George Chagelishvili

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.

Acoustic waves in unbounded shear flows

The linear evolution of acoustic waves in a fluid flow with uniform mean density and uniform shear of velocity is investigated. The process of the mean flow energy extraction by the three-dimensional acoustic waves, stimulated by the non-normal character of the linear dynamics in the shear flow, is analyzed. The thorough examination of the dynamics of different physical variables characterizing the wave evolution is presented. The physics of gaining of the shear energy by acoustic waves is described.

Linear coupling and overreflection phenomena of magnetohydrodynamic waves in smooth shear flows

Special features of magnetohydrodynamic waves linear dynamics in smooth shear flows are studied. Quantitative asymptotic and numerical analysis are performed for wide range of system parameters when basic flow has constant shear of velocity and uniform magnetic field is parallel to the basic flow. The special features consist of magnetohydrodynamic wave mutual transformation and overreflection phenomena. The transformation takes place for arbitrary shear rates and involves all magnetohydrodynamic wave modes. While the overreflection occurs only for slow magnetosonic and Alfven waves at high shear rates. Studied phenomena should be decisive in the elaboration of the self-sustaining model of magnetohydrodynamic turbulence in the shear flows.

Compressible hydromagnetic shear flows with anisotropic thermal pressure: Nonmodal study of waves and instabilities

The evolution of linear magnetohydrodynamic waves and plasma instabilities (firehose and mirror) in a compressible, magnetized plane Couette flow with anisotropic thermal pressure is investigated. In the present study we revealed that the pressure anisotropy brings significant novelty to the effect of coupling and linear reciprocal transformation of the wave modes originally discovered [Chagelishvili, Rogava, and Tsiklauri, Phys. Rev. E 53, 6028 (1996)]. It is found that behavior of the firehose and mirror instabilities is drastically changed due to the presence of shear in the flow. These novel effects are caused by the non-normality of linear dynamics in shear flows and they have been revealed through use of the nonmodal approach.

Stability and nonlinear adjustment of vortices in Keplerian flows

Aims. We investigate the stability, nonlinear development and equilibrium structure of vortices in a background shearing Keplerian flow Methods. 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. Results. 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. Conclusions. 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.

Linear coupling of modes in two-dimensional radially stratified astrophysical discs

We investigate mode coupling in a two-dimensional compressible disc with radial stratification and differential rotation. We employ the global radial scaling of linear perturbations and study the linear modes in the local shearing-sheet approximation. We employ a three-mode formalism and study the vorticity (W), entropy (S) and compressional (P) modes and their coupling properties. The system exhibits asymmetric three-mode coupling: this includes mutual coupling of S and P modes, S and W modes, and asymmetric coupling between the W and P modes. P-mode perturbations are able to generate potential vorticity through indirect three-mode coupling. This process indicates that compressional perturbations can lead to the development of vortical structures and influence the dynamics of radially stratified hydrodynamic accretion and protoplanetary discs.

Velocity shear-induced effects on electrostatic ion perturbations

Linear evolution of electrostatic perturbations in an unmagnetized electron–ion plasma shear flow is studied. New physical effects, arising due to the non-normality of linear dynamics are disclosed. A new class of nonperiodic collective mode with vortical motion of ions, characterized by intense energy exchange with the mean flow, is found. It is also shown that the velocity shear induces extraction of the mean flow energy by ion-sound waves and that during the shear-induced evolution the ion-sound waves turn eventually into ion plasma oscillations.

Fast variation of Cygnus X-1 and related sources

A new model is offered for explaining the millisecond variability of Cyg X-1 and related sources, based on the bimodal accretion model for Cyg X-1. In the region of the main energy, release action of the Parker instability leads to the formation of three to five (depending on concrete circumstances) oblong-shaped magnetic arcs within the whole azimuth. Those are the magnetic arcs which make up, consequently, an optically thin hot corona needed for explaining the low state spectrum of Cyg X-1. Rapid rotation of the stretched magnetic arcs leads to fast variations of their lengths scales along the line of sight. Accordingly, the optical depth of each arc with respect to Thomson scattering, tau, will also vary, leading to the variations of spectral indices of arcs determined in terms of tau for the inverse Compton scattering. In its turn, it leads to rapid variations of photon count rates in the proper energy range. The described mechanism is effective when n = 3 (n is the number of arcs) but for n = 5 it is essentially weakened; i.e., in the latter case fast variations are actually absent. 24 refs.

Revisiting linear dynamics of non-axisymmetric perturbations in weakly magnetized accretion discs

We investigate the linear dynamics of non-axisymmetric perturbations in incompressible, vertically stratified Keplerian discs threaded by a weak non-ze ro net vertical magnetic field in the local shearing box approximation. Perturbations are decomposed into shearing waves, or spatial harmonics whose temporal evolution is then followed via numerical integration of the linearized ideal MHD equations of the shearing box. There are two basic modes in the system ‐ inertia-gravity waves and magnetic mode, which displays the magnetorotational instability (MRI). As distinct from previous related studies, we introduce “eigen-variables” characterizing each (counter-propagating) component of the inertia-gravity and magnetic modes, which are governed by a set of four first order coupled ordinary differential equations. This allowed us to identify a new process of linear coupling of the two above non-axisymmetric modes due to the disc’s differential rotation. We also carried out a comparative analysis of the dynamics of non-axisymmetric and axisymmetric magnetic mode perturbations. It is demonstrated that the growth of “optimal” and close-to-optimal non-axisymmetric harmonics of this mode, having transient nature, can prevail over the exponential growth of axisymmetric ones (i.e., over the axisymmetric MRI) during dynamical time. A possible implication of this result for axisymmetric channel solutions emerging in numerical simulations is discussed. In particular, the formation of the (axisymmetric) channel may be affected/impeded by nonaxisymmetric modes already at the early linear stage leading to its untimely disruption ‐ the outcome strongly depends on the amplitude and spectrum of initial perturbation. So, this competition may result in an uncertainty in the magnetic mode’s non-linear dynamics. Although we consider incompressible perturbations, in the final part , speculate on the dynamics in the compressible case. It is shown that a maximum growth of non-axisymmetric magnetic mode occurs at vertical wavelengths close to the disc scale-heig ht for which compressibility effects are important. This indirectly suggests that compressibil ity plays a role in the dynamics of the non-axisymmetric MRI and, ultimately, in the resulting turbulent state.

New Linear Mechanisms of Acoustic Wave Generation in Smooth Shear Flows (Nonmodal Study)

This lecture presents new linear mechanisms of acoustic wave generation in smooth shear flows using a non-modal study.