Showing papers on "Hydrostatic equilibrium published in 2002"

An introduction to atmospheric gravity waves

Abstract: 1. Fundamentals 2. The Linear Theory 3. Terrain-Generated Gravity Waves 4. Ducted Gravity Waves 5. Gravity Wave Energetics 6. Waves and Turbulence 7. The Parameterization of Wave Stress 8. Observational Techniques 9. Data Analyses and Numerical Methods Appendix A: The Hydrostatic Atmosphere Appendix B: Computer Codes and Data on CD-ROM

The mass profile of A1413 observed with XMM-Newton: Implications for the M-T relation

Abstract: We present an XMM-Newton observation of A1413, a hot (kT= 6:5 keV) galaxy cluster at z= 0:143. We construct gas and temperature profiles over the radial range up to1700 kpc. This radius corresponds to a density contrast 500 with respect to the critical density at the redshift of the cluster, or equivalently0:7r200. The gas distribution is well described by a model in the outer regions, but is more concentrated in the inner250 kpc. We introduce a new parameterisation for the inner regions, which allows a steeper gas density distribution. The radial temperature profile does not exhibit a sharp drop, but rather declines gradually towards the outer regions, by20% between 0:1r200 and 0:5r200. The projected temperature profile is well described by a polytropic model with= 1:07 0:01. We find that neither projection nor PSF eects change substantially the form of the temperature profile. Assuming hydrostatic equilibrium and spherical symmetry, we use the observed temperature profile and the new parametric form for the gas density profile to produce the total mass distribution of the cluster. The mass profile is remarkably well fitted with the Moore et al. (1999) parameterisation, implying a very centrally peaked matter dis- tribution. The concentration parameter is in the range expected from numerical simulations. There are several indications that beyond a density contrast 600, the gas may no longer be in hydrostatic equilibrium. There is an oset with respect to adia- batic numerical simulations in the virialised part of the cluster, in the sense that the predicted mass for the cluster temperature is40% too high. The gas distribution is peaked in the centre primarily as a result of the cusp in the dark matter profile. The X-ray gas to total mass ratio rises with increasing radius to fgas 0:2. These data strongly support the validity of the current approach for the modeling of the dark matter collapse, but confirm that understanding the gas specific physics is essential.

The structure and stability of molecular cloud cores in external radiation fields

Abstract: We have considered the thermal equilibrium in pre-protostellar cores in the approximation where the dust tempera- ture is independent of interactions with the gas and where the gas is heated both by collisions with dust grains and ionization by cosmic rays. We have then used these results to study the stability of cores in hydrostatic equilibrium in the limit where thermal pressure dominates over magnetic field and turbulence. We compare the density distribution derived in this manner with results obtained in the isothermal case. We find that for cores with characteristics similar to those observed in nearby molecular clouds, the gas and dust temperatures are coupled in the core interior with densities above ∼3×10 4 cm −3 . As a consequence, one expects that the gas temperature like the dust temperature decreases towards the center of these objects. However, the regime where gas and dust temperatures are coupled coincides approximately with that in which CO and many other molecular species deplete onto dust grain surfaces. At larger radii and lower densities, the gas and dust temperatures decouple and the gas temperature tends to the value expected for cosmic ray heating alone. The density structure which one computes taking into account such deviations from isothermality are not greatly different from that expected for an isothermal Bonnor-Ebert sphere. It is impossi- ble in the framework of these models to have a stable equilibrium core with mass above ∼5 Mand column density compatible with observed values (NH > 2 × 10 22 cm −2 or AV > 10 mag). We conclude from this that observed high mass cores are either supported by magnetic field or turbulence or are already in a state of collapse. Lower mass cores on the other hand have stable states where thermal pressure alone provides support against gravitation and we conclude that the much studied object B68 may be in a state of stable equilibrium if the internal gas temperature is computed in self-consistent fashion. Finally we note that in molecular clouds such as Ophiuchus and Orion with high radiation fields and pressures, gas and dust temperatures are expected to be well coupled and hence in the absence of an internal heat source, one expects temperatures to decrease towards core centers and to be relatively high as compared to low pressure clouds like Taurus.

