J. G. Lominadze

On hydrodynamic shear turbulence in Keplerian disks: Via transient growth to bypass transition

This paper deals with the problem of hydrodynamic shear turbulence in non-magnetized Keplerian disks. Several papers have appeared recently on the subject, on possible linear instabilities which may be due to the presence of a stable stratification, or caused by deviations from cylindrical rotation. Here we wish to draw attention to another route to hydrodynamic turbulence, which seems to be little known by the astrophysical community, but which has been intensively discussed among fluid dynamicists during the past decade. In this so-called bypass concept for the onset of turbulence, perturbations undergo transient growth and if they have initially a finite amplitude they may reach an amplitude that is suciently large to allow positive feedback through nonlinear interactions. This transient growth is linear in nature, and thus it diers in principle from the well-known nonlinear instability. We describe the type of perturbations that according to this process are the most likely to lead to turbulence, namely non-axisymmetric vortex mode perturbations in the two dimensional limit. We show that the apparently inhibiting action of the Coriolis force on the dynamics of such vortical perturbations is substantially diminished due to the pressure perturbations, contrary to current opinion. We stress the similarity of the turbulent processes in Keplerian disks and in Cartesian flows and conclude that the prevalent skepticism of the astrophysical community about the occurrence of hydrodynamic shear turbulence in such disks is not founded.

THEORY OF NP 0532 PULSAR RADIATION AND THE NATURE OF THE ACTIVITY OF THE CRAB NEBULA

Plasma processes in the magnetospheres of pulsars are considered. A self-consistent radiation model of the pulsar NP 0532 and the Crab Nebula is presented. It is based on the consideration of cyclotron instability in a relativistic electron-positron plasma in a strong magnetic field. This instability onsets near the light cylinder of pulsar NP 0532. The pitch-angle and energy distribution of particles, caused by cyclotron instability development is found. It is shown that X- and γ-ray radiation of the pulsar is explained by the synchrotron radiation of beam particles. The scattering of excited oscillations on plasma particles is responsible for nonzero pitch-angles of the latter. As a result, synchrotron radiation originates which is within optical frequencies. The synchrotron luminosity evaluated coincides with that observed for NP 0532 in that spectral region. Cyclotron waves are pumped to lower frequencies due to nonlinear scattering by plasma particles and leave the pulsar magnetosphere as observable radio waves.The spectrum of ultra-relativistic electron-positron pairs ejected from the NP 0532 pulsar magnetosphere into the Crab Nebula is calculated. The expected spectrum of the synchrotron radiation of these particles in the Nebula agrees well with its observed spectrum at optical and X-ray frequencies.

Nonlinear wave conversion in electron-positron plasmas

Wave conversion mechanisms causing large-frequency shifts are considered for an electron-positron plasma in a strong magnetic field. In particular, we discuss the effects of the nonlinear Čerenkov as well as the cyclotron resonances in order to associate pulsar radio-emissions with our present model for nonlinear conversion of high-frequency radiation into the low-frequency region.

On hydrodynamic shear turbulence in stratified Keplerian disks: Transient growth of small-scale 3D vortex mode perturbations

This is a sequel to Paper I (Chagelishvili et al. 2003), where we presented the so-called bypass concept for the onset of turbulence in shearing flows. According to this concept, which was worked out during the last decade by the hydrodynamic community for spectrally stable flows, vortical perturbations undergo transient growth by extracting energy from the shear (a linear process), thereby reaching an amplitude which is sucient to allow for non-linear interactions which, by positive feedback, sustain turbulence. In Paper I we described this transient growth for 2D perturbations in a Keplerian disk; we showed that their kinematics was the same as in plane-parallel flow, and thus that they were not modified by the presence of the Coriolis force. In the present paper, we pursue our goal of applying the bypass scenario to astrophysical disks: we investigate the linear dynamics of 3D small-scale vortical perturbations for single spatial harmonics, in stably stratified, di erentially rotating disks, again in the framework of a nonmodal analysis. We find that these 3D perturbations also undergo substantial transient growth, and that they reach a peak amplitude that is comparable to that of 2D perturbations, as long as their vertical scale remains of the order of the azimuthal scale. When the vertical wave-number exceeds the azimuthal one, the amplification rate is reduced, but this may be more than compensated to by the huge Reynolds number and the high shear rate characterizing astrophysical Keplerian disks. Whereas in 2D the Coriolis force had no impact on the transient growth, in 3D this force somewhat constricts the characteristics of the perturbation dynamics in disk flows, and the initial transient growth is followed by some reduction in amplitude. These dierences are quantitative, rather than of fundamental character. But the 3D case presents two interesting novelties. In plane parallel flow, the perturbations do not decay after their transient amplification, but their energy stays on a plateau before being dissipated through viscous friction. More importantly, especially for the astrophysicist, in disk flow the 3D vortex mode perturbations excite density-spiral waves, whose energy also settles on a plateau before viscous dissipation. These local vortex mode perturbations fit naturally into the bypass concept of hydrodynamic shear turbulence, which was first developed for plane-parallel flows. We submit that these perturbations will also play an important role in the onset and in the maintenance of turbulence in Keplerian disks.

