Point-wise Self-similar Solution for Spiral Shocks in an Accretion Disk with Mass Outflow in a Binary

We examine the properties of spiral shocks from a steady, adiabatic, non-axisymmetric accretion disk around a compact star in a binary. We first incorporate all possible influences from a binary through adopting the Roche potential and Coriolis forces in the basic conservation equations. In this paper, we assume spiral shocks to be point-wise and self-similar, and that the flow is in vertical hydrostatic equilibrium to simplify the study. We also investigate mass outflow due to shock compression and apply it to an accreting white dwarf in a binary. We find that our model will be beneficial for overcoming the ad hoc assumption of an optically thick wind generally used in studies of the progenitors of supernovae Ia.

Faraday–Fresnel rotation and splitting of orbital angular momentum carrying waves in a rotating plasma

Rotational Fresnel drag – or orbital Faraday rotation – in a rotating magnetised plasma is uncovered and studied analytically for Trivelpiece–Gould and whistler–helicon waves carrying orbital angular momentum (OAM). Plasma rotation is shown to introduce a non-zero phase shift between OAM-carrying eigenmodes with opposite helicities, similarly to the phase shift between spin angular momentum eigenmodes associated with the classical Faraday effect in a magnetised plasma at rest. By examining the dispersion relation for these two low-frequency modes in a Brillouin rotating plasma, this Faraday–Fresnel rotation effect is traced back to the combined effects of Doppler shift, centrifugal forces and Coriolis forces. In addition, the longitudinal group velocity in the presence of rotation is shown to depend both on rotation and azimuthal mode, therefore predicting the Faraday–Fresnel splitting of the envelope of a wave packet containing a superposition of OAM-carrying eigenmodes with opposite helicities.

Steady circular hydraulic jump on a rotating disk

The paper deals with the steady axially symmetric flow of a viscous liquid layer over a rotating disk. The liquid is fed near the axis of rotation and spreads due to inertia and the centrifugal force. The viscous shallow-water approach gives a system of ordinary differential equations governing the flow. We consider inertia, gravity, centrifugal and Coriolis forces and estimate the effect of surface tension. We found four qualitatively different flow regimes. Transition through these regimes shows the continuous evolution of the flow structure from a hydraulic jump on a static disk to a monotonic thickness decrease on a fast rotating one. We show that, in the absence of surface tension, the intensity of the jump gradually vanishes at a finite distance from the axis of rotation while the angular velocity increases. The surface tension decreases the jump radius and destroys the steady solution for a certain range of parameters.

Stability Analysis for Complex Rotational Flow

Based on the earlier developed mathematical model of the complex flow due to the double rotations in two perpendicular directions, the stability analysis is performed in the paper. The Navier-Stokes equations are derived in the coordinate system rotating around the two perpendicular different axes, the vertical one of them is arranged on some distance from the other axis of rotation, the horizontal axis is directed along the tangential line to the circle of the vertical rotation. The two centrifugal and Coriolis forces create the unique features in high oscillating flow, with localities of the stretched liquid, due to their action varying by the circumferential cylindrical coordinate in the channel flow. Stability analysis for the complex rotational flow under double rotations creating strongly varying mass forces and stretching of the liquid is considered at first

Global upper-atmospheric heating at Jupiter by the recirculation of auroral energy

<p>Jupiter's upper atmosphere is significantly hotter than expected based on the amount of solar heating it receives. This temperature discrepency is known as the 'energy crisis' due to it's nearly 50-year duration and the fact it also occurs at Saturn, Uranus and Neptune. At Jupiter, magnetosphere-ionosphere coupling gives rise to intense auroral emissions and enormous energy deposition in the magnetic polar regions, so it was presumed long ago that redistribution of this energy could heat the rest of the planet. However, most global circulation models have difficulty redistributing auroral energy globally due to the strong Coriolis forces and ion drag on this rapidly rotating planet. Consequently, other possible heat sources have continued to be studied, such as heating by gravity and acoustic waves emanating from the lower atmosphere. Each global heating mechanism would imprint a unique signature on global temperature gradients, thus revealing the dominant heat source, but these gradients have not been determined due a lack of planet-wide, high-resolution data. The last global map of Jovian upper-atmospheric temperatures was produced using ground-based data taken in 1993, in which the region between 45<sup>o</sup> latitude (north & south) and the poles was represented by just 2 pixels. As a result, those maps did not (or could not) show a clear temperature gradient, and furthermore, they even showed regions of hot atmosphere near the equator, supporting the idea of an equatorial heat source, e.g. gravity and/or acoustic wave heating. Therefore observationally and from a modeling perspective, a concensus has not been reached to date. Here we report new infrared spectroscopy of Jupiter's major upper-atmospheric ion H<sub>3</sub><sup>+</sup>, with a spatial resolution of 2<sup>o</sup> longitude and latitude extending from pole to equator, capable of tracing the global temperature gradients. We find that temperatures decrease steadily from the auroral polar regions to the equator. Further, during a period of enhanced activity possibly driven by a solar wind compression, a high-temperature planetary-scale structure was observed which may be propagating from the aurora. These observations indicate that Jupiter's upper atmosphere is predominantly heated via the redistribution of auroral energy, and therefore that Coriolis forces and ion drag are observably overcome.</p>

ANALYTICAL STUDY OF THE UNLOADING PROCESS OF ELEVATOR BUCKETS

The purpose of the article is to analyze the main results of the works that are used in the calculations of elevators with moderate speed modes, to clarify the suitability of their individual positions for developing the parameters of centrifugal unloading of high-speed elevators. Works devoted to the study of the operation of high-speed elevators, the results of which have not received a decent interpretation and development, are of considerable interest. As the efficiency of high-speed elevators is determined by the quality of centrifugal unloading and by the operation of the belt-drum mechanism without slipping, there is a need to analyze the work aimed at solving this problem. The paper presents known solutions for determining the parameters of centrifugal unloading, which are based on various hypotheses of the movement of material particles inside the bucket. The physical and mechanical phenomena that affect the movement of material particles in the elevator bucket are studied. The advantages and disadvantages of each hypothesis are revealed. The theoretical study of the process of centrifugal unloading is complicated by the fact that during the movement and exit of the material from the bucket, there is an unstable movement of the bulk material under the influence of a changing system of forces: the forces of attraction, centrifugal and coriolis forces, and the friction force. Meanwhile, even the simplest cases of material motion under a gravitational or mixed discharge regime are difficult to analyze theoretically. In this regard, the dependencies and methods of constructing the trajectories of the material movement are established, as well as the relevance of using a particular equation.

Mathematical Modelling and Computer Simulation of the Flow in Thin Gap Channel due to Alternating Volumetric Mass Forces

The mathematical modelling and computer simulation are presented for the complex flow in thin gap channel due to alternating volumetrically distributed mass forces. The flow equations and obtained analytical solutions for limit cases are considered in the cylindrical coordinate system with the axis directed along the channel, which is rotating around its axis. The channel is placed inside the cylinder on the edge of the circular horizontal disk, which is rotating around vertical axis in its centre. The two rotations around different perpendicular axes create complex unknown features in a flow due to the alternating centrifugal and Coriolis forces, which substantially vary by the angle. The centrifugal force from the disk rotation is directed to its edge, while the centrifugal force due to rotation of the channel is acting by the channel’s radius. As a result, the two different centrifugal forces are directed counter currently in one side of the channel and vary by the angle up to adding of the two of them in the same direction in the opposite side of the channel. The conditions may fit to the strong cavitation regime inside the volume of fluid flow due to a stretching of the liquid in some locations.