Showing papers on "Hydrostatic equilibrium published in 2005"
TL;DR: In this article, the authors analyzed the particular example of an unbalanced instability of a balanced, horizontally uniform, vertically sheared current, as it occurs within the Boussinesq equations.
Abstract: Under the influences of stable density stratification and the earth’s rotation, large-scale flows in the ocean and atmosphere have a mainly balanced dynamics—sometimes called the slow manifold—in the sense that there are diagnostic hydrostatic and gradient-wind momentum balances that constrain the fluid acceleration. The nonlinear balance equations are a widely successful, approximate model for this regime, and mathematically explicit limits of their time integrability have been identified. It is hypothesized that these limits are indicative, at least approximately, of the transition from the larger-scale regime of inverse energy cascades by anisotropic flows to the smaller-scale regime of forward energy cascade to dissipation by more nearly isotropic flows and intermittently breaking inertia–gravity waves. This paper analyzes the particular example of an unbalanced instability of a balanced, horizontally uniform, vertically sheared current, as it occurs within the Boussinesq equations. This ageo...
216 citations
TL;DR: In this article, physically self-consistent models of dusty molecular tori in Active Galactic Nuclei (AGN) with the goal of interpreting VLTI observations and fitting high-resolution mid-IR spectral energy distributions (SEDs) are explored.
Abstract: We explore physically self-consistent models of dusty molecular tori in Active Galactic Nuclei (AGN) with the goal of interpreting VLTI observations and fitting high resolution mid-IR spectral energy distributions (SEDs). The input dust distribution is analytically calculated by assuming hydrostatic equilibrium between pressure forces - due to the turbulent motion of the gas clouds - and gravitational and centrifugal forces as a result of the contribution of the nuclear stellar distribution and the central black hole. For a fully three-dimensional treatment of the radiative transfer problem through the tori we employ the Monte Carlo code MC3D. We find that in homogeneous dust distributions the observed mid-infrared emission is dominated by the inner funnel of the torus, even when observing along the equatorial plane. Therefore, the stratification of the distribution of dust grains - both in terms of size and composition - cannot be neglected. In the current study we only include the effect of different sublimation radii which significantly alters the SED in comparison to models that assume an average dust grain property with a common sublimation radius, and suppresses the silicate emission feature at 9.7 µm. In this way we are able to fit the mean SED of both type I and type II AGN very well. Our fit of special objects for which high angular resolution observations (≤0.3 �� ) are available indicates that the hottest dust in NGC 1068 reaches the sublimation temperature while the maximum dust temperature in the low-luminosity AGN Circinus falls short of 1000 K.
172 citations
TL;DR: In this article, the authors study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones.
Abstract: We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical geopotential and shallow atmosphere approximations in addition to the hydrostatic approximation. As is well known, a consistent application of the shallow atmosphere approximation requires omission of those Coriolis terms that vary as the cosine of latitude and of certain other terms in the components of the momentum equation. An approximate model is here regarded as consistent if it formally preserves conservation principles for axial angular momentum, energy and potential vorticity, and (following R. Muller) if its momentum component equations have Lagrange's form. Within these criteria, four consistent approximate global models, including the HPEs themselves, are identified in a height-coordinate framework. The four models, each of which includes the spherical geopotential approximation, correspond to whether the shallow atmosphere and hydrostatic (or quasi-hydrostatic) approximations are individually made or not made. Restrictions on representing the spatial variation of apparent gravity occur. Solution methods and the situation in a pressure-coordinate framework are discussed. © Crown copyright 2005.
144 citations
TL;DR: In this article, the relationship between pore space anisotropy and petrophysical properties was investigated using magnetic susceptibilities and acoustic wave velocities under ambient laboratory conditions.
104 citations
TL;DR: In this paper, the authors developed a model that will adequately simulate the dynamics of tsunami propagating across the continental shelf by using the three-dimensional Reynolds averaged Navier-Stokes equations to yield a set of equations that are similar to the shallow water equations but retain the non-hydrostatic pressure terms.