Analytical Approximations to Hydrostatic Solutions and Scaling Laws of Coronal Loops

Abstract: We derive accurate analytical approximations to hydrostatic solutions of coronal loop atmospheres, applicable to uniform and nonuniform heating in a large parameter space. The hydrostatic solutions of the temperature T(s), density ne(s), and pressure profile p(s) as a function of the loop coordinate s are explicitly expressed in terms of three independent parameters: the loop half-length L, the heating scale length sH, and either the loop-top temperature Tmax or the base heating rate EH0. The analytical functions match the numerical solutions with a relative accuracy of 10-2-10-3. The absolute accuracy of the scaling laws for loop base pressure p0(L, sH, Tmax) and base heating rate EH0(L, sH, Tmax), previously derived for uniform heating by Rosner et al., and for nonuniform heating by Serio et al., is improved to a level of a few percent. We generalize also our analytical approximations for tilted loop planes (equivalent to reduced surface gravity) and for loops with varying cross sections. There are many applications for such analytical approximations: (1) the improved scaling laws speed up the convergence of numeric hydrostatic codes as they start from better initial values, (2) the multitemperature structure of coronal loops can be modeled with multithread concepts, (3) line-of-sight integrated fluxes in the inhomogeneous corona can be modeled with proper correction of the hydrostatic weighting bias, (4) the coronal heating function can be determined by forward-fitting of soft X-ray and EUV fluxes, or (5) global differential emission measure distributions dEM/dT of solar and stellar coronae can be simulated for a variety of heating functions.

Modeling Intra-Cluster Gas in Triaxial Dark Halos : An Analytical Approach

Abstract: We present the first physical model for the non-spherical intra-cluster gas distribution in hydrostatic equilibrium under the gravity of triaxial dark matter halos. Adopting the concentric triaxial density profiles of the dark halos with constant axis ratios proposed by Jing & Suto (2002), we derive an analytical expression for the triaxial halo potential on the basis of the perturbation theory, and find the hydrostatic solutions for the gas density and temperature profiles both in isothermal and polytropic equations of state. The resulting iso-potential surfaces are well approximated by triaxial ellipsoids with the eccentricities dependent on the radial distance. We also find a formula for the eccentricity ratio between the intra-cluster gas and the underlying dark halo. Our results allow one to determine the shapes of the underlying dark halos from the observed intra-cluster gas through the X-ray and/or the Sunyaev-Zel'dovich effects clusters.

Stability of thermocapillary flows in non-cylindrical liquid bridges

Abstract: The thermocapillary flow in liquid bridges is investigated numerically. In the limit of large mean surface tension the free-surface shape is independent of the flow and temperature fields and depends only on the volume of liquid and the hydrostatic pressure difference. When gravity acts parallel to the axis of the liquid bridge the shape is axisymmetric. A differential heating of the bounding circular disks then causes a steady two-dimensional thermocapillary flow which is calculated by a finite-difference method on body-fitted coordinates. The linear-stability problem for the basic flow is solved using azimuthal normal modes computed with the same discretization method. The dependence of the critical Reynolds number on the volume fraction, gravity level, Prandtl number, and aspect ratio is explained by analysing the energy budgets of the neutral modes. For small Prandtl numbers (Pr = 0.02) the critical Reynolds number exhibits a smooth minimum near volume fractions which approximately correspond to the volume of a cylindrical bridge. When the Prandtl number is large (Pr = 4) the intersection of two neutral curves results in a sharp peak of the critical Reynolds number. Since the instabilities for low and high Prandtl numbers are markedly different, the influence of gravity leads to a distinctly different behaviour. While the hydrostatic shape of the bridge is the most important effect of gravity on the critical point for low-Prandtl-number flows, buoyancy is the dominating factor for the stability of the flow in a gravity field when the Prandtl number is high.

Simultaneous effects of hydrostatic stress and an electric field on donors in a GaAs-(Ga, Al)As quantum well

Abstract: Theoretical calculations on the influence of both an external electric field and hydrostatic stress on the binding energy and impurity polarizability of shallow-donor impurities in an isolated GaAs-(Ga, Al)As quantum well are presented. A variational procedure within the effective-mass approximation is considered. The pressure-related Γ-X crossover is taken into account. As a general feature, we observe that the binding energy increases as the length of the well decreases. For the low-pressure regime we observe a linearly binding energy behaviour. For the high-pressure regime the simultaneous effects of the barrier height and the applied electric field bend the binding energy curves towards smaller values. For low hydrostatic pressures the impurity polarization remains constant in all cases with an increasing value as the field increases. This constant behaviour shows that the small variations in well width, effective mass, and dielectric constant with pressure do not appreciably affect polarizability. For high hydrostatic pressure, we see a non-linear increase in polarizability, mainly due to the decrease of barrier height as a result of the external pressure, which allows further deformation of the impurity.

