Showing papers on "Hydrostatic equilibrium published in 1992"

On the equations of the large-scale ocean

Abstract: As a preliminary step towards understanding the dynamics of the ocean and the impact of the ocean on the global climate system and weather prediction, the authors study the mathematical formulations and attractors of three systems of equations of the ocean, i.e. the primitive equations (the PEs), the primitive equations with vertical viscosity (the PEV2s), and the Boussinesq equations (the BEs), of the ocean. These equations are fundamental equations of the ocean. The BEs are obtained from the general equations of a compressible fluid under the Boussinesq approximation, i.e. the density differences are neglected in the system except in the buoyancy term and in the equation of state. The PEs are derived from the BEs under the hydrostatic approximation for the vertical momentum equation. The PEV2s are the PEs with the viscosity for the vertical velocity retained. This retention is partially based on the important role played by the viscosity in studying the long time behaviour of the ocean, and the Earth's climate.

Creep, compaction and the weak rheology of major faults

Abstract: Field and laboratory observations suggest that the porosity within fault zones varies over earthquake cycles so that fluid pressure is in long-term equilibrium with hydrostatic fluid pressure in the country rock. Between earthquakes, ductile creep compacts the fault zone, increasing fluid pressure, and finally allowing frictional failure at relatively low shear stress. Earthquake faulting restores porosity and decreases fluid pressure to below hydrostatic. This mechanism may explain why major faults, such as the San Andreas system, are weak.

Atmospheric pressure and gravity

Abstract: SUMMARY Gravity Green's functions for a column load of a model atmosphere on a spherical, elastic Earth are presented and they are used to evaluate the contribution of global atmospheric pressure variations to local gravity. The Green's functions are found to be relatively insensitive to the details of the model atmosphere, but they are dependent on the temperature at the base of the column, and on the relative height difference between the base of the column and the gravity station. The total signal that global pressure systems contribute to gravity is about 30 μgal, of which about 90 per cent is produced by the atmosphere within 50 km of the gravity station. A zone between 50 and 1000km from the gravity station contributes a couple of μgal, as does the remainder of the globe. This pattern, the coherence scale of pressure fluctuations, the time and spatial scales appropriate to the hydrostatic approximation, and the distance of the gravity station from the oceans, suggest a division of the globe into local, regional, and global zones. Data requirements, processing details, and the reliability of the computed signal are different in each zone. The local zone is within about 50 km of the gravity station. Within this zone pressure changes rapidly in time, but is spatially coherent, so that hourly observations of pressure and temperature at the gravity site alone are sufficient to compute an accurate correction, except when a front is passing through. The regional zone extends from the edge of the local zone to between several hundred and a thousand kilometres. The signal from this zone is small and is only weakly coherent with the signal from the central zone, so that a rather sparse array of hourly samples of pressure and temperature are required. The gravity signal from the global zone can reach about a μgal. It varies on a time-scale of days, and is influenced by the response of the oceans to pressure variations. Previously reported observations that the admittance between local pressure and gravity residuals depends on epoch, frequency, or site, are most probably due to incorrect modelling. A proper local, regional, temperature, and global correction can adequately account for the gravity signal from the atmosphere to within a few tens of ngal in the diurnal band, and about 100 ngal in the days to seasonal band, except during extreme weather conditions. The application of the local correction lowers the power spectral density of the gravity residuals in every band from seasonal to hourly. The regional, global, and temperature corrections lower the residual noise in the seasonal and synoptic bands, but are not consistently effective at periods less than about half a day.

Density Structure and Star Formation in Dense Cores with Thermal and Nonthermal Motions

Abstract: An equilibrium model of a spherically symmetric dense core which incorporates both thermal and nonthermal motions is presented. This model use the spatial structure of the thermal and non-thermal motions to specify the core density structure in hydrostatic equilibrium. The thermal motions are spatially uniform, and the nonthermal motions increase with radius r as a power law, as indicated by observations

Two-dimensional viscous accretion disk models. I - On meridional circulations in radiative regions

Abstract: It has been suggested that thin Keplerian disks, like rotating stars, cannot attain hydrostatic and thermal equilibrium simultaneously if the angular velocity is a function of radius only. To address the problem of vertical structure and stability of thin accretion disks, we performed 2D axisymmetric calculations by solving the set of fully nonlinear hydrodynamic equations, including radiation transport. The results indicate that the variation of the rotational velocity with height is too small to sustain hydrostatic equilibrium. Instead, the variation of the radial (inflow) velocity with height suffices to establish a stationary state. In particular, we find that for low values of the viscosity parameter alpha, there is mass outflow in the central parts of the disk close to the equatorial plane, and inflow only near the surface. Only for modestly high values of alpha, the flow throughout the disk is directed inward. Thus, the flow within the disk is the result of viscous radial inflow plus a circulatory flow directed outward in the midplane and inward near the surface.