Abstract: The objective of this research is to develop a model that will adequately simulate the dynamics of tsunami propagating across the continental shelf. In practical terms, a large spatial domain with high resolution is required so that source areas and runup areas are adequately resolved. Hence efficiency of the model is a major issue. The three-dimensional Reynolds averaged Navier–Stokes equations are depth-averaged to yield a set of equations that are similar to the shallow water equations but retain the non-hydrostatic pressure terms. This approach differs from the development of the Boussinesq equations where pressure is eliminated in favour of high-order velocity and geometry terms. The model gives good results for several test problems including an oscillating basin, propagation of a solitary wave, and a wave transformation over a bar. The hydrostatic and non-hydrostatic versions of the model are compared for a large-scale problem where a fault rupture generates a tsunami on the New Zealand continental shelf. The model efficiency is also very good and execution times are about a factor of 1.8 to 5 slower than the standard shallow water model, depending on problem size. Moreover, there are at least two methods to increase model accuracy when warranted: choosing a more optimal vertical interpolation function, and dividing the problem into layers. Copyright © 2005 John Wiley & Sons, Ltd.
86 citations
TL;DR: In this paper, the effect of hydrostatic pressure on chip formation was studied using the experiments and the difference in cutting forces between cutting a groove into the specimen and cutting a slab was investigated at atmospheric pressure.
75 citations
TL;DR: In this article, the authors investigate a model of galaxy clusters in which the hot intracluster gas is efficiently heated by dynamical friction (DF) of galaxies and show that DF-induced heating alone is an unlikely solution to the cooling flow problem, although it can still be an important heat supplier.
Abstract: We investigate a model of galaxy clusters in which the hot intracluster gas is efficiently heated by dynamical friction (DF) of galaxies. We allow for both subsonic and supersonic motions of galaxies and use the gravitational drag formula in a gaseous medium presented by Ostriker. The energy lost by the galaxies is either redistributed locally or into a Gaussian centered on the galaxy. We find that the condition of hydrostatic equilibrium and strict energy balance yields a trivial isothermal solution Tiso, independent of radius, or rising temperature distributions, provided Tiso/γ < T < Tiso, where γ is the adiabatic index of the gas. The isothermal temperature corresponds to the usual scaling relation between the gas temperatures and the velocity dispersions of galaxies. However, the minimal temperature associated with the rising solutions is ~ Tvir, larger than that inferred from observations, the radial distribution of galaxy masses notwithstanding. Heating by supersonically moving galaxies cannot suppress thermal instability, although it can lengthen the growth time up to the level comparable to the ages of clusters when the Mach number of galaxies is less than about 2. We show using numerical hydrodynamic simulations that DF-induced heating is generally unable to produce stable equilibrium cores by evolving arbitrary nonequilibrium clusters, although it can lengthen the cooling time. We conclude that DF-induced heating alone is an unlikely solution to the cooling flow problem, although it can still be an important heat supplier, considerably delaying the cooling catastrophe. We discuss other potential consequences of DF of galaxies in galaxy clusters.
60 citations
TL;DR: In this paper, generalized Kippenhahn-Schluter equilibrium and steady-flow solutions of the magnetohydrodynamic (MHD) equations are constructed of arrays of laminated isothermal KS prominence sheets whose temperatures, sag angles, and dip positions may vary arbitrarily from sheet to sheet.
Abstract: We present generalized Kippenhahn-Schluter (KS) equilibrium and steady-flow solutions of the magnetohydrodynamic (MHD) equations. These solutions are constructed of arrays of laminated isothermal KS prominence sheets whose temperatures, sag angles, and dip positions may vary arbitrarily from sheet to sheet. Moreover, the sheets can move at arbitrary constant uniform velocities relative to each other within their planes. This great versatility allows us to model the filamentary structure of prominences and illustrate why their observed dimensions differ from their characteristic hydrostatic scale lengths. We are also able to explain observed vertical and horizontal velocities as naturally arising steady rigid motions of plasma sheets in local force equilibrium but global nonequilibrium.
54 citations
TL;DR: In this article, the authors present the analysis of the velocity structure of the intracluster gas near the core of Abell 3526 obtained with two off-center Chandra observations, specifically designed to eliminate errors due to spatial variations of the instrumental gain.
