Unsteady MHD flow past a porous plate with step function change in suction at slip flow regime

Unsteady two-dimensional hydromagnetic flow of an electrically conducting viscous incompressible fluid past a semi-infinite porous flat plate with step function change in suction velocity is studied allowing a first order velocity slip at the boundary condition. The solution of the problem is obtained in closed form and the results are discussed with the aid of graphs for various parameters entering in the problem.Notations B intensity of magnetic field - H magnetic field parameter,H=(M+1/4)^1/2–1/2 - h rarefaction parameter - L ₁ slip coefficient; ;I, mean free path of gas molecules;f, Maxwell's reflection coefficient - M magnetic field parameter - r suction parameter - t time - t dimensionless time - u velocity of the fluid - u dimensionless velocity of the fluid - U velocity of the fluid at infinity - v suction velocity - v ₁ suction velocity att<=0 - v ₂ suction velocity att>0 - x distance parallel to the plate - y distance normal to the plate - y nondimensional distance normal to the plate - v kinematic viscosity - electric conductivity of the fluid - density of the fluid - shear stress at the wall - nondimensional shear stress at the wall - erf error function - erfc complementary error function     

Unusual coronal activity following the flare of 6 November 1980

For almost 30 hr after the major (gamma-ray) two-ribbon flare on 6 November 1980, 03:30 UT, the Hard X-Ray Imaging Spectrometer (HXIS) aboard the SMM satellite imaged in > 3.5 keV X-rays a gigantic arch extending above the active region over the limb. Like a similar configuration on 22 May 1980, this arch formed the lowest part of a stationary post-flare radio noise storm recorded at metric wavelengths at Nançay and Culgoora. 6.5 hr after the flare a coronal region below the arch started quasi-periodic pulsations in X-ray brightness, observed by several SMM instruments. These brightness variations had no response in the chromosphere (H), very little in the transition layer (O v), but they clearly correlated with similar variations in brightness at 169 MHz. There were 13 pulses of this kind, with apparent periodicity of about 20 min, until another flare occurred in the active region at 15:00 UT. All the brightenings appeared within a localized area of about 30000 km² in the northern part of the active region, but they definitely did not occur all at the same place.The top of the X-ray arch, at an altitude of 155 000 km, was continuously and smoothly decaying, taking no part in the striking variations below it. Therefore, the area variable in brightness does not seem to be the footpoint of the arch, as we supposed for similar variations on 22 May. More likely, it is a separate region connected directly with the source of the radio storm; particles accelerated in the storm may be dumped into the low corona and cause the X-ray enhancements. The X-ray arch was enhanced by two orders of magnitude in 3.5–5.5 keV X-ray counts and the temperature increased from 7.3 × 10⁶ to 9 × 10⁶ K when the new two-ribbon flare occurred at 15:00 UT. Thus, it is possible that energy is brought into the arch via the upper parts of the reconnecting flare loops - a process that can continue for hours.     

On geological processes on venus: Analysis of the relationship between altitude and degree of surface roughness

Aiming to study the relationship between Venus surface heights and surface roughness, the Pioneer Venus surface altitude map and map of r.m.s. slope in m-dkm scale have been analy sed for the Beta and Ishtar regions using a system of digital image processing. To integrate the data obtained, the results of geomorphological analysis of Venera 9 and 10 TV panoramas as well as gamma-spectrometric and photometric measurements were used. The analysis gives proof that Venera 9 and 10 landing sites represent geologic-morphologic situations typical of Venus, thus enabling the results of observations made at landing sites to be extended to large provinces. Apparently this conclusion is also applicable to the Venera 8 landing site. No strong relationship exists between the roughness of the surface and its altitude or the amount of a regional slope; neither for the Beta nor for the Ishtar region. A weak direct correlation observable for roughness-altitude pairs for the Beta region and roughness-altitude, roughness-slope pairs for the Ishtar region are quite obviously a consequence of regional roughness control, i.e. of an overall character of geological structure. On Venus the factors contributing to higher surface roughness on the m-dkm scale are, obviously, mostly volcanic and tectonic in their nature whilst those responsible for smoothing-out of the surface are chiefly exogenic. The rate of exogenic transformation of the Cytherean surface may be fairly high. On Venus, similarly as on the Earth, active tectono-magmatic processes have possibly taken place in recent geological epochs. One of the places where they are manifest is an extensive zone running from north to south across the Beta, Phoebe and Themis highlands. Within its limits occur both the process of basaltic shield-type volcanism and areal basalt effusions at low hypsometric levels accounting for the formation of lowland plains at the expense of ancient rolling plains. The basalts of the shield volcano Beta show some differences in composition compared to those of areal effusions at low hypsometric levels. The overall character of Cytherean tectonics in the recent geologic epoch is apparently block-type with a predominance of vertical movements. Against the background of the sinking of some of the blocks the other ones are rising and, possibly, such compensation upheavals have been responsible for the formation of the Ishtar region.     

