Equilibrium Convection on a Tidally Heated and Stressed Icy Shell of Europa for a Composite Water Ice Rheology

Water ice I rheology is a key factor for understanding the thermal and mechanical state of the outer shell of the icy satellites. Ice flow involves several deformation mechanisms (both Newtonian and non-Newtonian), which contribute to different extents depending on the temperature, grain size, and applied stress. In this work I analyze tidally heated and stressed equilibrium convection in the ice shell of Europa by considering a composite viscosity law which includes diffusion creep, basal slip, grain boundary sliding and dislocation creep, and. The calculations take into account the effect of tidal stresses on ice flow and use grain sizes between 0.1 and 100 mm. An Arrhenius-type relation (useful for parameterized convective models) is found then by fitting the calculated viscosity between 170 and 273 K to an exponential regression, which can be expressed in terms of pre-exponential constant and effective activation energy. I obtain convective heat flows between ~40 and ~60 mW m^?2, values lower than those usually deduced (~100 mW m^?2) from geological indicators of lithospheric thermal state, probably indicating heterogeneous tidal heating. On the other hand, for grain sizes larger than ~0.3 mm the thicknesses of the ice shell and convective sublayer are ~20–30 km and ~5–20 km respectively, values in good agreement with the available information for Europa. So, some fundamental geophysical characteristics of the ice shell of Europa could be arising from the properties of the composite water ice rheology.     

Equilibrium problems in a rotating convection zone

This paper is a continuation of the author's work on stellar convection (Vandakurov, 1975a; hereafter referred to as Paper I). The approximate equations for convective perturbations in Paper I are somewhat corrected and generalized to include both nonlinear terms and possible variations in molecular weight. A crude estimate of the nonlinear terms is given by means of an expansion of the solution in powers of the perturbation amplitude. We assume that only the most rapidly growing unstable modes are of significance and that the initial kinetic energy of each independent mode is the same. An expansion in powers of the angular velocity is also performed. (This means that some upper stellar layers with small, but not very small, superadiabaticity are considered.) It is shown that an azimuth-averaged azimuthal force is created by the unstable perturbations. In particular, it is most likely that in the upper part of any stellar convection envelope the rigid rotation is nonequilibrious. A simple formula for the above azimuthal force is derived in the case of a latitudedependent angular velocity and a small viscosity of the medium. If the perturbed characteristic scaleheight is sufficiently small, the azimuthal force created by the most unstable modes is equivalent to a viscous force, but with a negative viscosity coefficient. In the approximation under consideration, the heat flux is spherically symmetric.     

Artificial viscosity in simulation of shock waves by smoothed particle hydrodynamics

This paper reconsiders artificial viscosity in smoothed particle hydrodynamics in order to prevent interparticle penetration, unwanted heating, and unphysical solutions. The coefficients in the Monaghan’s standard artificial viscosity are considered as a time variable, and we propose a restriction on them such that we avoid the undesired effects in the subsonic regions. We use the shock formation in adiabatic and isothermal cases to study the ability of this modified artificial viscosity recipe. Our computer experiments show that the proposal appears to work and the accuracy of this restriction is acceptable.     

Five dimensional bulk viscous cosmological model with wet dark fluid in general relativity

In this paper, we have constructed a five dimensional LRS Bianchi type I cosmological model with wet dark fluid (WDF) in general relativity with the matter field described as bulk viscosity. It is found that in presence of bulk viscosity an inflationary effective stiff fluid cosmological model is obtained, whereas in absence of bulk viscosity the wet dark fluid degenerate to stiff fluid. Some physical and geometrical properties of the model are also discussed.     

Anisotropic bulk viscous cosmological models with particle creation

This paper is devoted to the study of role of particle creation and bulk viscosity on evolution of homogeneous and anisotropic model of the universe represented by Bianchi type I space time metric. Particle creation and bulk viscosity have been considered as separated irreversible processes. In order to discuss physical and geometrical behaviour of the model, a new set of exact solutions of Einstein’s field equation have been obtained in non-causal, truncated and full causal theories. Dynamical behaviours of models have also been discussed.     