Abstract: We present the analysis of the velocity structure of the intracluster gas near the core of Abell 3526 obtained with two off-center Chandra observations, specifically designed to eliminate errors due to spatial variations of the instrumental gain. We detected a significant velocity gradient along the direction NE-SW direction, roughly perpendicular to the direction of the incoming sub-group Cen45, in agreement with previous ASCA SIS measurements. The presence of gas bulk velocities is observed both with and without the inclusion of the FeK line complex in the spectral fittings. The configuration and magnitude of the velocity gradient is consistent with near transonic circulatory motion, either bulk or eddy-like. The velocity difference obtained using the best calibrated central regions of ACIS-S3 is found to be (2.4+-1.0)E03 km/s for rectangular regions 2'.4 x 3' roughly diametrically opposed around the cluster's core. There are also indications of a high velocity zone towards the Southern region with similar magnitudes. The detection of velocity gradients is significant at the >99.4% confidence and simulations show that intrachip gain fluctuations > 1800 km/s are required to explain the velocity gradient by chance. The measurements suggest that >1% of the total merger energy can still be bulk kinetic 0.4 Gyr after the merging event. This is the first direct confirmation of velocity gradients in the intracluster gas with independent instruments and indicates that strong departure from hydrostatic equilibrium is possible even for cool clusters that do not show obvious signs of merging.
48 citations
TL;DR: In this paper, the authors investigated the relationship between the temperature and the density of a solar coronal loop and demonstrated that radiative energy loss from the transition region is the dominant physical process that governs the down-flow by which mass is lost from the corona.
Abstract: The robust $T \propto n^\delta$ power-law relationship between the temperature ( T ) and the density ( n ) that arises during the radiative cooling phase of a solar coronal loop is investigated. Using an analytical model and numerical hydrodynamic simulations, we demonstrate that radiative energy loss from the transition region is the dominant physical process. It governs the down-flow by which mass is lost from the corona and hence controls the evolution of the entire loop. We also show that the down-flow is initiated by a weakening of the pressure gradient between the corona and the transition region, such that the plasma can no longer be supported in hydrostatic equilibrium. Rather than driving the down-flow, the pressure gradient actually regulates it and acts as a brake against gravitational acceleration.
48 citations
TL;DR: In this article, the authors used stellar structure dynamics arguments to extract bounds on the relevant parameters of two scalar field models: the putative Scalar Field mediator of a fifth force with a Yukawa potential and the new variable mass particle models.
Abstract: We use stellar structure dynamics arguments to extract bounds on the relevant parameters of two scalar field models: the putative scalar field mediator of a fifth force with a Yukawa potential and the new variable mass particle models. We also analyze the impact of a constant solar inbound acceleration, such as the one reported by the Pioneer anomaly, on stellar astrophysics. We consider the polytropic gas model to estimate the effect of these models on the hydrostatic equilibrium equation and fundamental quantities such as the central temperature. The current bound on the solar luminosity is used to constrain the relevant parameters of each model.
TL;DR: The impact of a sphere with velocity u0 on a fine, loose granular system under the acceleration due to gravity has been studied by fast video photography and the behavior of the granular bed is found to be similar to a fluid during initial impact, followed by a cavity drag during projectile penetration.
Abstract: The impact of a sphere with velocity u0 on a fine, loose granular system under the acceleration due to gravity has been studied by fast video photography. The behavior of the granular bed is found to be similar to a fluid during initial impact, followed by a cavity drag during projectile penetration. From the trajectory of the projectile it is found that the drag on the projectile can be well described by adding a bulk frictional force f to the hydrostatic force kappa(z) where kappa is a constant and z denotes the penetration depth. Both kappa and f are u0 dependent. This form of the drag force suggests that fluidlike viscous dissipations in the bed can be neglected in these three-dimensional (3D) experiments. However, due to the imposed boundary this hydrodynamic term of the drag force is found to be not negligible in quasi-2D granular beds.
TL;DR: In this article, a new numerical model based on the incompressible, nonhydrostatic Navier-Stokes equations for free surface flow is developed, where the equations are transformed vertically to the σ coordinate system and laterally to an orthogonal curvilinear system and solved in a fractional step manner.
