Linking dissipation-induced instabilities with nonmodal growth: the case of helical magnetorotational instability

The helical magnetorotational instability is known to work for resistive rotational flows with comparably steep negative or extremely steep positive shear. The corresponding lower and upper Liu limits of the shear are continuously connected when some axial electrical current is allowed to flow through the rotating fluid. Using a local approximation we demonstrate that the magnetohydrodynamic behavior of this dissipation-induced instability is intimately connected with the nonmodal growth and the pseudospectrum of the underlying purely hydrodynamic problem.Comment: 5 pages, 4 figure

Linear stability analysis of magnetized relativistic rotating jets

We carry out a linear stability analysis of a magnetized relativistic rotating cylindrical jet flow using the approximation of zero thermal pressure. We identify several modes of instability in the jet: Kelvin-Helmholtz, current driven and two kinds of centrifugal-buoyancy modes -- toroidal and poloidal. The Kelvin-Helmholtz mode is found at low magnetization and its growth rate depends very weakly on the pitch parameter of the background magnetic field and on rotation. The current driven mode is found at high magnetization, the values of its growth rate and the wavenumber, corresponding to the maximum growth, increase as we decrease the pitch parameter of the background magnetic field. This mode is stabilized by rotation, especially, at high magnetization. The centrifugal-buoyancy modes, arising due to rotation, tend also to be more stable when magnetization is increased. Overall, relativistic jet flows appear to be more stable with respect to their non-relativistic counterpart.Comment: 15 pages, 15 figures, accepted for pubblication in MNRA

Dynamics of perturbation modes in protoplanetary discs : new effects of self-gravity and velocity shear

Protoplanetary discs, composed of gas and dust, usually surround young stellar objects and serve two main purposes: they determine the accretion of matter onto the central object and also represent sites of planet formation. The accretion proceeds through the transport of angular momentum outwards allowing the disc matter to fall towards the centre. A mechanism responsible for the transport can be turbulence, waves or other coherent structures originating from various instabilities in discs that could, in addition, play a role in the planet formation process. For an understanding of these instabilities, it is necessary to study perturbation dynamics in differentially rotating, or sheared media. Thus, this thesis focuses on new aspects in the perturbation dynamics in non-magnetised protoplanetary discs that arise due to their self-gravity and velocity shear associated with the disc’s differential rotation. The analysis is carried out in the framework of the widely employed local shearing box approximation. We start with 2D discs and then move on to 3D ones. In 2D discs, there are two basic perturbation types/modes – spiral density waves and vortices – that are responsible for angular momentum transport and that can also contribute to accelerating planet formation. First, in the linear regime, we demonstrate that the vortical mode undergoes large growth due to self-gravity and in this process generates density waves via shear-induced linear mode coupling phenomenon. This is noteworthy, because commonly only density waves are considered in self-gravitating discs. Then we investigate vortex dynamics in the non-linear regime under the influence of self-gravity by means of numerical simulations. It is shown that vortices are no longer well-organised and long-lived structures, unlike those occurring in non-self-gravitating discs. They undergo recurring phases (lasting for a few disc rotation periods) of formation, growth and eventual destruction. We also discuss the dust trapping capability of such transient vortices. Perturbation dynamics in 3D vertically stratified discs is richer, as there are more mode types. We first consider non-axisymmetric modes in non-self-gravitating discs and then only axisymmetric modes in the more complicated case when self-gravity is present. Specifically, in non-self-gravitating discs with superadiabatic vertical stratification, motivated by the recent results on the transport properties of incompressible convection, we show that when compressibility is taken into account, the non-axisymmetric convective mode excites density waves via the same shear-induced linear mode coupling mechanism mentioned above. These generated density waves transport angular momentum outwards in the trailing phase, and we suggest that they may aid and enhance the transport due solely to convection in the non-linear regime, where the latter becomes outward. In the final part of the thesis, we carry out a linear analysis of axisymmetric vertical normal modes in stratified self-gravitating discs. Although axisymmetric modes do not display shear-induced couplings, their analysis provides insight into how gravitational instabilities develop in the 3D case and their onset criterion. We examine how the structure of dispersion curves and eigenfunctions of 3D modes are influenced by self-gravity, which mode first becomes gravitationally unstable and thus determines the onset criterion and nature of the gravitational instability in stratified discs. We also contrast the more exact instability criterion obtained with our 3D model with that of density waves in 2D discs. Based on these findings, we discuss the origin of 3D behaviour of perturbations involving noticeable disc surface distortions, as seen in some numerical simulations of self-gravitating discs