Three-dimensional numerical modelling of free surface flows with non-hydrostatic pressure

Abstract: A three-dimensional numerical model is developed for incompressible free surface flows. The model is based on the unsteady Reynolds-averaged Navier-Stokes equations with a non-hydrostatic pressure distribution being incorporated in the model. The governing equations are solved in the conventional sigma co-ordinate system, with a semi-implicit time discretization. A fractional step method is used to enable the pressure to be decomposed into its hydrostatic and hydrodynamic components. At every time step one five-diagonal system of equations is solved to compute the water elevations and then the hydrodynamic pressure is determined from a pressure Poisson equation. The model is applied to three examples to simulate unsteady free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field. Emphasis is focused on applying the model to wave problems. Two of the examples are about modelling small amplitude waves where the hydrostatic approximation and long wave theory are not valid. The other example is the wind-induced circulation in a closed basin

Normal modes of deep atmospheres. I: Spherical geometry

Abstract: Numerical weather- and climate-prediction models have traditionally applied the hydrostatic approximation and also, in particular, the shallow-atmosphere approximation. In addition, and probably as a result, studies of the normal modes of the atmosphere too have made the shallow-atmosphere approximation. The approximation appears to be based on simple scaling arguments. Here, the forms of the unforced, linear normal modes for the deep atmosphere on a sphere are considered and compared with those of the shallow atmosphere. Also, the impact of ignoring the vertical variation of gravity is investigated. For terrestrial parameters, it is found that relaxing either or both of these approximations has very little impact on the spatial form of the energetically significant components of most normal modes. The frequencies too are only slightly changed. However, relaxing the shallow-atmosphere approximation does lead to significant changes in the tropical structure of internal acoustic modes. Relaxing the shallow-atmosphere approximation also leads to non-zero vertical-velocity and potential-temperature fields for external acoustic and Rossby modes; these fields are identically zero when the shallow-atmosphere approximation is made. For a finite-difference numerical model to be able to represent well the behaviour of the free atmosphere it must be able to capture accurately the structures of the normal modes. Therefore, the structures of normal modes can have implications for the choice of prognostic variables and grid staggering. In particular, the vertical structure of normal modes suggests that density and temperature should be analytically eliminated in favour of pressure and potential temperature as the prognostic thermodynamic variables, and that potential temperature and vertical velocity should be staggered in the vertical with respect to the other dynamic prognostic variables, the so-called Charney– Phillips grid. © Royal Meteorological Society, 2002. N. Wood's and A. Staniforth's contributions are Crown copyright.

The Duality between the Boussinesq and Non-Boussinesq Hydrostatic Equations of Motion

Abstract: The hydrostatic equations of motion for ocean circulation, written in terms of pressure as the vertical coordinate, and without making the Boussinesq approximation in the continuity equation, correspond very closely with the hydrostatic Boussinesq equations written in terms of depth as the vertical coordinate. Two mathematical equivalences between these non-Boussinesq and Boussinesq equation sets are demonstrated: first, for motions over a level bottom; second, for general motions with a rigid lid. A third non-Boussinesq equation set, for general motions with a free surface, is derived and is shown to possess a similar duality with the Boussinesq set after making due allowance for exchange of the roles of bottom pressure and sea surface height in the boundary conditions, a reversal of the direction of integration of the hydrostatic equation, and substitution of specific volume for density in the hydrostatic equation. The crucial simplification in these equations of motion comes from the hydrostat...