Abstract: A new numerical model based on the incompressible, nonhydrostatic Navier-Stokes equations for free surface flow is developed. The equations are transformed vertically to the σ coordinate system and laterally to an orthogonal curvilinear system and solved in a fractional step manner in which the pressure is split into hydrostatic and nonhydrostatic components. The model treats the nonhydrostatic term implicitly and uses a collocated grid and pressure interpolation to prevent checkerboard solutions that occur when the velocity and pressure become decoupled. Advection and hydrostatic pressure terms are integrated explicitly with a second-order accurate predictor-corrector scheme. The corrector utilizes fluxes that are computed in a Godunov-based manner by solving a Riemann problem at each cell face. Flow variables are reconstructed at each cell face to obtain second-order spatial accuracy. Numerical simulations of Stokes, cnoidal, and solitary waves with the proposed method and a reference method in which th...
TL;DR: In this paper, the authors report on the development of a machining device which is capable of carrying out precision machining experiments under external hydrostatic pressure, which enhances the critical cross sectional area and reduces the cracks and chippings of all the tested materials.
Abstract: This paper reports on the development of a machining device which is capable of carrying out precision machining experiments under external hydrostatic pressure. Machining trials were conducted on hard-brittle materials such as soda glass, quartz glass, silicon and quartz wafers using the newly developed machining device under the externally applied hydrostatic pressures of zero and 400 MPa. The machined traces were analyzed by laser microscope. From the trace profiles, crack ratio and area of cross section of the trace were estimated. The applied hydrostatic pressure enhanced the critical cross sectional area and reduced the cracks and chippings of all the tested materials. Effects of hydrostatic pressure on the machining characteristics of the crystalline and glassy materials are discussed in detail. The mechanism behind the enhancement of ductile-brittle transition by the externally applied hydrostatic pressure is also elucidated by a theoretical model.
TL;DR: In this paper, it was shown that the thermal properties of foam neoprene under hydrostatic pressure cannot be predicted by theoretical means, and that uni-axial pressure cannot simulate hydrostatic compression.
Abstract: The purpose of this study was to show that the thermal properties of foam neoprene under hydrostatic pressure cannot be predicted by theoretical means, and that uni-axial pressure cannot simulate hydrostatic compression. The thermal conductivity and compressive strain of foam neoprene were measured under hydrostatic pressure. In parallel, uni-axial compressive strain data were collected. The experimental set-up and data were put into perspective with past published studies. It was shown that uni-axial compression yielded strains 20–25% greater than did hydrostatic compression. This suggests the need for direct hydrostatic pressure measurement. For comparison to hydrostatic experimental data, a series of thermal conductivity theories of two phase composites based on particulate phase geometry were utilized. Due to their dependence on the porosity and constituent thermal conductivities, a model to predict porosity under hydrostatic pressure was used and an empirical correlation was derived to calculate the thermal conductivity of pure neoprene rubber from experimental data. It was shown that, although some agreement between experimental data and thermal conductivity theories was present, no particular theory can be used because they all fail to model the complex structure of the pores. It was therefore concluded that an experimental programme, such as reported here, is necessary for direct measurement.
TL;DR: In this paper, fluid stationary models are used to reproduce the observed, negative vertical gradient of the rotation velocity of the extraplanar gas in spiral galaxies, based on the simple condition that the pressure of the medium does not depend on density alone (baroclinic instead of barotropic solutions).
Abstract: We show that fluid stationary models are able to reproduce the observed, negative vertical gradient of the rotation velocity of the extra-planar gas in spiral galaxies. We have constructed models based on the simple condition that the pressure of the medium does not depend on density alone (baroclinic instead of barotropic solutions: isodensity and isothermal surfaces do not coincide). As an illustration, we have successfully applied our method to reproduce the observed velocity gradient of the lagging gaseous halo of NGC 891. The fluid stationary models discussed here can describe a hot homogeneous medium as well as a "gas" made of discrete, cold HI clouds with an isotropic velocity dispersion distribution. Although the method presented here generates a density and velocity field consistent with observational constraints, the stability of these configurations remains an open question.
TL;DR: In this article, a simplified one-dimensional and isothermal model of the magma chamber emptying and conduit flow was developed and coupled together to investigate the temporal evolution of fundamental flow conditions in the Magma chamber plus conduit system during sustained magmatic explosive eruptions.
TL;DR: In this article, the authors compare isothermal models to models including cooling with a simple but self-consistent treatment of the coupling between gas, grains and radiation field temperatures, and show that isothermal model fails to account for the innermost slow infall motions observed, even with the most hydrostatic initial conditions.
