Showing papers on "Hydrostatic equilibrium published in 1983"

Vertical Differencing of the Primitive Equations in Sigma Coordinates

Abstract: A vertical finite-difference scheme for the primitive equations in sigma coordinates is obtained by requiring that the discrete equations retain some important properties of the continuous equations. A family of schemes is derived whose members conserve total energy, maintain an integral constraint on the vertically integrated pressure gradient force, have a local differencing of the hydrostatic equation, and give exact forms of the hydrostatic equation and the pressure gradient force for particular atmospheres. The proposed scheme is a member of this family that in addition conserves the global mass integral of the potential temperature under abiabatic processes.

Magnetic neutral sheets in evolving fields. I - General theory. II - Formation of the solar corona

Abstract: The problem of the hydrostatic equilibrium of a large-scale magnetic field embedded in a fluid with infinite electrical conductivity is considered. It is pointed out that a necessary condition for static equilibrium is the invariance of the small-scale pattern in the field along the large-scale direction. A varying topological pattern implies that no fluid pressure distribution exists for which the field is everywhere static. Magnetic neutral sheets form, and dynamical reconnection of the field takes place. It is shown here that the invariance is also a sufficient condition for the existence of a fluid pressure distribution producing static equilibrium. Even in the simplest cases, however, the requirements on the fluid pressure are extreme and, a priori, are unlikely. It is concluded that almost all twisted flux tubes packed together produce dynamical nonequilibrium and dissipation of their twisting. This is the basic effect underlying the long-standing conjecture that the shuffling of the footpoints of the bipolar magnetic fields in the sun is responsible for heating the active corona. Attention is then given to the consequences of this general dynamical dissipation in the magnetic fields that produce the active corona of the sun. The footpoints of the field are continually manipulated by the subphotospheric convection in such a way that the lines of force are continually wrapped and rotated about one another.

A non-reflective upper boundary condition for limited-height hydrostatic models.

Abstract: A simple upper boundary condition for hydrostatic, Boussinesq models is derived from a linear internal wave theory, assuming a uniform stratification and no Coriolis effects. This condition is applied in a two-dimentional nonlinear model of the planetary boundary layer. The numerical implementation and some stability problems are discussed. A comparison of the results of numerical experiments using different vertical extensions with analytical solutions is used to show that the condition provides a satisfactory solution to the problems of radiation of upward propagating energy.

The Adequacy of the Hydrostatic Assumption in Sea Breeze Modeling over Flat Terrain.

Abstract: Using a linear analytic model and a nonlinear numerical model, the adequacy of the hydrostatic model is investigated for use in the simulation of sea and land breezes over flat terrain. Among the results it is found that for a given horizontal scale of heating, the hydrostatic assumption becomes less valid as the intensity of surface heating increases, and as the synoptic temperature lapse rate becomes less stable. The spatial scale at which the hydrostatic assumption fails is substantially smaller than suggested by Orlanski (1981). For sufficiently stable large-scale thermodynamic stratifications, for instance, aspect ratios of order unity can still produce nearly identical solutions, regardless of whether or not the hydrostatic assumption is used. The difference in the conclusions between our study and that of Orlanski is attributed to Orlanksi's analyses of the characteristic wave equations in the free atmosphere, whereas in a sea-breeze simulation the requirement that vertical velocity at the...

Thermally Driven Flow in a Rotating Spherical Shell: Axisymmetric States

Abstract: A spherical analogue of the rotating annulus experiments modeling atmospheric motion, in which a liquid is contained between two rigid, corotating and concentric hemispheres upon both of which thermal gradients are imposed, is presently studied by means of numerical models. Temperatures are lower on the inner than on the outer sphere, and decrease towards the pole. Using Navier-Stokes equations which assume symmetry about the polar axis, finite difference numerical models yield steady-state solutions to the equations. Hydrostatic and nonhydrostatic solutions are compared for cylindrical and spherical cases, and it is found in the case of the spherical shell that the differences between hydrostatic and nonhydrostatic solutions are small and largely confined to the regions near the pole and equator. It is suggested that nonhydrostatic effects on the axisymmetric state will not affect the flow's baroclinic stability.

