The Hall instability of thin weakly-ionized stratified Keplerian disks

The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio. The leading order of the asymptotic expansions in the aspect ratio is applied to both equilibrium as well as the perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial, and unstable to vertical short-wave perturbations. The marginal stability surface is found in the space of the local Hall and inverse plasma beta parameters, as well as the free parameter of the model which is related to the total current through the disk. To estimate the minimal values of the equilibrium magnetic field that leads to instability, the latter is constructed as a sum of a current free magnetic field and the simplest approximation for magnetic field created by a distributed electric current.Comment: 13 pages, 7 figure

An optimal transient growth of small perturbations in thin gaseous discs

A thin gaseous disc with an almost keplerian angular velocity profile, bounded by a free surface and rotating around point-mass gravitating object is nearly spectrally stable. Despite that the substantial transient growth of linear perturbations measured by the evolution of their acoustic energy is possible. This fact is demonstrated for the simple model of a non-viscous polytropic thin disc of a finite radial size where the small adiabatic perturbations are considered as a linear combination of neutral modes with a corotational radius located beyond the outer boundary of the flow.Comment: 15 pages, 5 figures, accepted for publication in Ast

Evolution of unsteady jets in the Rayleigh-Taylor instability

International audienceThe paper concerns the temporal evolution of the Rayleigh-Taylor instability of two superimposed fluids in a vertical channel. At large times the instability results in the formation of a wide nearly-steady bubble of the lighter fluid rising through the channel, and thin long unsteady jets of the heavier fluid flowing down the channel walls. The jet flow appears to be tractable asymptotically by the method of matched expansions. The solution has been obtained with the planar tips of jets characterized by the jump of the interface slope

Generation of intermediately-long sea waves by weakly sheared winds

The present study concerns the numerical modeling of sea-wave instability under the effect of logarithmic-wind profile in hurricane conditions. The central point of the study is the calculation of the wave growth rate, which is proportional to the fractional input energy from the weakly-sheared (logarithmic) wind to the wave exponentially varying with time. It is shown for hurricane conditions that the Miles-type stability model based on the Charnock's formula with the standard constant coefficient underestimates the growth rate ~5 to 50 times as compared with the model employing the roughness adopted from experimental data for hurricane winds. The drag reduction with wind speed at hurricane conditions coupled with the similar behavior of the dimensionless gravity acceleration, leads to the minimum in the maximal growth rate and the maximum in the most unstable wavelength.Comment: This paper has been withdrawn by the author due to misprinting error

The Sensitivity of Cognitive Processes to the Inhomogeneity of Natural Magnetic Fields

Three experiments were carried out to study the influence of inhomogeneity of natural magnetic field (MF) on animal cognition. Wistar rats (n = 90) were placed in a complicated problem environment, in which they were to form food-operant behavior under conditions of natural MF (Cond. 1) and MFs produced by iron objects (Cond. 2) or by magnets (Cond. 3). Unlike the control group (Cond. 1), all rats in Cond. 2 and 3 were unable to form operant behavior. Weak MF caused both locomotor and emotional depression, and there was no exploratory activity shown during 6 sessions. Brief external stimulation removed locomotor depression, and animals formed operant behavior similar to latent learning (Cond. 2) or “insight” (Cond. 3). Performance efficiency was lower while the level of stress manifestation was higher in Cond. 2 and 3 than in the control at the stage of stabilization. It has been proposed that MF reduces the activity of brain motivation centers and prevents the development of complicated forms of cognitive activity