Abstract: We compute numerical simulations of spherical collapse triggered by a slow increase in external pressure. We compare isothermal models to models including cooling with a simple but self-consistent treatment of the coupling between gas, grains and radiation field temperatures. The hydrostatic equilibrium appears to hold past the marginally stable state, until the collapse proceeds. The last hydrostatic state before collapse has a lower central gas temperature in the centre due to the enhanced coupling between gas, grains and radiation field. This results in slightly lower pressure gradients in the bulk of the envelope which is hence slightly more extended than in the isothermal case. Due to the sensitivity of the collapse on these initial conditions, protostellar infall velocities in the envelope turn out to be much slower in the case with cooling. Our models also compute the radiative transfer and a rather large chemical network coupled to gas dynamics. However, we note that the steady-state chemisorption of CO is sufficient to provide an accurate cooling function of the gas. This justifies the use of post-processing techniques to account for the abundance of observed molecules. Existing observations of infall signatures put very stringent constraints on the kinematics and temperature profile of the class 0 protostar IRAM 04191+1522. We show that isothermal models fail to account for the innermost slow infall motions observed, even with the most hydrostatic initial conditions. In contrast, models with cooling reproduce the general shape of the temperature profile inferred from observations and are in much better agreement with the infall signatures in the inner 3000 AU.
TL;DR: In this article, the authors derived analytical solutions for the semi-diurnal tides on a slightly elliptical homogeneous incompressible elastic model and extended these analytical results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the tilt and the deviation of the vertical with reference to the Earth's axis.
Abstract: Tidal forces acting on the Earth cause deformations and mass redistribution inside the planet involving surface motions and variation in the gravity field, which may be observed in geodetic experiments. Because for space geodesy it is now necessary to achieve the mm level in tidal displacements, we take into account the hydrostatic flattening of the Earth in the computation of the elasto-gravitational deformations. Analytical solutions are derived for the semi-diurnal tides on a slightly elliptical homogeneous incompressible elastic model. That simple analytical Earth’s model is not a realistic representation of any real planet, but it is useful to understand the physics of the problem and also to check numerical procedures. We rediscover and discuss the Love’s solutions and obtain new analytical solutions for the tangential displacement. We extend these analytical results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the tilt and the deviation of the vertical with reference to the Earth’s axis.
TL;DR: In this article, the adjustment of a compressible, stably stratified atmosphere to sources of hydrostatic and geostrophic imbalance using a linear model is investigated using a time-dependent injections of mass, heat, or momentum that model those processes considered "external" to the scales of motion on which the linearization and other model assumptions are justifiable.
Abstract: The adjustment of a compressible, stably stratified atmosphere to sources of hydrostatic and geostrophic imbalance is investigated using a linear model. Imbalance is produced by prescribed, time-dependent injections of mass, heat, or momentum that model those processes considered “external” to the scales of motion on which the linearization and other model assumptions are justifiable. Solutions are demonstrated in response to a localized warming characteristic of small isolated clouds, larger thunderstorms, and convective systems. For a semi-infinite atmosphere, solutions consist of a set of vertical modes of continuously varying wavenumber, each of which contains time dependencies classified as steady, acoustic wave, and buoyancy wave contributions. Additionally, a rigid lower-boundary condition implies the existence of a discrete mode—the Lamb mode— containing only a steady and acoustic wave contribution. The forced solutions are generalized in terms of a temporal Green's function, which repres...
TL;DR: In this article, a new elasto-gravitational earth model is proposed, which takes into account lateral variations, deviatoric pre-stresses and topographies of the Earth and finds that global lateral variations within the Earth, such as ellipticity, have a weak impact (about 1 per cent) on the deformation induced by atmospheric loading.