Pore pressure terminology

Abstract: Fluid pressures in the pore spaces of rocks are critical to several aspects of petroleum exploration and production. However, a general understanding of some basic concepts has been obscured by a lack of consistency in terminology. It is the intent of this paper to clarify the meaning of certain terms so that the many disciplines involved with, and affected by, pore pressures can communicate effectively and clearly. A most confusing aspect of pressure terminology arises from mixing the terms for pressure and pressure gradients. The word “gradient” is often dropped when referring to pressure increases with depth. Even when the gradient distinction is made, it can confuse because it can either mean pressure changes referenced from the surface or pressure changes measured over short depth ranges. It is important to understand pressures in absolute terms before beginning to work with gradients. Please note that the terms “pressure” and “stress” are used interchangeably in the following. They are not strictly the same, but can be so considered for this discussion. (Stress is a tensor while fluid pressure is isotropic.) Figure 1, a very stylized diagram of pressure versus depth for a fictional well, illustrates several concepts. The “hydrostatic” line gives the pressure due to a column of water. The slope would be .433 psi/ft for pure water, but is usually .45–.465 for formation waters. An important concept is that, for a simple porous rock with pore spaces continuously connected to the surface (i.e. an open system), the pressure of the fluid in the pore space is just the pressure exerted by the weight of the overlying fluids. This “normal or hydrostatic pressure” is simply the pressure due to a column of water. Figure 1. Pressure plotted against depth in a fictional well. Overpressure is the amount of pore pressure in excess of …

Dependence of the superconducting transition temperature of single- and polycrystalline MgB2 on hydrostatic pressure

Abstract: The dependence of Tc for MgB2 on purely hydrostatic or nearly hydrostatic pressure has been determined to 23 GPa for single-crystalline and to 32 GPa for polycrystalline samples, and found to be in good agreement. Tc decreases from 39 K at ambient pressure to 15 K at 32 GPa with an initial slope dTc/dP = -1.11(2) K/GPa. Evidence is presented that the differing values of dTc/dP reported in the literature result primarily from shear-stress effects in nonhydrostatic pressure media and not differences in the samples. Although comparison of these results with theory supports phonon-mediated superconductivity, a critical test of theory must await volume-dependent calculations based on the solution of the anisotropic Eliashberg equations.

Polishing system including a hydrostatic fluid bearing support

Abstract: A polishing system such as a chemical mechanical belt polisher includes a hydrostatic fluid bearing that supports polishing pads and incorporates one or more of the following novel aspects. One aspect uses compliant surfaces surrounding fluid inlets in an array of inlets to extend areas of elevated support pressure around the inlets. Another aspect modulates or reverses fluid flow in the bearing to reduce deviations in the time averaged support pressure and to induce vibrations in the polishing pads to improve polishing performance. Another aspect provides a hydrostatic bearing with a cavity having a lateral extent greater than that of an object being polished. The depth and bottom contour of cavity can be adjusted to provide nearly uniform support pressure across an area that is surrounded by a retaining ring support. Changing fluid pressure to the retaining ring support adjusts the fluid film thickness of the bearing. Yet another aspect of the invention provides a hydrostatic bearing with spiral or partial cardiod drain grooves. This bearing has a non-uniform support pressure profile but provides a uniform average pressure to a wafer that is rotated relative to the center of the bearing. Another aspect of the invention provides a hydrostatic bearing with constant fluid pressure at inlets but a support pressure profile that is adjustable by changing the relative heights of fluid inlets to alter local fluid film thicknesses in the hydrostatic bearing.

Hydrostatic Expansion and Spin Changes during Type I X-Ray Bursts

Abstract: We present calculations of the spin-down of a neutron star atmosphere due to hydrostatic expansion during a type I X-ray burst. We show that Cumming & Bildsten incorrectly calculated the change in the moment of inertia of the atmosphere during a type I burst, resulting in a factor of 2 overestimation of the magnitude of the spin-down for rigidly rotating atmospheres. We derive the angular momentum conservation law in general relativity, both analytically for the case of slow rotation and numerically for rapidly rotating stars. We show that general relativity has a small effect on the angular momentum conservation law, at the level of 5%-10%. We show how to rescale our fiducial results to different neutron star masses, rotation rates, and equations of state and present some detailed rotational profiles. Comparing our results with recent observations of large frequency shifts in MXB 1658-298 and 4U 1916-053, we find that the spin-down expected if the atmosphere rotates rigidly is a factor of 2-3 less than the observed values. If differential rotation is allowed to persist, we find that the upper layers of the atmosphere do spin down by an amount comparable to or greater than the observed values. However, there is no compelling reason to expect the observed spin frequency to be that of only the outermost layers of the atmosphere. We conclude that hydrostatic expansion and angular momentum conservation alone cannot account for the largest frequency shifts observed during type I bursts.