A spectral fully compressible nonhydrostatic mesoscale model in hydrostatic sigma coordinates: Formulation and preliminary results

Abstract: The set of fully compressible nonhydrostatic equations governing a broad spectrum of atmospheric motion was transformed fromz coordinates to sigma coordinates under a hydrostatic base state. The hydrostatic base state may be either time-independent, such as a hydrostatic balance with-out motion or with motion such as a thermal wind balance, or time-dependent such as might be obtained from the result of integrating a hydrostatic model. The transformed set of equations can be used to predict and study all scales of at mospheric phenomena.

Gravity and topography

Abstract: The paper summarizes the fundamental gravity field constants for Mars and a brief historical review of early determinations and current-day accurate estimates. These include the planetary gravitational constant, global figure, dynamical oblateness, mean density, and rotational period. Topographic results from data acquired from the 1967 opposition to the most recent, 1988, opposition are presented. Both global and selected local topographic variations and features are discussed. The inertia tensor and the nonhydrostatic component of Mars are examined in detail. The dimensionless moment of inertia about the rotational axis is 0.4 for a body of uniform density and 0.37621 if Mars were in hydrostatic equilibrium. By comparing models of both gravity and topography, inferences are made about the degree and depth of compensation in the interior and stresses in the lithosphere.

Analysis of Turbulent Hydrostatic Bearings With a Barotropic Cryogenic Fluid

Abstract: Hydrostatic journal bearings handling low viscosity cryogenic liquids operate under extreme conditions of external pressurization. The regime of operation of these bearings is fully turbulent with large fluid inertia effects. Furthermore, cryogenic liquid propeties depend strongly on the local pressure and affect the bearing leakage and force response. The turbulent flow of a barotropic cryogenic fluid in a hydrostatic bearing is considered. Advection fluid inertia, recess-edge fluid inertia and liquid compressibility, and bearing surface roughnesses are included in the analysis. Numerical results for a liquid hydrogen hydrostatic bearing show that an incompressible fluid model overpredicts flow rate and force coefficients when compared to the more realistic barotropic fluid model.

Gravitational Collapse of an Isothermal Sphere

Abstract: We investigate the spherical gravitational collapse of isothermal spheres using numerical hydrodynamics. The initial configuration is close to hydrostatic equilibrium. In the initial density profile has a finite core radius (i.e., it is not singular), supersonic velocities develop during the initial collapse. At the time of central core formation, when the central density diverges, the central inflow velocity approaches −3.3 times the sound speed and the central density approaches an r −2 profile. These conditions are similar to those found in the self-similar solution of Larson and Penston, but occur only at the center and not at all radii as in the self-similar solution at core formation

The excess propagation path of radio waves: study of the influence of the atmospheric parameters on its elevation dependence

Abstract: The atmosphere has three main effects on radio-wave propagation. It causes attenuation, time delay and angular bending. The accuracy of space-to-earth distance measurements is therefore often limited by how well the neutral atmosphere can be modelled. The time-delay translated into equivalent excess propagation path or path delay can be separated into two parts, the hydrostatic delay and the wet delay. In this report new models for the estimation of the hydrostatic delay are extensively tested and compared with four other well-known models. For the elevation dependence of the hydrostatic delay we base our analysis on a simple continuous fraction form. We present models with global and c1imatedependent parameters.

Analysis of hydrostatic journal bearings with end seals

Abstract: An approximate analysis,for the pressure, field and dynamic,force coefficients in turbulent flow, centered hydrostatic journal bearings (HJBs) with fluid inertia and liquid compressibility effects is presented. Results, from the analysis show that HJBs with end seals have increased damping, better dynamic stability characteristics, as well as lower flow rates, than conventional HJBs. However, hydrostatic (direct) stiffness may be lost if excessively tight end seals are used

A Semi-Implicit Finite Difference Model for Three-Dimensional Tidal Circulation

Abstract: A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.