Abstract: We have developed a new elasto-gravitational earth model able to take into account lateral variations, deviatoric pre-stresses and topographies. As a first application, we assume an el-lipsoidal earth with hydrostatic pre-stresses, and validate and discuss our numerical model by comparison with previous studies on the M 2 body tide. We then study the response of the ellipsoidal earth to zonal atmospheric loads, and find that global lateral variations within the Earth, such as ellipticity, have a weak impact (about 1 per cent) on the elasto-gravitational deformations induced by atmospheric loading. At low frequencies, the Earth is deformed mainly by luni-solar tides and by surface loads, including ocean, atmosphere, ice volumes and post-glacial rebound. In this work, we focus our attention on the Earth's body tides and atmospheric loadings. The most accepted Earth body-tide models presently deal with an ellipsoidal, rotating earth, containing a liquid core and an anelastic mantle with hydrostatic pre-stresses (Wahr 1981; Wahr & Bergen 1986). The Earth, however, is not an exact ellipsoid, but presents lateral variations and deviatoric pre-stresses: there are long-wavelength density anomalies within the mantle, as shown by geoid anomalies and tomography studies (e.g. Romanowicz & Gung 2002). Wang (1994) and Dehant et al. (1999) studied the influence of lateral heterogeneities on Earth tides and showed that this effect is small but not necessarily negligible. They did not, however, take into account possible deviatoric pre-stresses: these effects on the Earth's body tides are totally unknown. In addition to tidal forces, mass changes in the atmosphere also cause deformation and mass redistribution inside the planet, involving both local and global surface motions and variations in the gravity field, which may be observed in geodetic experiments. For several decades, satellite geodesy has provided information on the temporal variation of the Earth's geopotential, and especially on the low-degree zonal harmonics (J 2 , J 3. . .) (Gegout & Cazenave 1993), which are essentially controlled by surface loads. These hydrological , atmospheric or oceanic effects on the Earth's gravity field are usually modelled assuming a spherical earth with hydro-static pre-stress (e.g. Farrell 1972; Wahr et al. 1998). With the advent of the new generation of gravity measurements, one of the challenges of the coming decade will be to provide more realistic earth models that show the variation of gravity with time. In particular, global studies based on gravity data from satellites such as GRACE, GOCE, and future GRACE/GOCE follow-on ones require accurate body-tide deformation models. More realistic gravity variation models are also needed for local and ground measurements, particularly for the very accurate superconducting gravimeters and the associated gravimetric observatory network such as the Global Geodynamic Project (Crossley et al. 1999). The formalism developed to compute this elasto-gravitational model is usually based on spherical harmonic analysis. The addition of lateral variations leads to couplings between spherical harmonics , i.e. to a more complex formalism that requires a large numerical effort (e.g. Wang 1994; Plag et al. 1996). We develop here a new approach for a non-radially symmetrical earth model using a finite-element method known as the spectral element method. The efficiency of this method is less dependent on the shape of the lateral heterogeneities than the spherical harmonic method. Our method is therefore well adapted to studying the impact of global and local lateral variations on the Earth deformation. We solve the elasto-gravitational equations taking into consideration the lateral variations within the Earth by using a first-order perturbation theory (Smith 1974; Dahlen & Tromp 1998). This new model allows us to take into account lateral variations of density and rheological parameters, deviatoric pre-stresses and interface topography. In order to validate our calculations, we tackle a well-known problem: the impact of the hydrostatic ellipticity on the Earth body tides. An analytical solution for this problem can be derived for a simple model in which the earth is assumed to be homogeneous and incompressible. The gravitational potential and the vertical displacement on the surface of the deformed ellipsoid were first derived by Love (1911) and then corrected by Wang (1994). We have recently extended these analytical results to the tangential surface displacement (Greff-Lefftz et al. 2005). We first validate our model with our analytical solutions, and then compare our results with
TL;DR: In this article, a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium for self-gravitating systems is discussed.
Abstract: Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We discuss a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium for self-gravitating systems. It is suggested that the nonextensive parameter in Tsallis statistics has a clear physical meaning with regard to the non-isothermal nature of the systems with long-range interactions. Tsallis’ equilibrium distribution for the self-gravitating systems describes the property of hydrostatic equilibrium of the systems.
TL;DR: A comparison of hydrostatic and nonhydrostatic pressure components and their horizontal gradients in two seiches represents a deepwater wave oscillation and its effects are not negligible even when the aspect ratio is less than 0.05.
TL;DR: Using the scalar and tensor virial equations, the Lane-Emden equation expressing the hydrostatic equilibrium and small oscillations around the equilibrium, the authors showed how the cosmological constant Λ affects various astrophysical quantities important for large matter conglomeration.
