence creates ideal conditions for solid growth. However, the nature of this turbulence is still uncertain. In fast cooling parts of this zone the vertical shear instability (VSI) can operate, inducing a low level of gas turbulence and large-scale gas motions. Resolving the kinematic signatures of active VSI could reveal the origin of turbulence in planet-forming disk regions. However, an exploration of kinematic signatures of the interplay between VSI and forming planets is needed for a correct interpretation of radio interferometric observations. A robust detection of VSI would lead the way to a deeper understanding of the impact of gas turbulence on planet formation. Aims. The objective of this study is to explore the effect of VSI on the disk substructures triggered by an embedded fairly massive planet. We focus on the impact of this interplay on CO kinematic observations with the ALMA interferometer. Methods. We conducted global 3D hydrodynamical simulations of VSI-unstable disks with and without embedded massive planets, exploring Saturn- and Jupiter-mass cases. We studied the effect of planets on the VSI gas dynamics, and made a comparison with viscous disks. Post-processing the simulations with a radiative transfer code, we examined the kinematic signatures expected in CO molecular line emission, varying disk inclination. Further, we simulated deep ALMA high-resolution observations of our synthetic images, to test the observability of VSI and planetary signatures. Results. The embedded planet produces a damping of the VSI along a radial region, most effective at the disk midplane. For the Saturn case, the VSI modes are distorted by the planet’s spirals producing mixed kinematic signatures. For the Jupiter case, the planet’s influence dominates the overall disk gas kinematics. Conclusions. The presence of massive planets embedded in the disk can weaken the VSI large-scale gas flows, limiting its observability in CO kinematic observations with ALMA.

Microscale Updrafts within Northeast U.S. Coastal Snowstorms Using High-Resolution Cloud Radar Measurements

Abstract Limited knowledge exists about ∼100-m-scale precipitation processes within U.S. northeast coastal snowstorms because of a lack of high-resolution observations. We investigate characteristics of microscale updraft regions within the cyclone comma head and their relationships with snowbands, wind shear, frontogenesis, and vertical mass flux using high-spatiotemporal-resolution vertically pointing Ka-band radar measurements, soundings, and reanalysis data for four snowstorms observed at Stony Brook, New York. Updraft regions are defined as contiguous time–height plotted areas with upward Doppler velocity without hydrometeor sedimentation that is equal to or greater than 0.4 m s−1. Most updraft regions in the time–height data occur on a time scale of seconds (&lt;20 s), which is equivalent to spatial scales &lt; 500 m. These small updraft regions within cloud echo occur more than 30% of the time for three of the four cases and 18% for the other case. They are found at all altitudes and can occur with or without frontogenesis and with or without snowbands. The updraft regions with relatively large Doppler spectrum width (&gt;0.4 m s−1) occur more frequently within midlevels of the storms, where there are strong wind shear layers and moist shear instability layers. This suggests that the dominant forcing for the updrafts appears to be turbulence associated with the vertical shear instability. The updraft regions can be responsible for upward mass flux when they are closer together in space and time. The higher values of column mean upward mass flux often occur during snowband periods. Significance Statement Small-scale (&lt;500 m) upward motions within four snowstorms along the U.S. northeast coast are analyzed for the first time using high-spatiotemporal-resolution millimeter-wavelength cloud radar pointed vertically. The analysis reveals that updrafts appear in the storms regardless of whether snowbands are present or whether there is larger-scale forcing for ascent. The more turbulent and stronger updrafts frequently occur in midlevels of storms associated with instability from vertical shear and contribute to upward mass flux during snowband periods when they are closer together in space and time.