String fluid cosmological models in general relativity

LRS Bianchi type-I string cosmological models are studied in the frame work of general relativity when the source for the energy momentum tensor is a bulk viscous fluid containing one dimensional strings embedded in electromagnetic field. A barotropic equation of state for the pressure and density is assumed to get determinate solutions of the field equations. The bulk viscosity is assumed to be inversely proportional to the scalar expansion. The physical and kinematical properties of the models are discussed. The effect of viscosity and electromagnetic field on the physical and kinematical properties is also investigated.     

Entropy of viscous Universe models

The cosmological event horizon entropy and the apparent horizon entropy of the ΛCDM and the Bianchi type I Universe model with viscosity has been calculated numerically, and analytically in the large time limit. It is shown that for these Universe models the cosmological event horizon entropy increases with time and for large times it approaches a finite maximum value. The effect of viscosity upon the entropy is also studied and we have found that its role is to decrease the entropy. The bigger the viscosity coefficient is the less the entropy will be. Furthermore, the radiation entropy for the ΛCDM Universe model with and without viscosity is investigated, and together with the cosmological event horizon entropy are used to examine the validity of the generalized second law of thermodynamics, which states that the total rate of change of entropy of the Universe is never negative, in this Universe model.     

Bianchi Type I Bulk Viscous Stiff Fluid Tilted Cosmological Model in General Relativity

Bianchi Type I Bulk viscous fluid tilted cosmological model without shearviscosity is investigated. The behaviour of the model in presence andabsence of bulk viscosity is discussed. The physical and geometricalconsequences of the models are also discussed.     

Bulk viscous barotropic magnetised string cosmological models

Spatially homogeneous and anisotropic LRSBianchi type-I string cosmological models are studied in the frame work of general relativity when the source for the energy momentum tensor is a bulk viscous fluid containing one dimensional strings embedded in a magnetic field. A barotropic equation of state for the pressure and density is assumed to get determinate solutions of the field equations. The bulk viscous pressure is assumed to be proportional to the energy density. The effects of viscosity and electromagnetic field on the properties of the model are investigated. The role of bulk viscosity and electromagnetic field in getting an inflationary phase and in establishing a string phase in the universe is studied.     

非磁化吸积盘中的粘滞性和朗缪尔波湍动应力

粘滞性问题一直是吸积盘理论中十分重要而又难以解决的一个基本理论问题．最近,Balbus和Hawley建议在磁化吸积盘中存在一种局域的磁流体剪切不稳定性机制,它能导致磁化吸积盘中有效的角动量转移,从而可以部分地解决磁化吸积盘中的粘滞性问题．但是Balbus－Hawley机制对非磁化吸积盘仍然是无效的．在本文中,我们研究了一种非磁化吸积盘模型,其中粘滞性机制起源于等离子体朗缪尔波湍动应力,并与标准a吸积盘模型中起源于流体或磁流体湍流的雷诺应力的粘滞性机制进行了比较．结果表明等离子体朗缪尔波湍动应力不仅对非磁化吸积盘中粘滞性的起源有重要的贡献,而且有可能是比流体湍流或磁流体湍流的雷诺应力更加有效的粘滞性起源的物理机制．     

Non-Newtonian topographic relaxation on Europa

Models of topographic support on Europa by lateral shell thickness variations have previously assumed a Newtonian ice viscosity. Here I show that using a more realistic stress-dependent viscosity gives relaxation times which can be significantly different. Topography of wavelength 100 km cannot be supported by lateral shell thickness variations for ∼50 Myr, unless the shell thickness is <10 km or the ice grain size >10 mm. Shorter wavelength topography would require even thinner shells, but may be supported elastically. Global-scale variations in shell thickness, however, can be supported for geological timescales if the shell thickness is O(10 km).     

Oceans in the icy Galilean satellites of Jupiter?