Abstract: Using the scalar and tensor virial equations, the Lane-Emden equation expressing the hydrostatic equilibrium and small oscillations around the equilibrium, we show how the cosmological constant Λ affects various astrophysical quantities important for large matter conglomeration in the universe. Among others we examine the effect of Λ on the polytropic equation of state for spherically symmetric objects and find non-negligible results in certain realistic cases. We calculate the angular velocity for non-spherical oblate configurations which demonstrates a clear effect of Λ on high eccentricity objects. We show that for oblate as well as prolate ellipsoids the cosmological constant influences the critical mass and the temperature of the astrophysical object. These and other results show that the effect of Λ is large for flat astrophysical bodies.
TL;DR: In this article, a model for the equilibrium of solid planetary cores embedded in a gaseous nebula is presented, where the authors approximate the protoplanet as a spherically symmetric, isothermal, self-gravitating classical ideal gas envelope in equilibrium, around a rigid body of given mass and density.
Abstract: We present a model for the equilibrium of solid planetary cores embedded in a gaseous nebula. From this model we are able to extract an idealized roadmap of all hydrostatic states of the isothermal protoplanets. The complete classification of the isothermal protoplanetary equilibria should improve the understanding of the general problem of giant planet formation, within the framework of the nucleated instability hypothesis. We approximate the protoplanet as a spherically symmetric, isothermal, self-gravitating classical ideal gas envelope in equilibrium, around a rigid body of given mass and density, with the gaseous envelope required to fill the Hill-sphere. Starting only with a core of given mass and an envelope gas density at the core surface, the equilibria are calculated without prescribing the total protoplanetary mass or nebula density. In this way, a variety of hydrostatic core-envelope equilibria has been obtained. Two types of envelope equilibria can be distinguished: uniform equilibrium, were the density of the envelope gas drops approximately an order of magnitude as the radial distance increases to the outer boundary, and compact equilibrium, having a small but very dense gas layer wrapped around the core and very low, exponentially decreasing gas density further out. The effect of the envelope mass on the planetary gravitational potential further discriminates the models into the self-gravitating and the non-self gravitating ones. The static critical core masses of the protoplanets for the typical orbits of 1, 5.2, and 30 AU, around a parent star of 1 solar mass (M⊙) are found to be 0.1524, 0.0948, and 0.0335 Earth masses (M⊕), respectively, for standard nebula conditions (Kusaka et al. 1970). These values are much lower than currently admitted ones primarily because our model is isothermal and the envelope is in thermal equilibrium with the nebula. Our solutions show a wide range of possible envelopes. For a given core, multiple solutions (at least two) are found to fit into the same nebula. Some of those solutions posses equal envelope mass. This variety is a consequence of the envelope's self-gravity. We extend the concept of the static critical core mass to the local and global critical core mass. Above the global critical mass, only compact solutions exist. We conclude that the 'global static critical core mass' marks the meeting point of all four qualitatively different envelope regions.
TL;DR: In this article, a numerical solution based on the unsteady Reynolds-averaged Navier-Stokes equations on the unstructured grid was proposed for free-surface flow.
Abstract: Validation of 3D finite element model for free-surface flow is conducted using a high quality and high spatial resolution data set. The commonly numerical models with the conventional hydrostatic pressure still remain the most widely used approach for the solution of practical engineering problems. However, when a 3D description of the velocity field is required, it is useful to resort to a more accurate model in which the hydrostatic assumption is removed. The present research finds its motivation in the increasing need for efficient management of geophysical flows such as estuaries (multiphase fluid flow) or natural rivers with the presence of short waves and/or strong bathymetry gradient, and/or strong channel curvature. A numerical solution is based on the unsteady Reynolds-averaged Navier-Stokes equations on the unstructured grid. The eddy viscosity is calculated from the efficient k-e turbulence model. The model uses implicit fractional step time stepping, and the characteristics method is used to compute the convection terms in the multi-layers system (suitable for the vertical stratified fluid flow), in which the vertical grid is located at predefined heights and the number of elements in the water column depends on water depth. The bottommost and topmost elements of variable height allow a faithful representation of the bed and the time-varying free-surface, respectively. The model is applied to the 3D open channel flows of various complexity
TL;DR: In this article, a reduced-order approximation to the vertical and horizontal structure of a simplified model of the baroclinically unstable Martian atmosphere was derived, where the original model uses the full hydrostatic primitive equations on a sphere, but has only highly simplified schemes to represent the detailed physics of the Martian atmosphere.