Magnetohydrodynamic waves linear evolution in parallel shear flows: Amplification and mutual transformations

Evolution of three-dimensional magnetohydrodynamic (MHD) waves [fast magnetosonic (FMW), slow magnetosonic (SMW) and Alfven waves] is studied in unbounded parallel flows with uniform shear of velocity and uniform magnetic field directed along the flow. The energy exchange between the MHD waves and background flow is explored. This process is noticeably different for each type of wave and is characterized by the unusual (algebraic) behavior of the linear amplification processes. Another novelty is shown in the wave linear evolution process — the coupling of MHD waves and their mutual transformations are originated in a limited time interval for a wide range of systems (flow and waves) parameters. Significant transformation of Alfven waves into FMW may take place (depending on the parameters of the system) if the former has been initially generated in shear flow. It is possible to reveal these results by employing the nonmodal linear approach which has been extensively used in the study of evolution of pert...

A New Explanation of the High Effective Temperatures in Pulsar Radioemissions

A new nonlinear process, which can explain the high effective temperatures of pulsar radio emissions, is proposed. It is due to the excitation of low frequency Alfven waves by waves resonantly interacting with the electrons and positrons in the pulsar ultrarelativistic plasma.

A turbulence model in unbounded smooth shear flows: The weak turbulence approach

We discuss a new concept of the subcritical transition to turbulence in unbounded smooth (noninflectional) spectrally stable shear flows. This concept (the so-called bypass transition) follows from considering the nonnormality of the linear dynamics of vortex disturbances in shear flows and is most easily interpreted by tracing the evolution of spatial Fourier harmonics (SFHs) of the disturbances. The key features of the concept are as follows: the transition of the flow by only finite-amplitude vortex disturbances despite the fact that the phenomenon is energetically supported by a linear process (the transient growth of SFHs); the anisotropy of processes in the k space; the onset of chaos due to the dynamical (not stochastic) process—nonlinear processes that close the transition feedback loop by the angular redistribution of SFHs in the k space. The evolution of two-dimensional small-scale vortex disturbances in a parallel flow with a uniform shear is analyzed within the weak turbulence approach. This numerical test analysis is carried out to prove the most problematic statement of the concept, the existence of a positive feedback caused by the nonlinear process. Numerical calculations also show the existence of a threshold: if the amplitude of the initial disturbance exceeds the threshold value, the self-maintenance of disturbances becomes realistic. The latter is a characteristic feature of the flow transition to the turbulent state and its maintenance.

Generation of Crab Nebulae Wisps by Plasma Drift Instability

A new mechanism of wisp formation in the Crab Nebula, without recourse to a shock wave, is presented. The mechanism is based on the plasma processes taking place in the relativistic electron-positron plasma, in particular, on excitation of the drift instability in the slightly inhomogeneous magnetic field of the nebula. The magnetic field geometry is assumed to be untwisting spiral-like, concentrated around the rotational equatorial plane of the pulsar. We infer that the energy is transported from the pulsar to the nebula not only by the Poynting flux but also by the kinetic energy of the particles moving along the field lines. We consider a specific relativistic electron-positron plasma with Lorentz factor γ± ~ 10 penetrated by an ion beam with γb ~ 106. It is shown that in such a plasma, taking into account the drift, the generation of low-frequency waves propagating transversely to the magnetic field is possible. In this way the excited Br field causes additional alteration of the magnetic field geometry. The higher luminosity of certain spots is explained by the reorientation of the direction of motion of the synchrotron radiation source (Larmor circle) relative to the observer. The sizes, variability of luminosity, spatial asymmetry, polarization, and transfer velocity, i.e., the main properties of the wisps, are explained. Some predictions are also made.

Nonlinear hot plasma motions across a strong magnetic field

Abstract The aim of this work is the analysis of nonlinear waves propagating across the magnetic field with βi = 8ρnTi/B2 > m/M, when dispersion is connected with the larmor radius of ions. Nonlinear equations obtained for this case are analysed using Whitham method.

Double-layer disk and magnetic field dynamics in the Crab Nebula

The mechanism of the large-scale magnetic field generation in the Crab Nebula is proposed. The basis for the considered ‘fast’ mechanism is the model of the central region of Crab Nebula amorphous part having the form of slightly divergent double-layer disk consisting of the relativistic electron-positron plasma.The nebula toroidal magnetic field generation occurs in the double-layer disk in the immediate neighbourhood of the light cylinder of pulsar PSR 0531+21 due to the differential rotation by means of dynamo-mechanism. The generated field is transferred into the nebula by the pulsar wind which forms the double-layer disk.By use of the known parameters of pulsar PSR 0531+21, the considered mechanism yields the strength of magnetic fieldB=10−3 G observed in the nebula. The disk structure must be destroyed toward the edges of the nebula.