Equilibrium models of heat transfer by heat conduction and thermal convection show that the three satellites of Jupiter—Europa, Ganymede, and Callisto—may have internal oceans underneath ice shells tens of kilometers to more than a hundred kilometers thick. A wide range of rheology and heat transfer parameter values and present-day heat production rates have been considered. The rheology was cast in terms of a reference viscosity ν₀ calculated at the melting temperature and the rate of change A of viscosity with inverse homologous temperature. The temperature dependence of the thermal conductivity k of ice I has been taken into account by calculating the average conductivity along the temperature profile. Heating rates are based on a chondritic radiogenic heating rate of 4.5 pW kg⁻¹ but have been varied around this value over a wide range. The phase diagrams of H₂O (ice I) and H₂O + 5 wt% NH₃ ice have been considered. The ice I models are worst-case scenarios for the existence of a subsurface liquid water ocean because ice I has the highest possible melting temperature and the highest thermal conductivity of candidate ices and the assumption of equilibrium ignores the contribution to ice shell heating from deep interior cooling. In the context of ice I models, we find that Europa is the satellite most likely to have a subsurface liquid ocean. Even with radiogenic heating alone the ocean is tens of kilometers thick in the nominal model. If tidal heating is invoked, the ocean will be much thicker and the ice shell will be a few tens of kilometers thick. Ganymede and Callisto have frozen their oceans in the nominal ice I models, but since these models represent the worst-case scenario, it is conceivable that these satellites also have oceans at the present time. The most important factor working against the existence of subsurface oceans is contamination of the outer ice shell by rock. Rock increases the density and the pressure gradient and shifts the triple point of ice I to shallower depths where the temperature is likely to be lower then the triple point temperature. According to present knowledge of ice phase diagrams, ammonia produces one of the largest reductions of the melting temperature. If we assume a bulk concentration of 5 wt% ammonia we find that all the satellites have substantial oceans. For a model of Europa heated only by radiogenic decay, the ice shell will be a few tens of kilometers thinner than in the ice I case. The underlying rock mantle will limit the depth of the ocean to 80-100 km. For Ganymede and Callisto, the ice I shell on top of the H₂O-NH₃ ocean will be around 60- to 80-km thick and the oceans may be 200- to 350-km deep. Previous models have suggested that efficient convection in the ice will freeze any existing ocean. The present conclusions are different mainly because they are based on a parameterization of convective heat transport in fluids with strongly temperature dependent viscosity rather than a parameterization derived from constant-viscosity convection models. The present parameterization introduces a conductive stagnant lid at the expense of the thickness of the convecting sublayer, if the latter exists at all. The stagnant lid causes the temperature in the sublayer to be warmer than in a comparable constant-viscosity convecting layer. We have further modified the parameterization to account for the strong increase in homologous temperature, and therefore decrease in viscosity, with depth along an adiabat. This modification causes even thicker stagnant lids and further elevated temperatures in the well-mixed sublayer. It is the stagnant lid and the comparatively large temperature in the sublayer that frustrates ocean freezing.     

Radiating gravitational collapse with shear viscosity

A model is proposed of a collapsing radiating star consisting of an isotropic fluid with shear viscosity undergoing radial heat flow with outgoing radiation. The pressure of the star, at the beginning of the collapse, is isotropic but owing to the presence of the shear viscosity the pressure becomes more and more anisotropic. The behaviour of the density, pressure, mass, luminosity and the effective adiabatic index is analysed. Our work is compared to the case of a collapsing shearing fluid of a previous model, for a star with 6 M_⊙.     

A DETERMINATION OF THE ABSOLUTE AGES OF SEVEN FRONT FACE LUNAR BASINS†

Careful examination of seven giant front face basins on the moon will show that the basins most densely covered by younger craters are the oldest. With increasing age they exhibit lower external rims, not scarp heights. The rims are progressively more subdued with age. This paper proposes that absolute ages for these basins can be obtained by calculating an effective viscosity of the moon's outer layers from 3.85 × 10⁹ y, the date of Imbrium, to the present. Similarly viscosity measures can be determined for the oldest basin. To do this we need the present and the original rim heights. The present values are observed. The original heights are calculated by extrapolating the relationship between diameter and rim height for normal Class I craters. It turns out that as long as the larger basins have proportionately higher original heights than the smaller, the absolute values are of little importance and the ages are definitive. There are many similar families of viscosity changes with age and they yield similar absolute ages. In each case equations relating viscosity changes with age were derived and for each basin there is only one age that will yield the final rim height. Ages, × 10⁹ y, of the basins are: Orientale 3.82, Imbrium 3.85, Crisium 4.00, Nectaris 4.07, Serenitatis 4.14, Humorum 4.23 and an Unnamed basin between Werner and the Altai ring 4.30.     

