Showing papers on "Hydrostatic equilibrium published in 1999"

Tides for a convective Earth

Abstract: In this paper we give values of the tidal gravimetric factor as well as of the Love numbers for the tidal surface displacement and for the tidal mass redistribution potential that are consistent with the presently adopted definitions. We present analytical expressions for these quantities and compute numerical values for two rotating, nonspherical Earth models. In the first model the Earth is everywhere in hydrostatic equilibrium, and the inner core and mantle are both elastic. In the second model the Earth is ellipsoidal with an inelastic mantle and with a nonhydrostatic initial state for which the effects of mantle convection and its associated boundary deformations are considered. This latter model is constrained to reproduce the observed free core nutation period and global Earth dynamical flattening.

A supernova-regulated interstellar medium: Simulations of the turbulent multiphase medium

Abstract: The dynamic state of the interstellar medium, heated and stirred by supernovae (SNe), is simulated using a three-dimensional, nonideal MHD model in a domain extended 0.5×0.5 kpc horizontally and 2 kpc vertically, with the gravitational field symmetric about the midplane of the domain, z=0. We include both Type I and Type II SNe, allowing the latter to cluster in regions with enhanced gas density. The system segregates into two main phases: a warm, denser phase and a hot, dilute gas in global pressure equilibrium; there is also dense, cool gas compressed into filaments, shells, and clumps by expanding SN remnants. The filling factor of the hot phase grows with height, so it dominates at |z| 0.5 kpc. The multicomponent structure persists throughout the simulation, and its statistical parameters show little time variation. The warm gas is in hydrostatic equilibrium, which is supported by thermal and turbulent pressures. The multiphase gas is in a state of developed turbulence. The rms random velocity is different in the warm and hot phases, 10 and 40 km s-1, respectively, at |z| 1 kpc; the turbulent cell size (twice the velocity correlation scale) is about 60 pc in the warm phase.

On the derivation of homogeneous hydrostatic equations

Abstract: In this paper we study the derivation of homogeneous hydrostatic equations starting from 2D Euler equations, following for instance [2,9]. We give a convergence result for convex profiles and a divergence result for a particular inflexion profile.

Equilibrium atmospheres of a two-column radiative-convective model

Abstract: Interaction between steady, large-scale atmospheric circulations and a radiative-convective environment is considered. As a model tool, we use a two-column radiative-convective model with an explicit hydrological cycle that uses clear-sky conditions in the radiation calculation. A flow field is calculated by the linearized, hydrostatic equations of motion in a non-rotating frame of reference. Mechanical damping is represented by vertical diffusion of momentum and surface drag. the flow advects heat and moisture, and thereby modifies the local radiative-convective equilibrium. A dynamically passive ocean mixed layer is situated below the model atmosphere. All externally specified parameters are identical in the two columns, implying that local radiative-convective equilibrium is a steady solution. For weak mechanical damping (or small column length), the local equilibrium is generally unstable due to a positive feedback between large-scale subsidence and infrared cooling, which operates via advective drying. A circulating equilibrium, in which the air ascends in one column and descends in the other, is attained. Due to a reduced content of clear-sky water vapour, which is the major infrared absorber in the model, the circulating equilibrium can emit the absorbed solar radiation at a significantly lower surface temperature than the corresponding local equilibrium. In the limit of a nearly inviscid atmosphere, the intensity of the large-scale circulation is controlled chiefly by the mid-tropospheric radiative cooling in the downdraught column. In this regime, we find two distinct equilibria with circulation that are distinguished by the features of the downdraught column: one branch with deep convection but where the integrated convective heating vanishes due to evaporation of precipitation; and one branch with shallow (or no) convection where the surface boundary layer is disconnected from the free atmosphere.

