Showing papers on "Hydrostatic equilibrium published in 1985"

Measurements of rotating bubble shapes in a low-gravity environment

Abstract: Measurements of rotating equilibrium bubble shapes in the low-gravity environment of a free-falling aircraft are presented. Emphasis is placed on bubbles which intersect the container boundaries. These data are compared with theoretical profiles derived from Laplace's formula and are in good agreement with the measurements. The interface shape depends on the contact angle, the radius of intersection with the container, and the parameter F, which is a measure of the relative importance of centrifugal force to surface tension. For isolated bubbles F has a maximum value of 1/2. A further increase in F causes the bubble to break contact with the axis of rotation. For large values of F the bubble becomes more cylindrical and the capillary rise occurs over a thinner layer in order that the small radius of curvature can generate a sufficient pressure drop to account for the increased hydrostatic contribution.

Changes of solar luminosity and radius following secular perturbations in the convective envelope

Abstract: The effect on solar models of several types of slow, spherically symmetric perturbations, acting at various depths within the convective envelope, are calculated. Results are presented on perturbations of the efficiency of convective energy transport (alpha perturbations) and on changes in the nongas component of pressure (beta perturbations). The effects of magnetic fields concentrated near the interface between the radiative core and the convective envelope are explored. It is found that the response and relaxation diagnostics depend both on the type of perturbation and on the depth at which the perturbation is applied. In addition to the general depth dependence, model behavior is sensitive to the presence of major ionization zones near the perturbed layer. The time dependence of the solar model behavior is characterized by an initial hydrostatic reaction followed by a thermal readjustment on a time scale of about 100 years, and finally relaxation to a new thermal equilibrium on a Kelvin time scale.

Thick-plate flexure re-examined

Abstract: Summary. The flexure of an incompressible, thick elastic plate floating on an inviscid substratum and subject to an external gravity field is re-analysed. The solution is derived from momentum equations which account for the advection of hydrostatic pre-stress. This is contrasted with a recently published thick-plate solution derived from momentum equations without a pre-stress term. It is demonstrated that neglecting pre-stress advection renders the solution singular when the model degenerates into an inviscid half-space. If pre-stress advection is included, the solution remains correct in this limit. A numerical comparison of both types of thick-plate solution with results based on conventional thin-plate theory further shows that, for geophysically relevant models, the difference in the momentum balance entails discrepancies between the thick-plate solutions which are comparable to the errors introduced by the thin-plate approximation.

A nonlinear steady model for moist hydrostatic mountain waves

Abstract: The dynamics of hydrostatic gravity waves generated by the passage of a steady, stably stratified, moist flow over a two-dimensional topography is considered. Coriolis effects are neglected. The cloud region is determined by the dynamics, and within that region the Brunt-Vaisala frequency takes on a value smaller than the outside value. In both the dry and cloudy regions the Brunt-Vaisala frequency is constant with height. The moist layer is considered to be either next to the mountain or at midlevels and to be deep enough so that an entire cloud forms in that layer. The nonlinearity in the flow and lower boundary affects the dynamics of these waves and wave drag. The latter is found to depend upon: (1) the location of the moist layer with respect to the ground, (2) the amount of moisture, (3) the degree of nonlinearity and (4) the departure from symmetry in the bottom topography.

Type II supernova energetics

Abstract: In this paper we exploit the fact that the collapsing core of a massive star, at the endpoint of its thermonuclear life, rapidly becomes hydrostatic after bouncing at nuclear densities. The energy transferred by pdV work from the inner unshocked core as it becomes hydrostatic to the bounce shock in the outer core is, to a good approximation, the initial energy of the supernova. The magnitude of this energy, which goes into the entropization, dissociation, and kinetic energy of the shocked matter, determines in large measure whether the purely hydrodynamic mechanism of Type II supernovae works. It can be shown semi-analytically that this energy is equal, with minor qualifications, to the binding energy of the hydrostatic remnant. We present analytical formulae for the structure and binding energy of a hydrostatic residue modeled as a composite of two nested polytropes. It is shown that the binding energy of such a configuration, when taken as a function of mass, is independent of the details of the equation of state of the stiff inner polytrope and hence insensitive to the poorly known nuclear equation of state. The nuclear physics enters directly mainly through the ratio of pressure to density at the transition densitymore » where matter becomes stiff. Since all the relevant masses of the remnant can be determined by self-similar or hydrostatic analysis, th initial shock energy can be derived without recourse to hydrodynamic calculation. This perspective allows us to extract most of the essentials of bounce energetics.« less

Submerged multi-purpose facility

Abstract: A submerged multi-purpose facility is optimally located with respect to lateral forces and hydrostatic forces. Lateral force readings are first observed for the geographic location under consideration at a plurality of depths. From these readings, a lateral force curve is developed which is exponential in shape. The mid-range of this curve and just below the mid-range are the depths where the facility is ideally to be located. The facility can then be structured with respect to wall strength to withstand the hydrostatic forces at the depth location determined by the above technique.

