Showing papers on "Hydrostatic equilibrium published in 1981"

Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet sun

Abstract: The described investigation is concerned with the solution of the non-LTE optically thick transfer equations for hydrogen, carbon, and other constituents to determine semiempirical models for six components of the quiet solar chromosphere. For a given temperature-height distribution, the solution is obtained of the equations of statistical equilibrium, radiative transfer for lines and continua, and hydrostatic equilibrium to find the ionization and excitation conditions for each atomic constituent. The emergent spectrum is calculated, and a trial and error approach is used to adjust the temperature distribution so that the emergent spectrum is in best agreement with the observed one. The relationship between semiempirical models determined in this way and theoretical models based on radiative equilibrium is discussed by Avrett (1977). Harvard Skylab EUV observations are used to determine models for a number of quiet-sun regions.

The Quasi-Hydrostatic Approximation

Abstract: Second-order expansion of the aspect ratio gives rise to simple equations with a quasi-hydrostatic approximation that perform far better than the classical hydrostatic system in the simulation of moist convection in a mesoscale model. It also suggests that a simple modification to this system may extend the validity of schemes for aspect ratios larger than 1.

Atmospheres for hot, high-gravity stars. II. Pure helium models

Abstract: We present an extensive grid of pure helium stellar model atmosphere calculations for hot, high-gravity stars. These models are intended to help elucidate the nature and characteristics of the progenitors of the DB white dwarfs. The surface gravity in the model grid ranges from log g = 6.0 (1.0) 9.0, and the effective temperature ranges from T/sub e/ = 25,000 K at log g = 6.0 and 8.0 (T/sub e/ = 40,000 K at log g = 7.0 and 9.0) up to temperatures close to the Eddington limit at each gravity. All our models assume hydrostatic equilibrium, steady-state statistical equilibrium, pure helium composition, and plane-parallel geometry. Most of our models are unblanketed and in LTE, and include convective energy transport. In addition to these, smaller preliminary grids of NLTE models (assuming detailed radiative balance in the helium lines) and of LTE, helium-line--blanketed models (including convective energy transport) were computed to assess the importance of these effects.

The temperature-density structure of coronal loops in hydrostatic equilibrium

Abstract: The temperature and density structure are computed for a comprehensive set of coronal loops that are in hydrostatic and thermal equilibrium. The effect of gravity is to produce significant deviations from the usual uniform-pressure scaling law (T∼(pL) 1/3) when the loops are taller than a scale height. For thermally isolated loops it lowers the pressure throughout the loop, which in turn lowers the density significantly and also the temperature slightly; this modifies the above scaling law considerably. For more general loops, where the base conductive flux does not vanish, gravity lowers the summit pressure and so makes the radiation decrease by more than the heating. This in turn raises the temperature above its uniform pressure value for loops of moderate length but lowers it for longer loops. A divergence in loop cross-section increases the summit temperature by typically a factor of 2, and decreases the density, while an increase in loop height (for constant loop length) changes the temperature very little but can halve the density. One feature of the results is a lack of equilibrium when the loop pressure becomes too large. This may explain the presence of cool cores in loops which originally had temperatures below 2 × 106 K. Loops hotter than 2 × 106 K are not expected to develop cool cores because the pressure necessary to produce non-equilibrium is larger than observed.

Temperature gradient effects on the stability of magnetospheric plasmas

Abstract: The linear stability of magnetospheric plasmas to low-frequency electromagnetic perturbations is investigated, for the case where there exist equilibrium density and temperature gradients, as well as temperature anisotropies. The effects of the temperature gradients on the behavior of drift-compressional modes are given special attention. The effects of a gradient in the equilibrium magnetic field, required for hydrostatic equilibrium, are included to lowest nonvanishing order. The model is valid for moderate b magnetospheric plasmas. A two-component (hot and cold) multispecies plasma is considered, and a kinetic linear dispersion relation is derived, for arbitrary Larmor radius ordering. The destabilizing effects of the gradient in the perpendicular temperature (orientations are measured with respect to the unperturbed magnetic field) are discussed.

Effect of Temperature Feedback and Hydrostatic Adjustment in a Stratospheric Model

Abstract: Calculated perturbations to stratospheric ozone are generally thought to be reduced when temperature feedback is included in the model. We find that when self-consistent hydrostatic adjustment is included with temperature feedback, there can be significant differences in the computed change in local ozone concentration. We present results in two frames of reference (changes in ozone at constant altitude and changes at constant pressure) to illustrate the importance of the frame of reference. Including hydrostatic adjustment is particularly important for calculations of the change in local ozone at constant altitude due to CFM, CO2 and H2O perturbations because large changes in the temperature structure are predicted. Only small differences are computed for increases in N2O. Air density adjustment in a constant pressure frame of reference is important when local temperature changes are large.

On a self-consistent representation of earth models, with an application to the computing of internal flattening

Abstract: Most realistic Earth models published as yet have been given in tabulated form, with the noticeable exception of three simple parametric Earth models derived by Dziewonski et al. (1975). Simple interpolation in these tables may lead to inconsistencies, when we consider certain effects which depend crucially on detailed density structure. We establish algorithmic formulae, which may be used to compute all the mechanical properties of a model in an entirely consistent way, once the density as well as P- and S- wave velocities are known. We then use this formulation to integrate Clairaut’s equation in a very efficient way, and thus obtain the hydrostatic flattening to the first order in smallness at any point inside the model. For most geodynamic purposes, we may suffice with this approximation. Finally, we show the results of some calculations of hydrostatic flattening to the first and second order, using an iterative technique of solving the integral figure equations, for an Earth model consistent with all geophysical data available at present. We find that the hydrostatic flattening at the surface should be about 1/298.8, instead of 1/296.961 as quoted by Nakiboglu (1979) for essentially the same model. Moreover, from our results, we estimate the actual flattening of the coremantle boundary to be about 1/390.3.