Mars global reference atmosphere model (Mars-GRAM)

Abstract: Mars-GRAM is an empirical model that parameterizes the temperature, pressure, density, and wind structure of the Martian atmosphere from the surface through thermospheric altitudes. In the lower atmosphere of Mars, the model is built around parameterizations of height, latitudinal, longitudinal, and seasonal variations of temperature determined from a survey of published measurements from the Mariner and Viking programs. Pressure and density are inferred from the temperature by making use of the hydrostatic and perfect gas laws relationships. For the upper atmosphere, the thermospheric model of Stewart is used. A hydrostatic interpolation routine is used to insure a smooth transition from the lower portion of the model to the Stewart thermospheric model. Other aspects of the model are discussed.

Effect of gravity on visco-elastic surface waves in solids involving time rate of strain and stress of first order

Abstract: The aim of the present paper is to study the effect of gravity on visco-elastic surface waves in solids. The wave velocity equations are deduced from Biot’s theory of initial stress on the assumption that gravity creates a type of initial stress — hydrostatic in nature. Resulting equations are used to investigate surface waves of the Rayleigh, Love and Stoneley types. Results are in good agreement with corresponding classical results when gravity and viscosity are neglected.

An Idealized Simulation of the Indian Monsoon Using Primitive-Equation and Quasi-Equilibrium Models

Abstract: An idealized simulation of the Indian monsoon is performed using a prescribed heat source representative of the time-averaged latent heating due to convection over India, and a simple representation of the east African orography. A quasi-equilibrium model is used to solve this problem in three dimensions on a sphere. the model is shown to be able to simulate the cross-equatorial flow and monsoon circulations driven by this problem and to be in good agreement with parallel integrations carried out with a hydrostatic primitive-equation model except in areas affected by orographically forced gravity waves. the solutions given by these time-dependent models are in good agreement with those found by using linearized steady-state equations.

Oppenheimer-Volkoff equation inD space-time dimensions

Abstract: The equations which describe the hydrostatic equilibrium of a relativistic stellar configuration inD space-time dimensions (D ≥/ 4) with a spherical symmetric gravitational field are obtained. With suitable transformations, the equations of mass continuity and of hydrostatic equilibrium are given in a non-dimensional form. With the obtained equations the homogeneous stellar model is studied and some stability criteria are obtained inD (D ≥/ 4) space-time dimensions.

Sunspots: A Laboratory for Solar Physics

Abstract: After a brief discussion of sunspot morphology and the better-known aspects of the solar activity cycle, somewhat more detail is given on sunspot-to-photospheric continuum contrast, as a function of both wavelength and phase of the solar cycle. Umbral dots are a poorly understood phenomenon which may show the real limits on convection in the presence of a strong magnetic field. Simple, magnetostatic, and one-dimensional radiative transfer models of the observable layers of umbrae are introduced. Ultraviolet observations are used to determine whether the upper reaches of the umbral atmosphere are close to hydrostatic equilibrium, and models of umbral oscillations are discussed, as a paradigm of sunspots as “controls” for the less ordered parts of the solar atmosphere.

The application of the method of characteristics for the simulation of nearly horizontal flow in two and three spatial dimensions

Abstract: SUMMARY Certain free surface flows exhibit in nature negligible vertical accelerations and as a result the pressure within the fluid remains hydrostatic. The method of characteristics is developed as a solution technique for the integration of the partial differential equations describing this kind of flow. The equations are integrated over the depth to provide a two-dimensional model which is then tested and validated by comparing its results with tide-induced flows occurring in a number of cases where either analytical or observational data are available for comparison. On the basis of the results of the 2D model, a finite difference 3D model is developed which provides the values of the unknown velocities u, u and w along the three axes x, y and z. This combined 2D-3D model is verified by applying it in cases of wind-induced flow inside closed or open basins for which the classical Ekman solution may be used as a testing means.