A pressure integration technique for hydrostatic analysis

Abstract: The theory for calculating the hydrostatic characteristics of an arbitrary body by integrating the pressures over its submerged surface is presented. The theory describes a transformation of surface integrals to volume integrals which allows conventional naval architectural quantities to be derived directly from the integration of surface pressures. The theory is implemented in a general purpose program which can compute the hydrostatic characteristics of an arbitrary intact or damaged floating body after the body surface has been input as a series of panels.

Reflection of Hydrostatic Gravity Waves in a Stratified Shear Flow. Part I: Theory

Abstract: Continuous partial reflection of linear hydrostatic gravity waves that propagate through a stratified shear flow is examined. The complex reflection coefficient R satisfies a Riccati equation, which is a first-order nonlinear differential equation. It is shown that |R|<1 since critical levels and overreflection are not considered. In this case the conservation of wave action flux may be expressed as a relationship between |R| and El−1, where E is the wave energy and l a characteristic inverse vertical length scale of the background state. It is demonstrated that R for a layered model represents a limiting solution of the Riccati equation. A general solution is also derived, under the assumption that the characteristic woe l is directly proportional to the inverse scale height of the characteristic impedance associated with a stratified shear flow. It is shown that the vanishing of |R| at a specific level is analogous to the vanishing of |R| in a three layer model, when the characteristic impedanc...

Magnetohydrodynamic thermal instabilities in cool inhomogeneous atmospheres

Abstract: The stability of magnetic loops to current-driven filamentation instabilities is investigated. The unperturbed atmosphere is assumed to be composed of an (upper) isothermal optically thin low-density portion and a (lower) higher-density portion which is in radiative equilibrium; in both cases, the atmosphere is in hydrostatic equilibrium, so that gravitational stratification is taken into account. In order to provide specific equilibrium conditions for evaluation of the dispersion relation, conditions appropriate for the surface of a solar-type star are adopted; i.e., a fairly low temperature (T = 5000 K) appropriate for a 'precoronal' state associated, for example, with magnetic flux emerging from photospheric levels under the action of magnetic buoyancy. A linear stability analysis is performed, and numerical results show that physically plausible current densities, which would be generated by typical loop-footpoint motions, are effective in driving MHD instabilities in such a plasma. The instability growth rates are strongly dependent on the assumed current density distribution and on the density scale height.

A code for line blanketing without local thermodynamic equilibrium.

Abstract: A numerical code has been written which is designed to calculate radiation transport and atmospheric structure under the constraints of statistical equilibrium in atomic transitions and radiative and hydrostatic equilibrium in the medium In addition to the complete linearization and variable Eddington factor techniques of Auer and Mihalas, it uses a multi-frequency / multi-grey algorithm which admits the inclusion of many spectral lines in full statistical equilibrium The program can comfortably accept up to about 300 specific lines arising from about 30 lower states and any number of continua Cleverly constructed artificial model atoms can extend the number of lines to 3000 or more, where opacity sampling techniques can begin to approximate the blanketing accomplished by Kurucz in LTE By way of example, I present a model of a stellar atmosphere with effective temperature 35,000 K and surface gravity 104 cm s-2 The calculation includes 98 bound-free transitions and 93 bound-bound transitions (57 with radiative rates) between 91 states in 36 ions of 9 cosmically abundant species

Envelopes of rapidly rotating neutron stars

Abstract: Motivated by the discovery of the millisecond pulsars, we consider the effect of rapid rotation on the envelope of a neutron star. Solving the equation of hydrostatic equilibrium we find expressions for the density and oblateness as functions of radius and polar angle.

A Comparison of Hydrostatic and Nonhydrostatic Wave-CISK.

Abstract: Most conventional wave-CISK models have been used in the study of circulations with aspect ratios less than one, and as a result have been hydrostatic. In general, the most unstable waves in the models are the small-scale high frequency ones. For these waves the hydrostatic assumption is invalid. It therefore seems appropriate to consider a model in which the high aspect ratio waves are treated correctly, i.e., a nonhydrostatic one. In this paper, a comparison between a hydrostatic and a nonhydrostatic wave-CISK model is made. In the hydrostatic model, there is no coupling of the horizontal and vertical scales of the waves and this results in its lack of scale selection. The nonhydrostatic model has an explicit coupling in it and this leads to a preferred scale for the growth of the waves. For all the cases considered, the most unstable wave has an aspect ratio of order one.

On magnetohydrodynamic thermal instabilities in magnetic flux tubes

Abstract: The stability of current-driven filamentary modes in magnetic flux tubes embedded in a plane-parallel atmosphere in LTE and in hydrostatic equilibrium is discussed. Within the tube, energy transport by radiation only is considered. The dominant contribution to the opacity is due to H- ions and H atoms (in the Paschen continuum). A region in the parameter space of the equilibrium configuration in which the instability is effective is delimited, and the relevance of this process for the formation of structured coronae in late-type stars and accretion disks is discussed.

