Alexander G. Tevzadze

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.

Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic Field

In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two dimensionality and the shallower k^{2} subinertial range spectrum of kinetic energy forcing the magnetic field with a k^{4} subinertial range to attain larger-scale coherence. The inertial range shows a clear k^{-2} spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling.

Evolution of Primordial Magnetic Fields from Phase Transitions

We consider the evolution of primordial magnetic fields generated during cosmological, electroweak or QCD, phase transitions. We assume that the magnetic field generation can be described as an injection of magnetic energy to cosmological plasma at a given scale determined by the moment of magnetic field generation. A high Reynolds number ensures strong coupling between magnetic field and fluid motions. The subsequent evolution of the magnetic field is governed by decaying hydromagnetic turbulence. Both our numerical simulations and a phenomenological description allow us to recover “universal” laws for the decay of magnetic energy and the growth of magnetic correlation length in the turbulent (low viscosity) regime. In particular, we show that during the radiation dominated epoch, energy and correlation length of non-helical magnetic fields scale as conformal time to the powers 1/2 and +1/2, respectively. For helical magnetic fields, energy and correlation length scale as conformal time to the powers 1/3 and +2/3, respectively. The universal decay law of the magnetic field implies that the strength of magnetic field generated during the QCD phase transition could reach � 10 9 G with the present day correlation length � 50 kpc. The fields generated at the electroweak phase transition could be as strong as � 10 10 G with correlation lengths reaching � 0.3kpc. These values of the magnetic fields are consistent with the lower bounds of the extragalactic magnetic fields.

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...

Primordial magnetic field limits from cosmological data

We study limits on a primordial magnetic field arising from cosmological data, including that from big bang nucleosynthesis, cosmic microwave background polarization plane Faraday rotation limits, and large-scale structure formation. We show that the physically relevant quantity is the value of the effective magnetic field, and limits on it are independent of how the magnetic field was generated.

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.

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.

PHASE TRANSITION GENERATED COSMOLOGICAL MAGNETIC FIELD AT LARGE SCALES

We constrain a primordial magnetic field (PMF) generated during a phase transition (PT) using the big bang nucleosynthesis bound on the relativistic energy density. The amplitude of the PMF at large scales is determined by the shape of the PMF spectrum outside its maximal correlation length scale. Even if the amplitude of the PMF at 1 Mpc is small, PT-generated PMFs can leave observable signatures in the potentially detectable relic gravitational wave background if a large enough fraction (1%-10%) of the thermal energy is converted into the PMF.

Evolution of inflation-generated magnetic field through phase transitions

We study the evolution of an inflation-generated magnetic field, due to its coupling to fluid motions, during cosmological phase transitions. We find that the magnetic field stays almost unchanged on large scales, while on small scales, the spectrum is modified in such a way that power at small scales becomes progressively suppressed. We also show that the magnetic field generates turbulent motions in the initially turbulence-free plasma. On large scales, the slope of the resulting kinetic energy spectrum is consistent with that of white noise.