On corrugation mode radial wavelengths of the vertical shear instability

Abstract The vertical shear instability (VSI) is a promising mechanism to drive turbulence in protoplanetary disks. Numerical simulations in the literature demonstrate that the VSI non-linear saturation is predominated by the linear corrugation modes. These modes possess vertical wavelengths crucially longer than radial wavelengths. This paper aims to investigate the natural radial wavelength of corrugation modes upon VSI saturation, by a series of numerical simulations conducted in Athena++ at different grid resolutions, disk aspect ratios, and viscosity parameterized by ν. We find a sign of convergence emerges at 64 cells per gas scale height for fiducial simulations. Below it a continuous reduction of wavelengths with grid resolution is observed. Synthetic ALMA molecular line observations of $^{12}\rm CO(2-1)$ are performed to inspect the observability of the corrugation modes feature, which is significantly diminished with a resolution of 32 cells per scale height or above. Flared and viscous disks exhibiting longer saturation wavelengths may mitigate the observational difficulty.

Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks

Context. The vertical shear instability (VSI) is a hydrodynamical instability predicted to produce turbulence in magnetically inactive regions of protoplanetary disks. The regions in which this instability can occur and the physical phenomena leading to its saturation are a current matter of research. Aims. We explore the secondary instabilities triggered by the nonlinear evolution of the VSI and their role in its saturation. We also expand on previous investigations on stability regions by considering temperature stratifications enforced by stellar irradiation and radiative cooling, and including the effects of dust-gas collisions and molecular line emission. Methods. We modeled the gas-dust mixture in a circumstellar disk around a T Tauri star by means of high-resolution axisymmetric radiation-hydrodynamical simulations including stellar irradiation with frequency-dependent opacities, considering different degrees of depletion of small dust grains. Results. The flow pattern produced by the interplay of the axisymmetric VSI modes and the baroclinic torque forms bands of nearly uniform specific angular momentum. In the high-shear regions in between these bands, the Kelvin–Helmholtz instability (KHI) is triggered. A third instability mechanism, consisting of an amplification of eddies by baroclinic torques, forms meridional vortices with Mach numbers up to ∼0.4. Our stability analysis suggests that protoplanetary disks can be VSI-unstable in surface layers up to tens of au for reasonably high gas emissivities. Conclusions. The significant transfer of kinetic energy to small-scale eddies produced by the KHI and possibly even the baroclinic acceleration of eddies limit the maximum energy of the VSI modes, likely leading to the saturation of the VSI. Depending on the gas molecular composition, the VSI can operate at surface layers even in regions where the midplane is stable. This picture is consistent with current observations of disks showing thin midplane millimeter-sized dust layers while appearing vertically extended in optical and near-infrared wavelengths.

Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks

Context. Hydrodynamical instabilities are likely the main source of turbulence in weakly ionized regions of protoplanetary disks. Among these, the vertical shear instability (VSI) stands out as a rather robust mechanism due to its few requirements to operate, namely a baroclinic stratification, which is enforced by the balance of stellar heating and radiative cooling, and short thermal relaxation timescales. Aims. Our goal is to characterize the transport of angular momentum and the turbulent heating produced by the nonlinear evolution of the VSI in axisymmetric models of disks around T Tauri stars, considering varying degrees of depletion of small dust grains resulting from dust coagulation. We also explore the local applicability of both local and global VSI-stability criteria. Methods. We modeled the gas-dust mixture in our disk models by means of high-resolution axisymmetric radiation-hydrodynamical simulations including stellar irradiation with frequency-dependent opacities. This is the first study of this instability to rely on two-moment radiative transfer methods. Not only are these able to handle transport in both the optically thin and thick limits, but also they can be integrated via implicit-explicit methods, thus avoiding the employment of expensive global matrix solvers. This is done at the cost of artificially reducing the speed of light, which, as we verified for this work, does not introduce unphysical phenomena. Results. Given sufficient depletion of small grains (with a dust-to-gas mass ratio of 10% of our nominal value of 10−3 for &lt; 0.25 μm grains), the VSI can operate in surface disk layers while being inactive close to the midplane, resulting in a suppression of the VSI body modes. The VSI reduces the initial vertical shear in bands of approximately uniform specific angular momentum, whose formation is likely favored by the enforced axisymmetry. Similarities with Reynolds stresses and angular momentum distributions in 3D simulations suggest that the VSI-induced angular momentum mixing in the radial direction may be predominantly axisymmetric. The stability regions in our models are well explained by local stability criteria, while the employment of global criteria is still justifiable up to a few scale heights above the midplane, at least as long as VSI modes are radially optically thin. Turbulent heating produces only marginal temperature increases of at most 0.1% and 0.01% in the nominal and dust-depleted models, respectively, peaking at a few (approximately three) scale heights above the midplane. We conclude that it is unlikely that the VSI can, in general, lead to any significant temperature increase since that would either require it to efficiently operate in largely optically thick disk regions or to produce larger levels of turbulence than predicted by models of passive irradiated disks.