Abstract: In this paper we derive a reduced-order approximation to the vertical and horizontal structure of a simplified model of the baroclinically unstable Martian atmosphere. The original model uses the full hydrostatic primitive equations on a sphere, but has only highly simplified schemes to represent the detailed physics of the Martian atmosphere, e.g. forcing towards a plausible zonal mean temperature state using Newtonian cooling. Three different norms are used to monitor energy conversion processes in the model and are then compared. When four vertical modes (the barotropic and first three baroclinic modes) are retained in the reduced-order approximation, the correlation norm captures approximately 90% of the variance, while the kinetic energy and total energy norms capture approximately 83% and 78% of the kinetic and total energy respectively. We show that the leading order Proper Orthogonal Decomposition (POD) modes represent the dominant travelling waves in the baroclinically-unstable, winter hemisphere. In part 2 of our study we will develop a hierarchy of truncated POD-Galerkin expansions of the model equations using up to four vertical modes.
30 Mar 2005
TL;DR: Combining linear FEM methods with matrix condensation techniques and the tuned proportional feedback control allows for the simulation of a fluid-filled elastic object at real-time haptic update rates.
Abstract: We present a fast technique for simulating fluid-filled elastic objects with the Finite Element Method. By simulating the presence of fluid with hydrostatic fluid pressure, a quasi-static simulation of fluid can be achieved by applying a force boundary condition to the nodes on the fluidelastic interface. Using a proportional feedback control algorithm, a relationship between the volume and pressure of the fluid structure can be maintained. Optimal parameters for the control algorithm are found by determining the response of the elastic system to changes in pressure. This approach has been shown to agree with experimental deformation data taken from a fluid-filled gelatin phantom. Combining linear FEM methods with matrix condensation techniques and the tuned proportional feedback control allows for the simulation of a fluid-filled elastic object at real-time haptic update rates.
TL;DR: In this paper, a promising approach to control the material flow within deep drawing and working media based forming processes is the structuring of the tool surfaces in the contact zones between workpiece and die.
Abstract: A promising approach to control the material flow within deep drawing and workingmedia based forming processes is the structuring of the tool surfaces in the contact zones between workpiece and die. In order to obtain a sufficient and an optimised material flow respectively – especially for non-symmetric or non-uniform workpiece geometries – a locally adapted distribution of surface structures is a practicable solution. The macroscopic, and also the microscopic surface structures can be manufactured sufficiently by means of a high-speed cutting process. The shape of the tool surface structure has a significant influence on the tribological conditions between workpiece and die. To adjust the surface structure distribution to the required material flow distribution, detailed knowledge about the correlation of the material flow from the tribological conditions between sheet and the forming tool is required. A further innovative approach, particularly for decreasing the friction coefficient, is the use of an innovative hydrostatic pressure system using fluid ducts. Its functional principle is based on the reduction of the contact shear stress at the sheet surface in the contact zone with the forming tool by means of locally applying a hydrostatic fluid pressure. To obtain information about the correlation of the material flow from the tool surface structures and from the parameters of the hydrostatic pressure system respectively, fundamental investigations have been carried out. In order to optimise the material flow, these toolbased approaches can be used as stand-alone solution, or in addition to other systems. If the surface structures and a hydrostatic pressure system are used in combination with the multi-point blank holder, which has already been qualified for the high-pressure sheet metal forming (HBU), a powerful system for the material flow control is available.
TL;DR: The formation process of ultra low-mass objects is some kind of extension of the star formation process as mentioned in this paper, and the physical changes towards lower mass are discussed by investigating the collapse of cloud cores that are modelled as Bonnor-Ebert spheres.
Abstract: The formation process of ultra low-mass objects is some kind of extension of the star formation process. The physical changes towards lower mass are discussed by investigating the collapse of cloud cores that are modelled as Bonnor-Ebert spheres. Their collapse is followed by solving the equations of fluid dynamics with radiation and a model of time-dependent convection that has been calibrated to the Sun. For a sequence of cloud-cores with 1 to 0.01 solar masses, evolutionary tracks and isochrones are shown in the mass-radius diagram, the Hertzsprung-Russel diagram and the effective temperaturesurface gravity or Kiel diagram. The collapse and the early hydrostatic evolution to ages of few Ma are briefly discussed and compared to observations of objects in Upper Scorpius and the low-mass components of GG Tau. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)