Global gravitational stability for one-dimensional polytropes

Abstract: We investigate the stability and dynamics of an isolated cloud of gas which is contained by external pressure, and which has imposed one-dimensional symmetry, uniform density and polytropic equation of state. The energies of the cloud in its three internally conserved modes are summed to form a potential function controlling radial motions, and the associated Lagrangian is obtained. Families of stable equilibrium states are then derived – where they exist – along with conditions for marginal instability. We show that this simple global model mimics closely the behaviour of clouds in detailed hydrostatic balance (DHB); and we use the global model to discuss the onset of gravitational instability in real clouds, and in particular, to evaluate the role of non-quasistatic compression

Isolation of the Gravity-Inertial Motion Component in a Nonlinear Atmospheric Model

Abstract: Diagnostic methods me considered for isolating gravity-inertial motions in the output of a nonlinear atmospheric numerical model. The gravity-inertial component is defined by the nongeostrophic motions not directly incorporated with the synoptic-scale evolution according to quasi-scostrophic or balance model relationships. The analysis methods am applied to the solutions for a propagating jet stream maximum generated by a simple two-layer hydrostatic numerical model. Results identify a coherent pattern in the gravity-inertial motion component but details of the horizontal structure and propagation characteristics are only partially resolved. Results also elucidate relative merits of a number of physical variables and difference fields for defining the gravity-inertial component.

Turbulent Shear Flow in Hydrostatic Thrust Bearings

Abstract: This paper is concerned with the effects of a turbulent flow in hydrostatic thrust bearings. Applying an equation representing the "low of wall" to the three-dimensional turbulent shear flow, the local velocity distributions between a rotating disk and a fixed wall are calculated as a function of Reynolds number, local pressure gradient and the ratio of the film thickness to the radius. Using above results, the pressure distribution and the load capacity of hydrostatic thrust bearings with a circular recess are presented. The theoretical results agree well with the experimental data.

The hydrostatic motor: Utilization of hydrostatic pressure differentials in the deep sea

Abstract: A hydrostatic motor that converts hydrostatic pressure gradients in the deep sea into harnessable mechanical energy has been developed and successfully tested. Controlled equalization between higher ambient hydrostatic pressures at oceanic depths and lower pressures retained from atmospheric or sea-level conditions—sealed within a chamber as part of the motor assembly—produces reciprocating motion of a piston. This motion is utilized for power or work requirements. Our needs have been directed toward oceanographic instrumentation requirements but many other applications are likely.

Models of the open solar atmosphere

Abstract: McWhirter et al. (1975) have presented a standard model for the transition region and inner corona that matches with the Harvard Smithsonian Reference Atmosphere. They assume an open field line configuration and solve numerically the equations of energy and hydrostatic equilibrum. The purpose of the present paper is to generalise their model for the temperature and density as functions of height in several ways and, in particular, to determine the temperature maxium and its location. The effect of varying the following characteristics of the model is determined:

Wave-Permeable Lateral Boundary Conditions for Convective Cloud and Storm Simulations

Abstract: Linearized conditional instability theory is used to test the effects of lateral boundary conditions on convective elements. By this theory the outer environment of an amplifying convective element acts like an internal gravity wave with imaginary horizontal wavelength which propagates outward with a wave velocity slightly greater than that of hydrostatic modes. Lateral boundary conditions based on wave radiation principles are therefore appropriate and can eliminate the growth constraints produced by rigid or periodic boundaries.

Toroidal plasma equilibrium with gravity

Abstract: A toroidal magnetic field configuration in a gravitational field is calculated both from a simple force‐balance and by using magnetic surfaces. The configuration is found to be positionally stable in a star. The vibrational frequency near the equilibrium point is proportional to the hydrostatic frequency of a star multiplied by the ratio (WB/Wm)1/2, where WB is the magnetic field energy density, and Wm is the material pressure at the equilibrium point. It is proposed that this frequency may account for the observed solar spot cycles.

On variable hydrostatic transmission for road vehicles, powered by supply of fluid at constant pressure

Abstract: Various hydrostatic power transmission systems for automotive applications with power supply at constant pressure and unrestricted flow and with a Volvo Flygmotor variable displacement motor as the principal unit were investigated. Two most promising concepts were analyzed in detail and their main components optimized for minimum power loss at the EPA Urban Driving Cycle. The best fuel consumption is less than 10 lit. per 100 kM for a 1542 kG vehicle with a hydrostatic motor and a two speed gear box in series (braking power not recovered). Realistic system pressure affects the fuel consumption just slightly, but the package volume/weight drastically. Back pressure increases losses significantly. Special attention was paid to description of the behavior and modeling of the losses of variable displacement hydrostatic machines.

Energy and force conditions of hydrostatic pressing of blanks from powder materials

Abstract: An examination is made of the hydrostatic pressing of metal powders. The total work done in this process is made up of six components. Their determination and methods of calculating them are described. Equations are proposed for calculating the work done in overcoming friction in the gland of the hydrostatic pressure vessel plunger. The equations allow for the variation of the coefficient of friction in the gland, which is a function of pressure in the vessel. Energy expenditure in hydrostatic pressing determined by calculation is in accord with experimental data. This shows that the equations proposed can be employed for choosing plant in the development of new technological processes for the production of parts from metal powders by hydrostatic pressing.