Length of day variations due to zonal tides for an inelastic earth in non-hydrostatic equilibrium

Abstract: We present a refined theoretical model for length-of-day (lod) variations induced by the zonal part of the tide-generating potential. The model is computed from a numerical integration, from the Earth's centre up to the surface, of the equation of motion, the rheological equation of state and Poisson's equation. The Earth is modelled as a three-layered body, with an inelastic inner core, an inviscid fluid core and an inelastic mantle sustaining convection, which,induces deviations from hydrostatic equilibrium. The model also incorporates ocean corrections deduced from dynamic ocean models. It is shown that the non-hydrostatic structure inside the Earth has an effect of less than 0.1 per cent on the transfer functions, while the different modellings of mantle inelasticity (different combinations of possible values for the inelastic parameters) can lead to a wide range of results. Finally, we show that the precision of the geodetic observations of UT1 and the precision of the oceanic and atmospheric corrections are not yet sufficient to obtain information about mantle inelasticity from the comparison between theoretical models and geodetic observations.

Isentropic advection by gravity waves: Quasi‐universal M−3 vertical wavenumber spectra near the onset of instability

Abstract: A two-dimensional model was used to advect air parcels under the influence of a linear superposition of hydrostatic gravity waves. As wave amplitudes increased, vertically profiled wave perturbations became nonsinusoidal, producing increased spectral power at large wavenumbers M. At saturation amplitudes just before onset of convective instabilities, these “tail spectra” assumed universal M−3 shapes, similar to observed spectra in the atmosphere and oceans.

Rarefaction wave and gravitational equilibrium in a two-phase liquid-vapor medium

Abstract: The problems studied in this paper involve the action of laser radiation or a particle beam on a condensed material. Such an interaction produces a hot corona, and the recoil momentum accelerates the cold matter. In the coordinate frame tied to the accelerated target, the acceleration is equivalent to the acceleration of gravity. For this reason, the density distribution ρ is hydrostatic in the zeroth approximation. In this paper the structure of such a flow is studied for a two-phase equation of state. It is shown that instead of a power-law density profile, which obtains for a constant specific-heat ratio, a complicated distribution containing a region with a sharp variation of ρ arises. Similar characteristics of the density profile arise with isochoric heating of matter by an ultrashort laser pulse and the subsequent expansion of the heated layer. The formation of a rarefaction wave and the interaction of oppositely propagating rarefaction waves in a two-phase medium are studied. It is very important to take account of the two-phase nature of the material, since conditions (p a ∼1 Mbar) are often realized under which the foil material comes after expansion into the two-phase region of the phase diagram.

Moments of inertia and rotational stability of Mars: Lithospheric support of subhydrostatic rotational flattening

Abstract: A revised estimate of the spin axis precession rate of Mars has recently been obtained via analysis of range and range-rate data from the Viking and Pathfinder landers. When combined with existing estimates of the degree 2 spherical harmonic coefficients of the gravitational field, this yields a complete determination of the inertia tensor of Mars. Despite this progress, there are still numerous unresolved issues related to the internal structure and rotational dynamics of Mars. We compare results of two different approaches to this problem. In one approach, the observed gravitational field is conceptually partitioned into hydrostatic and nonhydrostatic contributions. In the other approach, the input to the system is partitioned into rotational and load components, and the internal structure (density and elastic rigidity) determines the response. We demonstrate that there is an important, and still unresolved trade-off between lithospheric thickness and the shape of the load component of the gravity field. As the lithospheric thickness is increased, the required load departs more from axial symmetry. The load corresponding to zero lithospheric thickness is nearly symmetric about an equatorial axis, but if the lithospheric thickness is closer to 100 km, the required load is a fully triaxial ellipsoid, with the intermediate moment of inertia halfway between the least and greatest moments. The symmetry of the load has considerable influence on the long-term rotational stability of Mars.

A vertical diffusion model for lakes

Abstract: The motion of a fluid in a lake with small depth compared to width is investigated. We prove that when the depth goes to 0, the solution of the stationary Navier--Stokes equations with adherence at the bottom and traction by wind at the surface, once conveniently normalized, goes to a three-dimensional limit which is the solution of an incompressible model with vertical diffusion. The limit velocity is given in terms of the vertical coordinate and of the limit pressure. This pressure, which depends only on the horizontal coordinates, is driven by a two-dimensional equation on the surface degenerating on the shore, which is solved in a weighted space. Thus, a three-dimensional approximation is obtained by a simple two-dimensional computation.