The role of Cosmic rays in hydrostatic equilibrium of the galactic halo

Abstract: The hydrostatic equilibrium of the gas field system is studied in the halo. Cosmic-ray distribution is considered independently from the magnetic field on the basis of the diffusion model of the propagation of cosmic rays. We show that the cosmic rays extend in the halo to distances of a few kiloparsecs. The magnetic field decreases slowly with height above the galactic plane.

A Comparison of Methods for Computing the Sigma-Coordinate Pressure Gradient Force for Flow over Sloped Terrain in a Hybrid Theta-Sigma Model

Abstract: In connection with the employment of the sigma coordinates introduced by Phillips (1957), problems can arise regarding an accurate finite-difference computation of the pressure gradient force. Over steeply sloped terrain, the calculation of the sigma-coordinate pressure gradient force involves computing the difference between two large terms of opposite sign which results in large truncation error. To reduce the truncation error, several finite-difference methods have been designed and implemented. The present investigation has the objective to provide another method of computing the sigma-coordinate pressure gradient force. Phillips' method is applied for the elimination of a hydrostatic component to a flux formulation. The new technique is compared with four other methods for computing the pressure gradient force. The work is motivated by the desire to use an isentropic and sigma-coordinate hybrid model for experiments designed to study flow near mountainous terrain.

Servo valve for ultra-fast pressure regulation with controlled system damping

Abstract: A liquid flow control servo valve where the flow controlling element is a magnetically loaded hydrostatic step bearing An electromagnet has a central liquid passage 3 through it, and flow from this passage 3 is closed off by a magnetically permeable flat plate which has a planar surface matching a corresponding planar surface of the electromagnet Pressure from passage 3 floats the plate on a thin liquid film in the manner of a hydrostatic step bearing, and the film thickness of this liquid film rapidly adjusts until the hydrostatic bearing pressure force W balances the magnetic forces on the plate This variation in film thickness adjusts flow rate past the plate The flow and pressure drop across the hydrostatic bearing plate rapidly adjusts to coil current in the low hysteresis electromagnet, so that P across the plate varies nearly in proportion to coil current I The geometry of the hydrostatic bearing can be tailored to produce a wide range of viscous damping characterization using conventional squeeze film equations So long as flow in the step bearing is laminar, the ratio of critical damping produced by the valve in a particular installation is invariant over a wide operating range of flows and fluid viscosities

The formation of prominences by thermal instability: A numerical study

Abstract: A two-dimensional model of prominence formation in a region containing a magnetic neutral sheet is constructed for a variety of initial conditions, assuming the coronal plasma to be described by the usual hydromagnetic approximation, with infinite electric conductivity. In each case the magnetic field is initially vertical, varying antisymmetrically with respect to the neutral sheet, to a maximum value at a distance of 70 000 km from the neutral sheet. In the first case, the plasma is initially in hydrostatic equilibrium, whereas in successive cases, the pressure is assumed to be of such a value that the plasma is in lateral equilibrium of total pressure (gas plus magnetic). In a variation of this case, the value of the solar gravitational field was artificially reduced, and the effects considered. Large lateral motions are produced in each case, thus apparently inhibiting the condensation of prominences, with the exception of the unrealistic case of artificially reduced gravity. The results suggest that consideration either of a third component of the magnetic field (horizontal and parallel to the neutral sheet), or a finite conductivity, allowing magnetic recombination across the neutral sheet, or both, would more realistically represent the problem and might thus show the development of prominences.

Effects of core perturbations on the structure of the sun

Abstract: The effects of perturbing the inner part of the solar core where the hydrogen abundance has been partially depleted by nuclear burning are investigated. Small regions are mixed within the core and the evolution of the resulting luminosity and radius perturbations is followed. The sensitivity of the solar luminosity and radius to mixing events of different sizes and at different locations in the core is determined and several relationships between the luminosity and radius perturbations are examined to see if the value of one of these perturbations can be inferred from a measurement of the other. It is found that any core perturbation which alters the hydrostatic structures will immediately affect the solar luminosity and radius. The behavior of these perturbations depends on the location of the mixing event within the core. Mixing events cannot produce the decrease in the solar radius without leading to a homogeneous evolution of the solar core and/or to a prohibitively large change in the solar luminosity.