Zero net flux MRI-turbulence in disks −- sustenance scheme and magnetic Prandtl number dependence

We investigate sustenance and dependence on magnetic Prandtl number (${\rm Pm}$) for magnetorotational instability (MRI)-driven turbulence in astrophysical Keplerian disks with zero net magnetic flux using standard shearing box simulations. We focus on the turbulence dynamics in Fourier space, capturing specific/noncanonical anisotropy of nonlinear processes due to disk flow shear. This is a new type of nonlinear redistribution of modes over wavevector orientations in Fourier space -- the nonlinear transverse cascade -- which is generic to shear flows and fundamentally different from usual direct/inverse cascade. The zero flux MRI has no exponentially growing modes, so its growth is transient, or nonmodal. Turbulence self-sustenance is governed by constructive cooperation of the transient growth of MRI and the nonlinear transverse cascade. This cooperation takes place at small wavenumbers (on the flow size scales) referred to as the vital area in Fourier space. The direct cascade transfers mode energy from the vital area to larger wavenumbers. At large ${\rm Pm}$, the transverse cascade prevails over the direct one, keeping most of modes' energy contained in small wavenumbers. With decreasing ${\rm Pm}$, however, the action of the transverse cascade weakens and can no longer oppose the action of direct cascade which more efficiently transfers energy to higher wavenumbers, leading to increased resistive dissipation. This undermines the sustenance scheme, resulting in the turbulence decay. Thus, the decay of zero net flux MRI-turbulence with decreasing ${\rm Pm}$ is attributed to topological rearrangement of the nonlinear processes when the direct cascade begins to prevail over the transverse cascade.Comment: 26 pages, 16 figures, accepted for publication in the Astrophysical Journa

Planet formation: The case for large efforts on the computational side

Modern astronomy has finally been able to observe protoplanetary disks in reasonable resolution and detail, unveiling the processes happening during planet formation. These observed processes are understood under the framework of disk-planet interaction, a process studied analytically and modeled numerically for over 40 years. Long a theoreticians' game, the wealth of observational data has been allowing for increasingly stringent tests of the theoretical models. Modeling efforts are crucial to support the interpretation of direct imaging analyses, not just for potential detections but also to put meaningful upper limits on mass accretion rates and other physical quantities in current and future large-scale surveys. This white paper addresses the questions of what efforts on the computational side are required in the next decade to advance our theoretical understanding, explain the observational data, and guide new observations. We identified the nature of accretion, ab initio planet formation, early evolution, and circumplanetary disks as major fields of interest in computational planet formation. We recommend that modelers relax the approximations of alpha-viscosity and isothermal equations of state, on the grounds that these models use flawed assumptions, even if they give good visual qualitative agreement with observations. We similarly recommend that population synthesis move away from 1D hydrodynamics. The computational resources to reach these goals should be developed during the next decade, through improvements in algorithms and the hardware for hybrid CPU/GPU clusters. Coupled with high angular resolution and great line sensitivity in ground based interferometers, ELTs and JWST, these advances in computational efforts should allow for large strides in the field in the next decade.Comment: White paper submitted to the Astro2020 decadal surve

Planet formation: The case for large efforts on the computational side

Modern astronomy has finally been able to observe protoplanetary disks in reasonable resolution and detail, unveiling the processes happening during planet formation. These observed processes are understood under the framework of disk-planet interaction, a process studied analytically and modeled numerically for over 40 years. Long a theoreticians' game, the wealth of observational data has been allowing for increasingly stringent tests of the theoretical models. Modeling efforts are crucial to support the interpretation of direct imaging analyses, not just for potential detections but also to put meaningful upper limits on mass accretion rates and other physical quantities in current and future large-scale surveys. This white paper addresses the questions of what efforts on the computational side are required in the next decade to advance our theoretical understanding, explain the observational data, and guide new observations. We identified the nature of accretion, ab initio planet formation, early evolution, and circumplanetary disks as major fields of interest in computational planet formation. We recommend that modelers relax the approximations of alpha-viscosity and isothermal equations of state, on the grounds that these models use flawed assumptions, even if they give good visual qualitative agreement with observations. We similarly recommend that population synthesis move away from 1D hydrodynamics. The computational resources to reach these goals should be developed during the next decade, through improvements in algorithms and the hardware for hybrid CPU/GPU clusters. Coupled with high angular resolution and great line sensitivity in ground based interferometers, ELTs and JWST, these advances in computational efforts should allow for large strides in the field in the next decade