Hydrostatic propulsion system for a marine vessel

Abstract: A hydrostatic marine propulsion system is provided with a valve that is able to bypass an infinitely variable amount of hydraulic fluid from a hydrostatic pump to bypass a hydrostatic motor which is used to drive a propeller shaft. The infinitely variable valve is connected between the hydrostatic pump and the hydrostatic motor with dual outlets which cause fluid to flow either to the hydrostatic motor or to a reservoir to be recycled through the hydrostatic pump. An engine control unit changes the amount of hydraulic fluid passing through the hydrostatic motor as a function of the operating condition of an engine which drives the hydrostatic pump. In this way, engine speed can be controlled during various modes of operation.

Does magnetic pressure affect the intracluster medium dynamics

Abstract: A possible discrepancy found between the determination of mass of the intracluster medium (ICM) from gravitational lensing data and that from X-ray observations has been much discussed in recent years. For instance, Miralda-Escude & Babul found that the mass estimate derived from gravitational lensing can be as much as a factor of 2–2.5 larger than the mass estimate derived from analysis of the X-ray observations. Another important discrepancy related to these data is that X-ray imaging, with some spectral resolution, suggests that the mass distribution of the gravitating matter, mostly dark matter, has a central cusp, or at least that the dark matter is more centrally condensed than the X-ray-emitting gas, and also with respect to the galaxy distribution (Eyles et al.), at variance with what is expected from the most accepted models of formation of large-scale structure. Could these discrepancies be a consequence of the standard description of the ICM, in which hydrostatic equilibrium maintained by thermal pressure is assumed? In analogy to the interstellar medium of the Galaxy, a non-thermal term of pressure is expected, which contains contributions of magnetic fields, turbulence and cosmic rays. We follow the evolution of the ICM, considering a term of magnetic pressure, aiming at answering the question of whether or not these discrepancies can be explained via non-thermal terms of pressure. Our results suggest that the magnetic pressure could only affect the dynamics of the ICM on scales as small as ≲1 kpc. Our models are constrained by the observations of large- and small-scale fields, and we are successful at reproducing available data, for both Faraday rotation limits and inverse Compton limits for the magnetic fields. In our calculations, the radius (from the cluster centre) in which magnetic pressure reaches equipartition is smaller than radii derived in previous works. The crucial difference in our models is our more realistic treatment of the magnetic field geometry, and the consideration of a sink term in the cooling flow which reduces the amplification of the field strength during the inflow. In addition, the magnetic field calculations are changed after the cooling flow has been formed.

The Active Gravitational Mass of a Heat Conducting Sphere Out of Hydrostatic Equilibrium

Abstract: We obtain an expression for the activegravitational mass of a relativistic heat conductingfluid, just after its departure from hydrostaticequilibrium, on a time scale of the order of relaxationtime. It is shown that an increase of acharacteristic parameter leads to larger (smaller)values of active gravitational mass of collapsing(expanding) spheres, enhancing thereby the instabilityof the system.

Lamb's Hydrostatic Adjustment for Heating of Finite Duration

Abstract: Lamb’s hydrostatic adjustment problem for the linear response of an infinite, isothermal atmosphere to an instantaneous heating of infinite horizontal extent is generalized to include the effects of heating of finite duration. Three different time sequences of the heating are considered: a top hat, a sine, and a sine-squared heating. The transient solution indicates that heating of finite duration generates broader but weaker acoustic wave fronts. However, it is shown that the final equilibrium is the same regardless of the heating sequence provided the net heating is the same. A Lagrangian formulation provides a simple interpretation of the adjustment. The heating generates an entropy anomaly that is initially realized completely as a pressure excess with no density perturbation. In the final state the entropy anomaly is realized as a density deficit with no pressure perturbation. Energetically the heating generates both available potential energy and available elastic energy. The former remains...