Fuel energy quantification system

Abstract: A fuel energy analysis system is disclosed utilizing a first hydrostatic sensor, calibrated to specific fuel tank geometries, to monitor fuel quantity; and an additional hydrostatic sensor located at a different geometric height from said first sensor, allowing determination of specific gravity through hydrostatic pressure, and thereafter computation of energy content as a function of mass. This system is particularly suitable for harsh environments such as vehicular applications wherein the quality of fuel input to a tank may frequently vary, and is readily corrected for fluid motion in the tank, by the addition of additional sensors in conjunction with baffles.

Variation objective analyses for cyclone studies

Abstract: The objectives were to: (1) develop an objective analysis technique that will maximize the information content of data available from diverse sources, with particular emphasis on the incorporation of observations from satellites with those from more traditional immersion techniques; and (2) to develop a diagnosis of the state of the synoptic scale atmosphere on a much finer scale over a much broader region than is presently possible to permit studies of the interactions and energy transfers between global, synoptic and regional scale atmospheric processes. The variational objective analysis model consists of the two horizontal momentum equations, the hydrostatic equation, and the integrated continuity equation for a dry hydrostatic atmosphere. Preliminary tests of the model with the SESMAE I data set are underway for 12 GMT 10 April 1979. At this stage of purpose of the analysis is not the diagnosis of atmospheric structures but rather the validation of the model. Model runs for rawinsonde data and with the precision modulus weights set to force most of the adjustment of the wind field to the mass field have produced 90 to 95 percent reductions in the imbalance of the initial data after only 4-cycles through the Euler-Lagrange equations. Sensitivity tests for linear stability of the 11 Euler-Lagrange equations that make up the VASP Model 1 indicate that there will be a lower limit to the scales of motion that can be resolved by this method. Linear stability criteria are violated where there is large horizontal wind shear near the upper tropospheric jet.

The relations between the linear and bilinear atmospheric tidal fields in geometric height and in log-pressure coordinates

Abstract: The relationships between the linearized meteorological variables as expressed in geometric height and in log-pressure coordinates are derived from the assumptions of classical atmospheric tidal theory. While the horizontal velocity components are the same to first-order in the two coordinate systems, a linearized vertical velocity differencew′-H0ω′ occurs because of the periodic vertical displacement of the constant pressure surfaces due to time-dependent, hydrostatic density perturbations; a linearized temperature differenceT′-τ′ also results when these displacements occur in the presence of a zero-order vertical gradient of temperature. Both of these differences can be expressed in terms of the tidal geopotential field. For a given tidal mode, both differences are generally proportional to the square root of the ratio of the tidal mode's equivalent depth and the atmospheric scale height; the temperature difference is also proportional to the background temperature lapse rate. It is further shown that the two classical tidal vertical structure equations commonly derived in their respective geometric height and log-pressure coordinate systems are in fact identical to first-orderas long as the same thermotidal forcing function is used. Expressions for the zonal-mean components of the tidal bilinear fluxes, formed by zonally averaging the product of two longitudinally varying, linearized tidal fields, are also derived for the two coordinate systems. For the bilinear fields the largest relative differences (a few tens of percent) are for the tidal zonal-mean forcing per unit mass of the zonal wind. For Earth and Mars, differences between the tidal vertical velocity fields are generally less than 25% but may be significantly larger in the Martian atmosphere during one of its episodic planetary-scale dust storms. Tidal temperature differences are generally smaller.

On magnetohydrodynamic thermal instabilities in magnetic flux tubes. [in plane parallel stellar atmosphere in LTE and hydrostatic equilibrium

Abstract: The stability of current-driven filamentary modes in magnetic flux tubes embedded in a plane-parallel atmosphere in LTE and in hydrostatic equilibrium is discussed. Within the tube, energy transport by radiation only is considered. The dominant contribution to the opacity is due to H- ions and H atoms (in the Paschen continuum). A region in the parameter space of the equilibrium configuration in which the instability is effective is delimited, and the relevance of this process for the formation of structured coronae in late-type stars and accretion disks is discussed.

Hydrostatic models of gas in clusters in an unsteady state in the irregular field

Abstract: A study is made of the hydrostatic distribution of gas in a system in a steady state in the regular field but an unsteady one in the irregular field. Such a system has a velocity distribution with mean square of the radial velocity greater than the mean square of the transversal. Clusters of galaxies probably have such a structure. It is found that the connection between the densities of the gas and the galaxies established by Cavaliere and Fusco-Femiano also holds for isothermal gas in the considered system. Hydrostatic equilibrium of the gas does not hold for clusters with very large asymmetry of the velocity distribution function of the galaxies. The surface brightness of the x-ray emission of the gas is calculated.