Effect of Applying Different Distribution Shapes for Velocities and Pressure on Simulation of Curved Open Channels

Abstract: Most of the computational models of curved open channel flows use the conventional depth averaged De St. Venant equations. De St. Venant equations assume uniform velocity and hydrostatic pressure distributions. They are thus applicable only to cases of meandering rivers and curved open channels where vertical details are not of importance. The two-dimensional vertically averaged and moment equations model, developed by the writers, is used to study the effect of applying different distribution shapes for velocities and pressure on the simulation of curved open channels. Linear and quadratic distribution shapes are proposed for the horizontal velocity components, while a quadratic distribution shape is considered for the vertical velocity. Linear hydrostatic and quadratic nonhydrostatic distribution shapes are proposed for the pressure. The proposed model is applied to problems involved in curved open channels with different degrees of curvature. The implicit Petrov–Galerkin finite element scheme is applied in this study. Computed values for depth averaged longitudinal and transverse velocities across the channel width and vertical profiles of longitudinal and transverse velocities are compared to the observed experimental data. A fairly good agreement is attained. Predictions of overall flow characteristics suggest that the results are not very sensitive to different approximations of the preassumed applied velocity and pressure distribution shapes.

Reprocessing of x-rays in agn. I. plane parallel geometry - test of pressure equilibrium

Abstract: We present a model of the vertical stratication and the spectra of an irradiated medium under the assumption of constant pressure Such a solution has properties intermediate between constant density models and hydrostatic equilibrium models, and it may represent a flattened conguration of gas clumps accreting onto the central black hole Such a medium develops a hot skin, thicker than hydrostatic models, but thinner than constant density models, under comparable irradiation The range of theoretical values of the ox index is comparable to those from hydrostatic models and both are close to the observed values for Seyfert galaxies but lower than in quasars The amount of X-ray Compton reflection is consistent with the observed range The characteristic property of the model is a frequently multicomponent iron K line

A thrust bearing and method for equalizing load

Abstract: A multi-pad (24), fluid film thrust bearing (8) has the pads suspended from the carrier ring on hydrostatic oil pressure regions. The oil is pressurized hydrodynamically by relative rotation between a load surface and the bearing surface of each pad; and the oil is passed through each pad to a rear cavity where the hydrostatic pressure region is established. A manifold interconnects all of the hydrostatic pressure regions for the individual pads in order to average the hydrostatic pressures and provide for static and dynamic load equalization.

Effects of misalignment on turbulent flow hybrid thrust bearings

Abstract: An extended computational bulk-flow analysis for prediction of performance in angled injection, orifice-compensated hydrostatic/hydrodynamic thrust bearings is presented. The fluid motion within the thin film lands is governed by mass conservation and momentum transport equations. Mass flow conservation and a simple model for momentum transport within the hydrostatic bearing recesses are also accounted for. A perturbation analysis for small amplitude shaft axial motions and angulations leads to zeroth and first-order equations describing the equilibrium and perturbed fluid flows. The computational procedure predicts the bearing flow rate, thrust load and restoring moments, drag torque, and 27 force and moment coefficients. The effects of misalignment on the dynamic performance of a refrigerant fluid-hybrid thrust bearing are evaluated at an optimal operating condition. The axial force/displacement stiffness coefficient and the direct moment/angle stiffness coefficients show a maximum for a certain recess pressure ratio, while the damping coefficient steadily increases with the applied load. As the misalignment angle increases, both moment and force coefficients also increase. Most operating conditions show a whirl frequency ratio equal to 0.50. Thus, thrust hybrid bearings offer the same limited stability characteristics as hydrodynamic thrust bearings when undergoing self-excited shaft angular motions.

Effects of hydrostatic approximation and resolution on the simulation of convective adjustment

Abstract: A two-dimensional non-hydrostatic ocean model and a hydrostatic version of the same modelare used to simulate convective adjustment, without the use of an instantaneous adjustmentparameterization. The model geometry is a domain on the vertical plane of width 40 km anddepth 500 m. Model results for four cases are examined: hydrostatic and non-hydrostatic, at0.1 and 1 km spatial resolution. The convectively adjusted stable state obtained in all four casesare qualitatively similar; thus the hydrostatic approximation does not eliminate convectiveadjustment. The details of the simulated convective plumes depend on resolution and whetherthe hydrostatic approximation is made. The adjusted state has significant stratification whichcannot be captured by the conventional instantaneous adjustment or diffusion-based parameterizations.We also compare the results to the case when an instantaneous adjustmentparameterization is used. DOI: 10.1034/j.1600-0870.2002.00162.x