Does magnetic pressure affect the ICM dynamics

Abstract: A possible discrepancy found in the determination of mass from gravitational lensing data, and from X-rays observations, has been largely discussed in the latest years (for instance, Miralda-Escude & Babul (1995)). Another important discrepancy related to these data is that the dark matter is more centrally condensed than the X-ray-emitting gas, and also with respect to the galaxy distribution (Eyles et al. 1991). Could these discrepancies be consequence of the standard description of the ICM, in which it is assumed hydrostatic equilibrium maintained by thermal pressure? We follow the evolution of the ICM, considering a term of magnetic pressure, aiming at answering the question whether or not these discrepancies can be explained via non-thermal terms of pressure. Our results suggest that the magnetic pressure could only affect the dynamics of the ICM on scales as small as < 1kpc. Our models are constrained by the observations of large and small scale fields and we are successful at reproducing available data, for both Faraday rotation limits and inverse Compton limits for the magnetic fields. In our calculations the radius (from the cluster center) in which magnetic pressure reaches equipartition is smaller than radii derived in previous works, as a consequence of the more realistic treatment of the magnetic field geometry and the consideration of a sink term in the cooling flow.

The contribution of the giraffe to hemodynamic knowledge: a unified physical principle for the circulation.

Abstract: Hemodynamics stands on three main physical principles: the hydrostatic pressure, firstly described by Stevino, the viscous flow pressure, described by Poiseuille and the total hydraulic energy, or Bernoulli's equation. However, neither of these physical principles gives a comprehensive description of the single pressure measurement in the cardiovascular system. Hence, all these principles should be used together to fully describe the physical forces acting in the circulation of blood. Experiments that measured the hydrostatic pressure in the jugular vein of the giraffe have shown that a few guidelines need to be followed to measure it correctly. Following these guidelines, it can be seen that hydrostatic and viscous flow pressures are strictly related to one another, and that this relationship is described in mathematical terms. In addition, it has been shown that hydrostatic and viscous pressures should be included in Bernoulli's principle, to give the combined Bernoulli-Poiseuille equation. This unified principle is helpful not only to measure correctly the pressure with a catheter connected to a pressure transducer, but also to give to the pressure measured in a patient with the mercury manometer, a strong connection with the description of the pressure as a physical force acting inside the circulation. In addition it provides a comprehensive view of the cardiovascular system as a closed hydrodynamic system, in which the heart is a pump, that does not normally work to overcome the force of gravity. The question at this point is: are there any pathophysiological conditions in which the heart needs to be confronted with the sudden appearance of the force of gravity inside the cardiovascular system?

Surface-Wave Analysis in the Taipei Basin from Strong-Motion Data

Abstract: A new spectral moist convection model that employs both the least assumptionsin moist physics and a very accurate solution method is presented.The temperature and pressure in the model are diagnostically determinedfrom thermodynamics.There is no need to predict water vaporand condensate separately;rather,they are diagnostically separated fromthe predicted total airborne water.The model allows a modular separationof dynamics and thermodynamics;the link between dynamics and thermodynamicsis through the pressure gradient force.The modular separationallows the possibility of having a detailed,fine resolution,nonhydrostaticcloud model and a coarse resolution,hydrostatic model which can be runside by side with the identical moist thermodynamics.The height coordinateof the nonhydrostatic model can also extend into the hydrostatic regime.The only differences between the hydrostatic and nonhydrostaticmodels are spatial resolution and the way vertical motion is computed.Wehave performed numerical experiments in the nonhydrostatic model foracoustic adjustment and moist convection.The discontinuity in thermodynamicsdue to phase change is modified in the model by the”gradual saturation”technique.