Dynamics of perturbation modes in protoplanetary discs : new effects of self-gravity and velocity shear

Protoplanetary discs, composed of gas and dust, usually surround young stellar objects and serve two main purposes: they determine the accretion of matter onto the central object and also represent sites of planet formation. The accretion proceeds through the transport of angular momentum outwards allowing the disc matter to fall towards the centre. A mechanism responsible for the transport can be turbulence, waves or other coherent structures originating from various instabilities in discs that could, in addition, play a role in the planet formation process. For an understanding of these instabilities, it is necessary to study perturbation dynamics in differentially rotating, or sheared media. Thus, this thesis focuses on new aspects in the perturbation dynamics in non-magnetised protoplanetary discs that arise due to their self-gravity and velocity shear associated with the disc’s differential rotation. The analysis is carried out in the framework of the widely employed local shearing box approximation. We start with 2D discs and then move on to 3D ones. In 2D discs, there are two basic perturbation types/modes – spiral density waves and vortices – that are responsible for angular momentum transport and that can also contribute to accelerating planet formation. First, in the linear regime, we demonstrate that the vortical mode undergoes large growth due to self-gravity and in this process generates density waves via shear-induced linear mode coupling phenomenon. This is noteworthy, because commonly only density waves are considered in self-gravitating discs. Then we investigate vortex dynamics in the non-linear regime under the influence of self-gravity by means of numerical simulations. It is shown that vortices are no longer well-organised and long-lived structures, unlike those occurring in non-self-gravitating discs. They undergo recurring phases (lasting for a few disc rotation periods) of formation, growth and eventual destruction. We also discuss the dust trapping capability of such transient vortices. Perturbation dynamics in 3D vertically stratified discs is richer, as there are more mode types. We first consider non-axisymmetric modes in non-self-gravitating discs and then only axisymmetric modes in the more complicated case when self-gravity is present. Specifically, in non-self-gravitating discs with superadiabatic vertical stratification, motivated by the recent results on the transport properties of incompressible convection, we show that when compressibility is taken into account, the non-axisymmetric convective mode excites density waves via the same shear-induced linear mode coupling mechanism mentioned above. These generated density waves transport angular momentum outwards in the trailing phase, and we suggest that they may aid and enhance the transport due solely to convection in the non-linear regime, where the latter becomes outward. In the final part of the thesis, we carry out a linear analysis of axisymmetric vertical normal modes in stratified self-gravitating discs. Although axisymmetric modes do not display shear-induced couplings, their analysis provides insight into how gravitational instabilities develop in the 3D case and their onset criterion. We examine how the structure of dispersion curves and eigenfunctions of 3D modes are influenced by self-gravity, which mode first becomes gravitationally unstable and thus determines the onset criterion and nature of the gravitational instability in stratified discs. We also contrast the more exact instability criterion obtained with our 3D model with that of density waves in 2D discs. Based on these findings, we discuss the origin of 3D behaviour of perturbations involving noticeable disc surface distortions, as seen in some numerical simulations of self-gravitating discs.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Tidally Forced Planetary Waves in the Tachocline of Solar-like Stars

Can atmospheric waves in planet-hosting solar-like stars substantially resonate to tidal forcing, perhaps at a level of impacting the space weather or even being dynamo-relevant? In particular, low-frequency Rossby waves, which have been detected in the solar near-surface layers, are predestined to respond to sunspot cycle-scale perturbations. In this paper, we seek to address these questions as we formulate a forced wave model for the tachocline layer, which is widely considered as the birthplace of several magnetohydrodynamic planetary waves, i.e., Rossby, inertia-gravity (Poincaré), Kelvin, Alfvén, and gravity waves. The tachocline is modeled as a shallow plasma atmosphere with an effective free surface on top that we describe within the Cartesian β -plane approximation. As a novelty to former studies, we equip the governing equations with a conservative tidal potential and a linear friction law to account for viscous dissipation. We combine the linearized governing equations into one decoupled wave equation, which facilitates an easily approachable analysis. Analytical results are presented and discussed within several interesting free, damped, and forced wave limits for both midlatitude and equatorially trapped waves. For the idealized case of a single tide-generating body following a circular orbit, we derive an explicit analytic solution that we apply to our Sun for estimating leading-order responses to Jupiter. Our analysis reveals that Rossby waves resonating to low-frequency perturbations can potentially reach considerable velocity amplitudes on the order of 10 ^1 –10 ^2 cm s ^−1 , which, however, strongly rely on the yet unknown frictional damping parameter