The Combined Effects of Vertical and Horizontal Shear Instabilities in Stellar Radiative Zones

Shear instabilities can be the source of significant amounts of turbulent mixing in stellar radiative zones. Past attempts at modeling their effects (either theoretically or using numerical simulations) have focused on idealized geometries, where the shear is either purely vertical or purely horizontal. In stars, however, the shear can have arbitrary directions with respect to gravity. In this work, we use direct numerical simulations to investigate the nonlinear saturation of shear instabilities in a stably stratified fluid, where the shear is sinusoidal in the horizontal direction and either constant or sinusoidal in the vertical direction. We find that in the parameter regime studied here (nondiffusive, fully turbulent flow), the mean vertical shear does not play any role in controlling the dynamics of the resulting turbulence, unless its Richardson number is smaller than 1 (approximately). As most stellar radiative regions have a Richardson number much greater than 1, our result implies that the vertical shear can essentially be ignored in the computation of the vertical mixing coefficient associated with shear instabilities for the purpose of stellar evolution calculations, even when it is much larger than the horizontal shear (as in the solar tachocline, for instance).

Dust Coagulation Reconciles Protoplanetary Disk Observations with the Vertical Shear Instability. I. Dust Coagulation and the VSI Dead Zone

Protoplanetary disks exhibit a vertical gradient in angular momentum, rendering them susceptible to the vertical shear instability (VSI). The most important condition for the onset of this mechanism is a short timescale of thermal relaxation (≲0.1 orbital timescales). Simulations of fully VSI active disks are characterized by turbulent, vertically extended dust layers. This is in contradiction with recent observations of the outer regions of some protoplanetary disks, which appear highly settled. In this work, we demonstrate that the process of dust coagulation can diminish the cooling rate of the gas in the outer disk and extinct the VSI activity. Our findings indicate that the turbulence strength is especially susceptible to variations in the fragmentation velocity of the grains. A small fragmentation velocity of ≈100 cm s−1 results in a fully turbulent simulation, whereas a value of ≈400 cm s−1 results in a laminar outer disk, being consistent with observations. We show that VSI turbulence remains relatively unaffected by variations in the maximum particle size in the inner disk regions. However, we find that dust coagulation can significantly suppress the occurrence of VSI turbulence at larger distances from the central star.

Uwarunkowania meteorologiczne silnych burz - analiza przypadku z 10 lipca 2020 roku

Considered the most dangerous type of thunderstorm, supercell thunderstorms appear in strictly defined meteorological conditions in the troposphere. Predicting their location is particularly problematic in an environment of strong vertical wind shear and low instability. An example of such a situation is the supercell that contributed to the development of the tornado on July 10, 2020 at 18:10 CEST in Ustronie Morskie. On that day, two dangerous supercells were also created, which, at the peak of activity, passed over Lubusz and Masovian Provinces. The tornado in Ustronie Morskie was formed on the wavy front, while the supercell developing in Lubusz and Mazovia Land was observed on the cold front. Large hail and damaging wind gusts associated with the downburst in the west of the country took place in higher atmospheric instability than the other cases. The MLCAPE was over 200 J kg–1 higher than that for peak activity of the other storms discussed in the paper. This could have been crucial for the formation of the largest hail recorded on July 10, 2020 in Poland. The highest values of wind shear and storm relative helicity occurred on the coast which could have influenced the formation of a tornado despite the low values of atmospheric instability. The hook echo radar signature in Mazovia Land developed with a similar MLCAPE as the tornado on the coast (nearly 500 J kg–1). On the other hand, the MUCAPE and SBCAPE was much higher there (approx. 500 J kg–1 more), and so was the LCL level. This proves a higher humidity deficit in the lower troposphere in the place where the hook echo passes. With regard to the ESTOFEX and Skywarn Polska convection outlook, the tornado was the most difficult phenomenon to predict. Hail and damaging wind gusts not related to rotation coincided to a greater extent with the convective outlook.