Properties of the Stellar Velocity Ellipsoid and Stability in Disks of Spiral Galaxies

Abstract: Disks of spiral galaxies are characterized by effectively exponential brightness and presumably density distributions in both the radial and vertical directions. It is to be expected that the ratio between the scalelength and -height bears a relation to the axis ratio of the stellar velocity ellipsiod. Hydrostatic equilibrium connects the vertical velocity dispersion to the scaleheight. In the radial direction the velocity dispersion relates to the scalelength through conditions of local stability. Preliminary applications are presented.

Gravity Waves Driven by Diurnal Fluctuations in Mesoscale Heating

Abstract: Observed convective systems, such as mesoscale convective complexes (MCCs), often undergo repeated cycles of nocturnal growth and daytime decay especially during the summer. The gravity wave response to these pulsations is poorly understood. The motivation for this study is to understand this response and especially its sensitivity to environmental factors such as horizontal wind and static stability. A semianalytical approach is used that focuses on the roles of singularities in a complex horizontal wavenumber space. The model is linear, Boussinesq, hydrostatic, and rotating with uniform ambient conditions. Prescribed, 2D, pulsating, upright, convective heating drives the waves. The Fourier transform technique is used to unravel the response into a discrete and continuous horizontal spectrum. Many features of the response depend on a Froude number, F 5 pU/(DN) where U 5 background wind, D 5 depth of source region, and N 5 buoyancy frequency. The most efficient forcing of the gravity wave field occurs near criticality (F 5 1). For typical values of U and D associated with midlatitude convective systems, the critical value of N is about one-fourth of average tropospheric values. The resulting enhanced loss of energy from the convective system due to gravity waves could limit the intensity of convective systems near criticality. At subcriticality (F , 1), the pulsating upstream response is dominated by unbalanced ageostrophic propagating modes upstream of the source region and by a balanced geostrophic mode downstream of the source. The latter advances with a speed equal to the background flow. No far-upstream response occurs for supercriticality ( F . 1). The downstream response for F . 1 is dominated by the geostrophic mode in the pressure, temperature, and source-parallel wind. In addition, a vigorous ageostrophic mode advances downstream from the subcritical source region giving rise to alternating regions of rising motion and subsidence. It is hypothesized that the latter could trigger new lines of convection in the downstream subcrticial Froude number regime. Mature MCCs often develop low-level cooling in response to evaporative cooling. This cooling primarily triggers the advective inertial gravity wave mode, which propagates downstream at the background wind speed. It is shown that subcritical flows ( F , 1; weak ambient flow and/or strong static stability) are tuned to strongly respond to this mode. It is suggested that the development of new convection might be suppressed near the system under subcritical conditions. Low-level cooling has little effect on the supercritical response.

The Classical Stellar Atmosphere Problem

Abstract: We introduce the classical stellar atmosphere problem and describe in detail its numerical solution. The problem consists of the solution of the radiation transfer equations under the constraints of hydrostatic, radiative and statistical equilibrium (non-LTE). We outline the basic idea of the Accelerated Lambda Iteration (ALI) technique and statistical methods which finally allow the construction of non-LTE model atmospheres considering the influence of millions of metal absorption lines. Some applications of the new models are presented.

Relaxation of a non-ideal incompressible plasma with mass flow

Abstract: The time evolution of an incompressible non-ideal magnetohydrodynamic (MHD), current-carrying plasma with mass flow is investigated. An approach for the reduction of the nonlinear vector MHD equations to a set of scalar partial differential equations is supposed. Analytical time-dependent solutions of this system are presented. They describe kinetic plasma equilibria both with well-defined nested-in magnetic and velocity surfaces and in the form of vortices. The obtained solutions may be called 'diffusion-like', since their temporal structure is very similar to the solutions of the diffusion problem. It is shown that the magnetic field and the velocity have different dumping rates. In the asymptotic limit t→∞, the plasma slowly relaxes towards the hydrostatic equilibrium of gravitating systems.