Tilted Bianchi type I cosmological models filled with disordered radiation in general relativity revisitedD

Tilted Bianchi type I cosmological models filled with disordered radiation in presence of a bulk viscous fluid and heat flow are investigated. The coefficient of bulk viscosity is assumed to be a power function of mass density. Some physical and geometric properties of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Radio Interferometric Observations of the Sun Using Commercial Dish TV Antennas

This memoir is a summary of my early childhood, education, and research career at the Naval Research Laboratory (NRL) in Washington, DC. I describe my early interest in astronomy and how I wound up working in the fields of solar physics and X-ray-UV spectroscopy of high temperature plasmas. I describe some of my home life and other interests, my education at the University of Pittsburgh, and the various projects and management activities that I have been fortunate to work on at NRL. I have been blessed with being able to work at a first-class research laboratory populated by outstanding scientists. I am particularly blessed to have worked with my many friends and colleagues in the NRL Space Science Division. Perhaps I am most blessed by having had wonderful parents that gave me the interests I have in life and the passion to pursue them, and an outstanding wife that has been my partner through good and bad times for over 50 years. I am now retired but for three years I was a participant in the NRL Voluntary Emeritus Program (VEP). However, this memoir is a personal account, and not work done as a VEP.

     

Self-creation theory of gravitation. A self-similar approach

The magnetorotational instability (MRI) in axisymmetric rotating dusty plasmas with viscous effects is investigated by means of a three-component model MRI with a vertical weak magnetic field. Starting from the three-fluid equations and Maxwell’s equations, I derive the general linear dispersion relation governing local MRI. The dust rotational flow is assumed to have the same angular velocity as ions and electrons. The dispersion relation of two special cases, without viscosity and dust effects respectively, is discussed in detail by taking into account the high-frequency approximation in order to make the perturbation frequency larger than the ion cyclotron frequency. The numerical results demonstrate that both the viscosity and dust effects can prevent the MRI growth, and the dust-induced effects are shown to be especially significant.     

Progress Toward Light Weight High Angular Resolution Multilayer Coated Optics

We have been working on 3 separate projects that together will give us the ability to make 1 arc second, light weightWolter I optics that work above 40 keV. The three separate tasks are: (a) plasma spraying of metal-coated micro-balloons; (b) coating of the inside of Wolter I mirrors, (c) actuator designs for improving figure quality.We give a progress report on our work on all three areas.     

Bulk viscous string cosmological models with electromagnetic field

LRS Bianchi type-I string cosmological models are studied in the frame work of general relativity when the source for the energy momentum tensor is a bulk viscous stiff fluid containing one dimensional strings embedded in electromagnetic field. The bulk viscosity is assumed to be inversely proportional to the scalar expansion. The physical and kinematical properties of the models are discussed. The effects of Viscosity and electromagnetic field on the physical and kinematical properties are also investigated.     

Bianchi Type I String Cosmological Models with Bulk Viscosity and Magnetic Field

Some locally rotationally symmetric (LRS) Bianchi type I cosmological models for a cloud string with bulk viscosity and magnetic field are presented. Where an equation of state ρ = kλ and a relation between metric potential R = AS ⁿ are considered. The solution describes a shearing and nonrotating model with a big bang start. In the absence of magnetic field it reduces to a string model with bulk viscosity, where the relation between the coefficient of bulk viscosity and energy density is ζ ∝ ρ^1/2. After choosing k = , it further reduces to a string model without viscosity and magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.