How to form compact and other longer-lived planet-induced vortices: VSI, planet migration, or re-triggers, but not feedback

ABSTRACT Past computational studies of planet-induced vortices have shown that the dust asymmetries associated with these vortices can be long-lived enough that they should be much more common in mm/sub-mm observations of protoplanetary discs, even though they are quite rare. Observed asymmetries also have a range of azimuthal extents from compact to elongated even though computational studies have shown planet-induced vortices should be preferentially elongated. In this study, we use 2D and 3D hydrodynamic simulations to test whether those dust asymmetries should really be so long-lived or so elongated. With higher resolution (29 cells radially per scale height) than our previous work, we find that vortices can be more compact by developing compact cores when higher-mass planets cause them to re-form, or if they are seeded by tiny compact vortices from the vertical shear instability (VSI), but not through dust feedback in 3D as was previously expected in general. Any case with a compact vortex or core(s) also has a longer lifetime. Even elongated vortices can have longer lifetimes with higher-mass planets or if the associated planet is allowed to migrate, the latter of which can cause the dust asymmetry to stop decaying as the planet migrates away from the vortex. These longer dust asymmetry lifetimes are even more inconsistent with observations, perhaps suggesting that discs still have an intermediate amount of effective viscosity.

Instabilities in dusty non-isothermal protoplanetary discs

ABSTRACT Protoplanetary discs (PPDs) can host a number of instabilities that may partake directly or indirectly in the process of planetesimal formation. These include the vertical shear instability (VSI), convective overstability (COS), streaming instability (SI), and dust settling instability (DSI), to name a few. Notably, the VSI and COS have mostly been studied in purely gaseous discs, while the SI and DSI have only been analysed in isothermal discs. How these instabilities operate under more general conditions is therefore unclear. To this end, we devise a local model of a PPD describing a non-isothermal gas interacting with a single species of dust via drag forces. Using this, we find that dust drag sets minimum length-scales below which the VSI and COS are suppressed. Similarly, we find that the SI can be suppressed on sufficiently small scales by the gas’ radial buoyancy if it cools on roughly a dynamical time-scale. We show that the DSI can be effectively stabilized by vertical buoyancy, except at special radial and vertical length-scales. We also find novel instabilities unique to a dusty, non-isothermal gas. These result in a dusty analogue of the COS that operates in slowly cooled discs, and a dusty version of the VSI that is strongly enhanced by dust settling. We briefly discuss the possible implications of our results on planetesimal formation.

Hydrodynamic turbulence in disks with embedded planets

The vertical shear instability (VSI) is a source of hydrodynamic turbulence that can drive vigorous vertical mixing and moderate levels of accretion in protoplanetary disks, and it could be observable in the near future. With high-resolution three-dimensional numerical hydrodynamics simulations, we modeled the behavior of the VSI in protoplanetary disks with and without embedded planets. We then measured its accretion and mixing capabilities by comparing the full Reynolds stress, which includes the contribution of nonaxisymmetric features, such as spiral arms and vortices, to the Reynolds stress due to the azimuthally averaged velocity field, which can be attributed to good approximation to the VSI. We verified that the VSI can contribute to the accretion stress and showed that, depending on disk conditions, an embedded planet can coexist with or suppress VSI turbulent stress. Specifically, the presence of spiral shocks launched by a planet or planet-generated vortices can interfere with the VSI near the planet’s vicinity, with the instability recovering at large enough distances from the planet or vortex. Our results suggest that observations of VSI signatures are unlikely in disks that contain massive, nonaxisymmetric features.