Hydrostatic extrusion of composite rod

Abstract: Hydrostatic extrusion is a process where the billet is completely immersed in pressurized liquid. Pressure at the die orifice is lower than that at the die entrance, and the resulting pressure differential causes metal flow toward the orifice or die exit. The force required to push the billet through the die is thus provided by the hydrostatic pressure instead of by a direct ram force. Composite rods or wire are composed of two or more different materials, each material having its own distinctive mechanical characteristics. Because a composite rod billet deforms more uniformly in hydrostatic extrusion than in conventional extrusion, it is considered that hydrostatic extrusion is one of the most effective processes to manufacture composite rods and wires. The aim of this work is to propose an analytical model for hydrostatic extrusion. In this model, the liquid surrounding the billet is considered as a kind of hydrodynamic lubrication. On the other hand, the upper-bound theorem is adopted to analyse the deformation of the composite rod or wire. A model describing plastic flow of these clad rods has been established. Work-hardening effects of the materials are taken into account in the model. The results show the deformation behavior of billets in hydrostatic extrusion under different processing conditions. Finally an experiment of hydrostatic extrusion of round rod has been conducted and its results found to be very close to the model analysis.

Three-Dimensional MHD Simulations of the Emergence of Twisted Magnetic Flux Tubes in the Solar Atmosphere

Abstract: The emergence of twisted magnetic flux tubes in the Solar atmosphere is studied by three-dimensional magnetohydrodynamic (MHD) simulations. The initial state is a plane parallel, hydrostatic atmosphere with convectively unstable layer, isothermal cool photosphere/chromosphere and hot corona. A horizontal, twisted flux tube with Gold-Hoyle magnetic field distribution is imbedded in the convection zone. Small amplitude perturbation is imposed on the initial state. Typical number of grid points used in the simulations is 125 × 125 × 208.

Reliability analysis of base sliding of concrete gravity dams subjected to earthquakes

Abstract: Concrete gravity dams are typically constructed in blocks separated by vertical contraction joints. The design of straight concrete gravity dams is traditionally performed by assuming each block to be independent, except for gravity dams in valleys with relatively small width to height ratios. Understanding the 2-D behaviour of individual monoliths is thus considered relevant and 2-D models are usually employed in safety evaluations of existing dams. During a strong seismic event, low to medium height concrete gravity dams tend to crack at the base as opposed to tall dams, which attract high stresses and cracking at the level of a slope change on the downstream side of a dam. The state-of-the-practice in the seismic evaluation of concrete gravity dams requires that the failure mode of the dam monolith sliding at its base be considered. This study focused on the post-crack dynamic response of existing concrete gravity dams in order to investigate their safety against sliding considering non-linear effects in the damfoundation interface. Sliding response of a single monolith of a low to medium height concrete gravity dam at the failure state was studied and, therefore, the monolith separated or unbonded from its foundation was considered. The work included experimental, analytical and reliability studies. During the experimental study, a model of an unbonded concrete gravity dam monolith was developed and tested using a shake table. The model, preloaded by a simulated hydrostatic force, was subjected to a selected variety of base excitations. Other effects, such as hydrodynamic and uplift pressures were not considered in the experiments. A strong influence of amplitude and frequency of the base motions on the sliding response of the model was observed during the tests. Simple and more detailed numerical models to simulate the experiments were developed during the analytical study. It was observed that a simple rigid model could simulate acceptably the tests only in a limited range of excitation frequencies. A finite element (FE) model simulated the experiments satisfactorily over a wider range of dominant frequencies of the base accelerations. The numerical models were used to simulate the seismic response of a 45 m high monolith of a concrete gravity dam subjected to three different earthquake excitations for varying reservoir's water level. The agreement between the results using the simple rigid and the FE models was found acceptable. The results of the numerical simulations were used in a reliability analysis to calculate probabilities of failure of the 45 m high monolith. Probability of failure was defined here as an annual chance of exceeding an allowable amount of the monolith's base sliding during an earthquake. The peak ground acceleration (PGA), the characteristics of the time history, and the reservoir's water level were considered as random parameters during this study. Using the FE model, the annual probabilities of failure ranged from 1. 1E-8 for the mean PGA of 0.2g and 20 cm of allowable sliding to 1.3E-3 for the mean PGA of 0.6g and 1 cm of allowable sliding. The probabilities of failure using the simple rigid model were found close to those using the FE model. It was concluded that the computationally less demanding simple rigid model may be adequately used in reliability calculations of low to medium height concrete gravity dam safety against base sliding.