Shear-induced instability and arch filament eruption: A magnetohydrodynamic (MHD) numerical simulation

We investigate, via a two-dimensional (nonplanar) MHD simulation, a situation wherein a bipolar magnetic field embedded in a stratified solar atmosphere (i.e., arch-filament-like structure) undergoes symmetrical shear motion at the footpoints. It was found that the vertical plasma flow velocities grow exponentially leading to a new type of global MHD-instability that could be characterized as a Dynamic Shearing Instability, with a growth rate of about 8{ovV} _A a, where {ovV} _A is the average Alfvén speed and a ^–1 is the characteristic length scale. The growth rate grows almost linearly until it reaches the same order of magnitude as the Alfvén speed. Then a nonlinear MHD instability occurs beyond this point. This simulation indicates the following physical consequences: the central loops are pinched by opposing Lorentz forces, and the outer closed loops stretch upward with the vertically-rising mass flow. This instability may apply to arch filament eruptions (AFE) and coronal mass ejections (CMEs).To illustrate the nonlinear dynamical shearing instability, a numerical example is given for three different values of the plasma beta that span several orders of magnitude. The numerical results were analyzed using a linearized asymptotic approach in which an analytical approximate solution for velocity growth is presented. Finally, this theoretical model is applied to describe the arch filament eruption as well as CMEs.     

Introduction to the restricted Jupiter orbiter problem

We consider a restricted six-body problem, consisting of Jupiter, the four Galilean satellites, and an orbiter. The Galilean satellites' orbits are circular and coplanar; Io, Europa, and Ganymede are in exact resonance; their mean longitudes obey the Laplace relation. We seek periodic orbits which avoid close approaches to any satellite; such orbits are of interest for mission planning. They are approximated as equilibrium points of sets of variational equations associated with time-averaged disturbing functions. Stability of the solutions is also determined. The orbits of greatest interest are:Planar: twice Callisto's period, eccentricity0.6Planar: four times Callisto's period, eccentricity0.75Slightly inclined: twice Callisto's period, eccentricity arbitraryPlanar: 4/5 or 5/4 Europa's period.     

The atmosphere of Io from Pioneer 10 radio occultation measurements

The occultation of the Pioneer 10 spacecraft by Io (JI) provided an opportunity to obtain two S-band radio occultation measurements of its atmosphere. The dayside entry measurements revealed an ionosphere having a peak density of about 6 × 10⁴ elcm^?3 at an altitude of about 100 km. The topside scale height indicates a plasma temperature of about 406 K if it is composed of Na⁺ and 495 K if N₂⁺ is principal ion. A thinner and less dense ionosphere was observed on the exit (night side), having a peak density of 9 × 10³ elcm^?3 at an altitude of 50 km. The topside plasma temperature is 160 K for N₂^? and 131 K for Na⁺. If the ionosphere is produced by photoionization in a manner analogous to the ionospheres of the terrestrial planets, the density of neutral particles at the surface of Io is less than 10¹¹?10¹² cm³, corresponding to a surface pressure of less than 10^?8 to 10^?9 bars. Two measurements of its radius were also obtained yielding a value of 1830 km for the entry and 192 km for the exit. The discrepancy between these values may indicate an ephemeris uncertainty of about 45 km. The two measurements yield an average radius of 1875 km, which is not in agreement with the results of the Beta Scorpii stellar occultation.