Gravity currents in rotating channels. Part 1. Steady-state theory

Abstract: A theory is developed for the speed and structure of steady-state non-dissipative gravity currents in rotating channels. The theory is an extension of that of Benjamin (1968) for non-rotating gravity currents, and in a similar way makes use of the steady-state and perfect-fluid (incompressible, inviscid and immiscible) approximations, and supposes the existence of a hydrostatic ‘control point’ in the current some distance away from the nose. The model allows for fully non-hydrostatic and ageostrophic motion in a control volume V ahead of the control point, with the solution being determined by the requirements, consistent with the perfect-fluid approximation, of energy and momentum conservation in V, as expressed by Bernoulli's theorem and a generalized flow-force balance. The governing parameter in the problem, which expresses the strength of the background rotation, is the ratio W = B/R, where B is the channel width and R = (g′H)1/2/f is the internal Rossby radius of deformation based on the total depth of the ambient fluid H. Analytic solutions are determined for the particular case of zero front-relative flow within the gravity current. For each value of W there is a unique non-dissipative two-layer solution, and a non-dissipative one-layer solution which is specified by the value of the wall-depth h0. In the two-layer case, the non-dimensional propagation speed c = cf(g′H)−1/2 increases smoothly from the non-rotating value of 0.5 as W increases, asymptoting to unity for W → ∞. The gravity current separates from the left-hand wall of the channel at W = 0.67 and thereafter has decreasing width. The depth of the current at the right-hand wall, h0, increases, reaching the full depth at W = 1.90, after which point the interface outcrops on both the upper and lower boundaries, with the distance over which the interface slopes being 0.881R. In the one-layer case, the wall-depth based propagation speed Froude number c0 = cf(g′h0)−1/2 = 21/2, as in the non-rotating one-layer case. The current separates from the left-hand wall of the channel at W0 ≡ B/R0 = 2−1/2, and thereafter has width 2−1/2R0, where R0 = (g′h0)1/2/f is the wall-depth based deformation radius.

Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime

Abstract: We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that $\Lambda > 0$ is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in $D$-dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed.

Experimental investigation of the liquid interface reorientation upon step reduction in gravity.

Abstract: Experiments have been carried out to investigate the settling behavior of a free liquid/gas interface in a partly filled right circular cylinder upon step reduction in gravity. Microgravity conditions were obtained within milliseconds after the release of a drop capsule in the drop tower facility in Bremen. In the experiments the cylinder radius was varied from 10 mm to 20mm with static contact angles of 2 degrees to 60 degrees. In addition to a series of silicone fluids, two different test liquids with a refractive index matched with the value of the cylinder material were used for experiments. The use of a digital high-speed recording system with a recording frequency of up to 500 fps allowed both an observation of the entire free liquid interface and a detail view on the moving contact line. Digital image processing techniques were applied to detect the contour of the free surface. For the initial condition the system is dominated by hydrostatic forces. In this case the equilibrium of the free liquid surface is characterized by a high Bond number yielding a flat surface and a small liquid ascent at the cylinder wall depending on the static contact angle. After transition to reduced gravity with a very low Bond number, capillary forces govern the flow and a capillary driven reorientation of the liquid to the new equilibrium position is established in a damped oscillation. The particular interest of this study is the investigation of the initial behavior of the free surface reorientation. It was found that the initial rise velocity of the contact point is determined by the Morton number and the static contact angle. Experimental results are presented that show an increasing rise velocity for decreasing Morton numbers. Further results characterize the initial behavior of the free surface at the center point as a function of characteristic time scales.

High-Velocity Clouds as a Probe of the Global Structure of the Gaseous Galactic Halo

Abstract: We construct a simplified pressure equilibrium model for the confinement of high-velocity clouds (HVCs) in the Galactic halo of the Milky Way. The ambient pressure is obtained from a model for the distribution of the coronal gas density. This is assumed as an isothermal plasma in hydrostatic equilibrium with the gravitational field of the Galaxy. The cloud internal pressure, for either subsonic or supersonic HVCs, is expressed in terms of its observed parameters and as a function of distance from the Sun. The distances to three HVCs in complex M, observationally determined by Danly and coworkers in 1993, are used to set the values of the two free parameters of the model, namely, the thermal pressure of the coronal gas in the solar vicinity (~4 ? 10-13 dyn cm-2) and its temperature Tg ~ 106 K. This model can be more rigorously tested when a set of cloud distances, velocities, velocity dispersion, column densities, and angular sizes becomes available.