Neutrino emission from a hot, dense, plane-parallel atmosphere in hydrostatic equilibrium. III: The three-flavored atmosphere

Abstract: We continue our investigation of plane-parallel neutrino atmospheres in hydrostatic equilibrium by relaxing one of the assumptions made in Paper I and allowing transport by all the flavors of neutrinos: electron, ..mu.., and tau. As in Paper I, we assume that the gas through which the neutrinos flow consists of free, nondegenerate, nonrelativistic nucleons, extreme relativistic positrons and electrons of arbitrary degeneracy, and photons. We do not allow for the presence of muons and tauons, since typical temperatures and chemical potentials are well below their rest energies. The atmosphere is constrained to be in hydrostatic equilibrium, and energy flux and the three lepton number fluxes are required to be conserved. The numerical method used is that described in Paper II, with the added constraints that ..mu.. and tau lepton number fluxes are constant throughout the atmosphere. Since ..mu.. and tau neutrinos are allowed to interact only via scattering and pair production-absorption processes, lepton number conservation is imposed only at the base of the atmosphere, and should be automatically conserved in layers above the base.

Gravitational collapse of gas clouds with spherical, cylindrical or plane symmetry in the linear wave flow approximation

Abstract: The equations of gas dynamics are solved, quasi-analytically by applying McVittie's method for spherical, cylindrical and plane configurations. The hypothesis of linear wave flow is applied and it is assumed that the final state of collapsing clouds is a hydrostatic equilibrium state, determined by complete polytropes. Complete analytical solutions are found when the generalized (to the three symmetries) Emden equation admits of analytical solutions. Otherwise the solutions are left in terms of the numerical solutions of the Emden equation. Numerical solutions to the Emden equation in the plane case are found and tabulated. A strong dependence of amplification, of density, pressure and temperature of the gas, on the symmetry is found. In addition, it is conclude that the flow remains subsonic, during the collapse, except toward the boundaries of the collapsing clouds.

Fluid Inertia Effects on the Characteristics of Spherical Hydrostatic Bearings : Part 2 Stability

Abstract: Based on a first-order perturbation solution in a modified Reynolds number, an analysis is presented to determine the fluid inertia effects on the stability characteristics of a spherical hydrostatic bearing that has continuous spherical surface. This analysis demonstrates that fluid inertia effects increase the stability threshold speed and that the increase in stability threshold depends on the inertia parameter δ=ρω2r02/p★ (ρ=lubricant density, ω=rotational angular velosity, r0=radius of sphere, p★=ambient pressure). It is found that centrifugal effect on load capacity is much greater than the other inertial effects, whereas centrifugal effect on dynamic coefficients is much smaller than the other inertial effects.

The Constraints of Energy-Conserving Vertical Finite Difference on the Hydrostatic Equations in a NWP Model

Abstract: In NWP models using energy-conserving finite-difference approximations in the vertical, the imposition of different constraints of the discrete energy equation leads to different forms of the hydrostatic equation. This paper shows, using the National Meteorological Center spectral model as a specific example, that the consistent application of all the constraints suggested by Phillips (1974) on the discrete energy equation leads to an algebraic hydrostatic system of (3K–1) unknowns and equations, K being the number of layers in the model. It is emphasized that in relating the vertical structure between the mass and thermal fields, these and only these equations must be satisfied. The introduction of any additional equations without introducing an equal number of unknowns may defeat the purpose of an energy-conserving finite-difference scheme.

Fluid Inertia Effects on the Characteristics of Spherical Hydrostatic Bearings : Part 1 Bearing Forces

Abstract: Based on a first-order perturbation solution in a modified Reynolds number, an analysis is presented to determine the fluid inertia effects on the dynamic characteristics of a spherical hydrostatic bearing that has a continuous spherical surface. This analysis demonstrates that fluid inertia influences the load capacity and dynamic properties. The corrections to the conventional elastic and damping coefficients derived on the assumption that inertia forces are negligible, are found not too small to neglect when inertia parameter δ=ρω2r02/p★>0.1 (ρ=lubricant density, ω=rotational angular velocity, r0=radius of spherical bearing, p★=ambient pressure). And the acceleration coefficients may become significant when the displacement of a rotor from the bottom of the bearing is smal1.