Spiral Density Wave Generation Research Articles

Gravito-turbulence and dynamo in poorly ionized protostellar discs – I. Zero-net-flux case

ABSTRACT In their early stages, protoplanetary discs are sufficiently massive to undergo gravitational instability (GI). This instability is thought to be involved in mass accretion, planet formation via gas fragmentation, the generation of spiral density waves, and outbursts. A key and very recent area of research is the interaction between the GI and magnetic fields in young protoplanetary discs, in particular whether this instability is able to sustain a magnetic field via a dynamo. We conduct 3D, stratified shearing-box simulations using two independent codes, PLUTO and Athena++, to characterize the GI dynamo in poorly ionized protostellar discs subject to ambipolar diffusion. We find that the dynamo operates across a large range of ambipolar Elssaser number Am (which characterizes the strength of ambipolar diffusion) and is particularly strong in the regime Am = 10–100, with typical magnetic to thermal energy ratios of order unity. The dynamo is only weakly dependent on resolution (at least for Am ≲ 100), box size, and cooling law. The magnetic field is produced by the combination of differential rotation and large-scale vertical roll motions associated with spiral density waves. Our results have direct implications for the dynamo process in young protoplanetary discs and possibly some regions of active galactic nucleus discs.

Excitation of spiral density waves by convection in accretion discs

Motivated by the recent results of \citet{Lesur_Ogilvie10} on the transport properties of incompressible convection in protoplanetary discs, in this paper we study the role of compressibility and hence of another basic mode -- spiral density waves -- in convective instability in discs. We analyse the linear dynamics of non-axisymmetric convection and spiral density waves in a Keplerian disc with superadiabatic vertical stratification using the local shearing box approach. It is demonstrated that the shear associated with Keplerian differential rotation introduces a novel phenomenon, it causes these two perturbation modes to become coupled: during evolution the convective mode generates (trailing) spiral density waves and can therefore be regarded as a new source of spiral density waves in discs. The wave generation process studied here owes its existence solely to shear of the disc's differential rotation, and is a special manifestation of a more general linear mode coupling phenomena universally taking place in flows with an inhomogeneous velocity profile. We quantify the efficiency of spiral density wave generation by convection as a function of azimuthal and vertical wavenumbers of these modes and find that it is maximal and most powerful when both these length-scales are comparable to the disc scale height. We also show that unlike the convective mode, which tends to transport angular momentum inwards in the linear regime, the spiral density waves transport angular momentum outwards. Based on these findings, we suggest that in the non-linear regime spiral density waves generated by convection may play a role in enhancing the transport of angular momentum due the convective mode alone, which is actually being changed to outward by non-linearity, as indicated by above-mentioned recent developments.

Hydrodynamic stability and mode coupling in Keplerian flows: local strato-rotational analysis

Aims. We present a qualitative analysis of key (but yet unappreciated) linear phenomena in stratified hydrodynamic Keplerian flows: (i) the occurrence of a vortex mode, as a consequence of strato-rotational balance, with its transient dynamics; (ii) the generation of spiral-density waves (also called inertia-gravity or gΩ waves) by the vortex mode through linear mode coupling in shear flows. Methods. Non-modal analysis of linearized Boussinesq equations were written in the shearing sheet approximation of accretion disk flows. Results. It is shown that the combined action of rotation and stratification introduces a new degree of freedom, vortex mode perturbation, which is in turn linearly coupled with the spiral-density waves. These two modes are jointly able to extract energy from the background flow, and they govern the disk dynamics in the small-scale range. The transient behavior of these modes is determined by the non-normality of the Keplerian shear flow. Tightly leading vortex mode perturbations undergo substantial transient growth, then, becoming trailing, inevitably generate trailing spiral-density waves by linear mode coupling. This course of events – transient growth plus coupling – is particularly pronounced for perturbation harmonics with comparable azimuthal and vertical scales, and it renders the energy dynamics similar to the 3D unbounded plane Couette flow case. Conclusions. Our investigation strongly suggests that the so-called bypass concept of turbulence, which has been recently developed by the hydrodynamic community for spectrally stable shear flows, can also be applied to Keplerian disks. This conjecture may be confirmed by appropriate numerical simulations that take the vertical stratification and consequent mode coupling into account in the high Reynolds number regime.

Stability and nonlinear adjustment of vortices in Keplerian flows

We investigate the stability, nonlinear development and equilibrium structure of vortices in a background shearing Keplerian flow. We make use of high-resolution global two-dimensional compressible hydrodynamic simulations. We introduce the concept of nonlinear adjustment to describe the transition of unbalanced vortical fields to a long-lived configuration. We discuss the conditions under which vortical perturbations evolve into long-lived persistent structures and we describe the properties of these equilibrium vortices. The properties of equilibrium vortices appear to be independent from the initial conditions and depend only on the local disk parameters. In particular we find that the ratio of the vortex size to the local disk scale height increases with the decrease of the sound speed, reaching values well above the unity. The process of spiral density wave generation by the vortex, discussed in our previous work, appear to maintain its efficiency also at nonlinear amplitudes and we observe the formation of spiral shocks attached to the vortex. The shocks may have important consequences on the long term vortex evolution and possibly on the global disk dynamics. Our study strengthens the arguments in favor of anticyclonic vortices as the candidates for the promotion of planetary formation. Hydrodynamic shocks that are an intrinsic property of persistent vortices in compressible Keplerian flows are an important contributor to the overall balance. These shocks support vortices against viscous dissipation by generating local potential vorticity and should be responsible for the eventual fate of the persistent anticyclonic vortices. Numerical codes have be able to resolve shock waves to describe the vortex dynamics correctly.

Spiral density wave generation by vortices in Keplerian flows

We perform a detailed analytical and numerical study of the dynamics of perturbations (vortex/aperiodic mode, Rossby and spiral-density waves) in 2D compressible disks with a Keplerian law of rotation. We draw attention to the process of spiral-density wave generation from vortices, discussing, in particular, the initial, most peculiar stages of wave emission. We show that the linear phenomenon of wave generation by vortices in smooth (without inflection points) shear flows found by using the so-called non-modal approach, is directly applicable to the present case. After an analytical non-modal description of the physics and characteristics of the spiral-density wave generation/propagation in the local shearing-sheet model, we follow the process of wave generation by small amplitude coherent circular vortex structures, by direct global numerical simulation, describing the main features of the generated waves.

Generation of spiral density waves by bars in differentially rotating disks

Generation of spiral density waves by bars in differentially rotating disks

Numerical investigation into the generation of spiral density waves by bars in rigidly rotating disks

A numerical study of the large-scale structure of a spiral galaxy is presented. The study involves the examination of the nonstationary response in a rigidly rotating gas disk to the potential of a bar. When the angular velocity of the bar exceeds the angular velocity of the disk, a quasi-stationary two-arm trailing spiral pattern, which rotates with the angular velocity of the bar, is generated. When the angular velocity of the disk exceeds that of the bar, there is no spiral pattern. Calculations confirm that the bars existing in the central regions of disk galaxies are capable of generating sustaining two-arm spiral patterns.