On the axis ratio of the stellar velocity ellipsoid in disks of spiral galaxies

Abstract: The spatial distribution of stars in a disk of a galaxy can be described by a radial scale length and a vertical scale height. The ratio of these two scale parameters contains infor- mation on the axis ratio of the velocity ellipsoid, i.e. the ratio of the vertical to radial stellar velocity dispersions of the stars, at least at some fiducial distance from the center. The radial veloc- ity dispersion correlates well with the amplitude of the rotation curve and with the disk integrated magnitude, as was found by Bottema (1993). These relations can be understood as the re- sult of the stellar disk being (marginally) stable against local instabilities at all length scales. This is expressed by Toomre's well-known criterion, which relates the sheer in the rotation to a minimum value that the radial stellar velocity dispersion should have for stability for a given surface density. Via the Tully-Fisher (1977) relation, the velocity dispersion then becomes related to the integrated magnitude and hence to the scale length. The vertical velocity dispersion relates directly to the scale height through hydrostatic equilibrium. It can be shown that the ratio of the two length scales relates to the axis ratio of the velocity ellipsoid only through the Toomre parameter Q and in particular does not require a choice of the mass-to-light ratio or a distance scale. We have applied this to the statistically complete sample of edge-on galaxies, for which de Grijs (1997) has performed surface photometry and has determined the length scales in the stellar light distribution.

Modeling of a galactic spiral arm as a bore­ shock combination

Abstract: We consider the interarm-to-arm transition for gas flow in the galactic disk, modeled as a thick, magnetized, cloudless layer of gas in hydrostatic equilibrium with external gravity from stars, and having parameters appropriate to the solar neighborhood. We neglect the self-gravity of the gas, shear, and radial variations in gravity. We show that such a transition, if supersonic, must present characteristics of both a hydraulic jump (or bore) and a shock. Our numerical simulations confirm this prediction. Modeling the spiral perturbation as a local one, we find that gas passing through it experiences sudden vertical acceleration upstream the arm, giving rise to a shock above the large vertical structure created, midplane density enhancements, and downflow regions behind the jump, as well as, sometimes, secondary jumps. Gravity waves generated in the thick disk appear to promote the formation of the marked density enhancements in the midplane

On the axis ratio of the stellar velocity ellipsoid in disks of spiral galaxies

Abstract: The spatial distribution of stars in a disk of a galaxy can be described by a radial scale length and a vertical scale height. The ratio of these two scale parameters contains information on the axis ratio of the velocity ellipsoid, i.e. the ratio of the vertical to radial stellar velocity dispersions of the stars, at least at some fiducial distance from the center. The radial velocity dispersion correlates well with the amplitude of the rotation curve and with the disk integrated magnitude, as was found by Bottema (1993). These relations can be understood as the result of the stellar disk being (marginally) stable against local instabilities at all length scales. This is expressed by Toomre's well-known criterion, which relates the sheer in the rotation to a minimum value that the radial stellar velocity dispersion should have for stability for a given surface density. Via the Tully-Fisher (1977) relation, the velocity dispersion then becomes related to the integrated magnitude and hence to the scale length. The vertical velocity dispersion relates directly to the scale height through hydrostatic equilibrium. It can be shown that the ratio of the two length scales relates to the axis ratio of the velocity ellipsoid only through the Toomre parameter Q and in particular does not require a choice of the mass-to-light ratio or a distance scale. We have applied this to the statistically complete sample of edge-on galaxies, for which de Grijs (1997) has performed surface photometry and has determined the length scales in the stellar light distribution.