An integral on the shape of isolated magnetic loops

Abstract: Stationary flows in isolated magnetic flux tubes are studied using the thin flux tube approximation method. Assuming that the external atmosphere is a plane-stratified fluid in hydrostatic equilibrium, then an important integral is found, (1 - (M A ) 2 )B cos θ = const., where M A is the local Alfven Mach number, B is the magnetic field strength and θ is the inclination of the flux tube with the horizontal direction. The integral is independent of the energy transfer mechanism and parameters of the ambient gas. Applying the integral, some theoretical results are obtained about the shape of isolated magnetic flux tubes and some numerical results of previous studies in this field examined

Engine for performing subsea operations and devices driven by such an engine

Abstract: A machine for performing work at great depths utilizes the energy which is released when surrounding water masses at great hydrostatic pressure are admitted into a low pressure reservoir via a hydraulic motor (2). The machine uses a built-in low pressure reservoir (3) as a hydrostatic accumulator, the energy which is released when the surrounding fluid is admitted into the low pressure reservoir being determined by the product of the pressure difference and the internal volume of the low pressure reservoir. In a special version (Fig. 10) the machine is designed as a hydrostatic sampler which is particularly adapted for taking core samples or marine sediments on the seabed.

An Impact of Hydrostatic Extraction Scheme on BMRC’s Global Spectral Model

Abstract: There are two important features in geophysical fluid dynamics. One is that the atmospheric and oceanic equations of motion include the Coriolis force; another is that they describe a stratified fluid. The hydrostatic extraction scheme, or standard stratification approximation, posed by Zeng (1979), reflects the second aspect of geophysical fluid dynamics. There exist two major advantages in this scheme; accurate computation of the pressure gradient force can be obtained over steep mountain slopes, and the accumulation error in vertical finite differencing can be reduced, especially near the tropopause.Chen et al (1987) introduced the hydrostatic extraction scheme into a global spectral model, which attained preliminary success at low resolution. Zhang and Sheng et al (1990) developed and improved the hydrostatic extraction scheme in a global spectral model, in which C0, the parameter that represents the stratification of the reference atmosphere, changes not only with height, but also with latitude. Th

Machine for subsea operations

Abstract: 2109107 9219836 PCTABS00017 A machine for performing work at great depths utilizes the energy which is released when surrounding water masses at great hydrostatic pressure are admitted into a low pressure reservoir via a hydraulic motor (2). The machine uses a built-in low pressure reservoir (3) as a hydrostatic accumulator, the energy which is released when the surrounding fluid is admitted into the low pressure reservoir being determined by the product of the pressure difference and the internal volume of the low pressure reservoir. In a special version (Fig. 10) the machine is designed as a hydrostatic sampler which is particularly adapted for taking core samples or marine sediments on the seabed.

An impact of hydrostatic extraction scheme on BMRC's global global spectral model

Abstract: There are two important features in geophysical fluid dynamics. One is that the atmospheric and oceanic equations of motion include the Coriolis force; another is that they describe a stratified fluid. The hydrostatic extraction scheme, or standard stratification approximation, posed by Zeng (1979), reflects the second aspect of geophysical fluid dynamics. There exist two major advantages in this scheme; accurate computation of the pressure gradient force can be obtained over steep mountain slopes, and the accumulation error in vertical finite differencing can be reduced, especially near the tropopause.

The Analytical Solution of the Stellar Interior Equations for Approximating Stellar and Protostellar Structure

Abstract: This work presents an analytical solution of the Stellar Interior Equations (SIE) in order to approximate the structure of a star. Herein we model the gradients of mass, pressure, temperature, and luminosity for a Main-Sequence star, such as the Sun. Also presented is an analytical method for approximating the hydrostatic core of a protostellar structure. The methods derive, dimensionless variables from the SIE which are then used to solve ‘linearly approximate’ equation, which are expanded about an initial point. The results are in good agreement with standard computer studies in existence (at least for the present Main-Sequence Sun).

Surface instability of elastic half spaces with hydrostatic loading on their surfaces

Abstract: In this paper, the plane-strain buckling of compressible and incompressible elastic half-spaces, whose surfaces are loaded by constant hydrostatic pressures, is studied by using a small-deformation-superposed-on-large-deformation analysis, and the buckling condition for each case is obtained. For Blatz-Ko and harmonic compressible materials as well as Mooney incompressible material, the influence of the surface hydrostatic pressure on the critical buckling condition is discussed in detail.

Strength of large-scale spheroplastic blocks

Abstract: A two-phase material consisting of hollow glass microspheres distributed in an epoxy matrix is considered. Productionprocess solutions to prevent cracking of the material under conditions of hydrostatic compression are described. A comparative analysis of the solutions is presented.