Showing papers on "Hydrostatic equilibrium published in 2010"

Radiative transfer with scattering for domain-decomposed 3D MHD simulations of cool stellar atmospheres

Abstract: We present the implementation of a radiative transfer solver with coherent scattering in the new BIFROST code for radiative magneto-hydrodynamical (MHD) simulations of stellar surface convection. The code is fully parallelized using MPI domain decomposition, which allows for large grid sizes and improved resolution of hydrodynamical structures. We apply the code to simulate the surface granulation in a solar-type star, ignoring magnetic fields, and investigate the importance of coherent scattering for the atmospheric structure. A scattering term is added to the radiative transfer equation, requiring an iterative computation of the radiation field. We use a short-characteristics-based Gauss-Seidel acceleration scheme to compute radiative flux divergences for the energy equation. The effects of coherent scattering are tested by comparing the temperature stratification of three 3D time-dependent hydrodynamical atmosphere models of a solar-type star: without scattering, with continuum scattering only, and with both continuum and line scattering. We show that continuum scattering does not have a significant impact on the photospheric temperature structure for a star like the Sun. Including scattering in line-blanketing, however, leads to a decrease of temperatures by about 350\,K below log tau < -4. The effect is opposite to that of 1D hydrostatic models in radiative equilibrium, where scattering reduces the cooling effect of strong LTE lines in the higher layers of the photosphere. Coherent line scattering also changes the temperature distribution in the high atmosphere, where we observe stronger fluctuations compared to a treatment of lines as true absorbers.

L1448 irs2e: a candidate first hydrostatic core

Abstract: Intermediate between the prestellar and Class 0 protostellar phases, the first core is a quasi-equilibrium hydrostatic object with a short lifetime and an extremely low luminosity. Recent magnetohydrodynamic (MHD) simulations suggest that the first core can even drive a molecular outflow before the formation of the second core (i.e., protostar). Using the Submillimeter Array and the Spitzer Space Telescope, we present high angular resolution observations toward the embedded dense core IRS2E in L1448. We find that source L1448 IRS2E is not visible in the sensitive Spitzer infrared images (at wavelengths from 3.6 to 70 μm) and has weak (sub-) millimeter dust continuum emission. Consequently, this source has an extremely low bolometric luminosity (<0.1 L ☉). Infrared and (sub-) millimeter observations clearly show an outflow emanating from this source; L1448 IRS2E represents thus far the lowest luminosity source known to be driving a molecular outflow. Comparisons with prestellar cores and Class 0 protostars suggest that L1448 IRS2E is more evolved than prestellar cores but less evolved than Class 0 protostars, i.e., at a stage intermediate between prestellar cores and Class 0 protostars. All these results are consistent with the theoretical predictions of the radiative/MHD simulations, making L1448 IRS2E the most promising candidate of the first hydrostatic core revealed so far.

Improved Middle Atmosphere Climate and Forecasts in the ECMWF Model through a Nonorographic Gravity Wave Drag Parameterization

Abstract: In model cycle 35r3 (Cy35r3) of the ECMWF Integrated Forecast System (IFS), the momentum deposition from small-scale nonorographic gravity waves is parameterized by the Scinocca scheme, which uses hydrostatic nonrotational wave dynamics to describe the vertical evolution of a broad, constant, and isotropic spectrum of gravity waves emanating from the troposphere. The Cy35r3 middle atmosphere climate shows the following: (i) an improved representation of the zonal-mean circulation and temperature structure; (ii) a realistic parameterized gravity wave drag; (iii) a reasonable stationary planetary wave structure and stationary wave driving in July and an underestimate of the generation of stationary wave activity in the troposphere and stationary wave driving in January; (iv) an improved representation of the tropical variability of the stratospheric circulation, although the westerly phase of the semiannual oscillation is missing; and (v) a realistic horizontal distribution of momentum flux in the ...

Galaxy clusters at the edge: temperature, entropy, and gas dynamics near the virial radius

Abstract: Recently, Suzaku has produced temperature and entropy profiles, along with profiles of gas density, gas fraction, and mass, for multiple galaxy clusters out to approximately the virial radius. In this paper, we compare these novel X-ray observations with results from N-body + hydrodynamic adaptive mesh refinement cosmological simulations using the Enzo code. There is excellent agreement in the temperature, density, and entropy profiles between a sample of 24 mostly substructure-free massive clusters in the simulated volume and the observed clusters. This supports our previous contention that clusters have "universal" outer temperature profiles. Furthermore, it appears that the simplest adiabatic gas physics used in these Enzo simulations is adequate to model the outer regions of these clusters without other mechanisms (e.g., non-gravitational heating, cooling, magnetic fields, or cosmic rays). However, the outskirts of these clusters are not in hydrostatic equilibrium. There is significant bulk flow and turbulence in the outer intracluster medium created by accretion from filaments. Thus, the gas is not fully supported by thermal pressure. The implications for mass estimation from X-ray data are discussed.

Flattening of the Earth: further from hydrostaticity than previously estimated

Abstract: SUMMARY The knowledge of the gravitational potential coefficients J2 and J4 of a hydrostatic Earth model is necessary to deal with non-hydrostatic properties of our planet. They are indeed fundamental parameters when modelling the 3-D density structure or the rotational behaviour of our planet. The most widely used values computed by Nakiboglu need to be updated for two reasons. First, we have noted a mistake in one of his formulae. Secondly, the value of the inertia ratio I/MR2 chosen at the time of prem is not any more the best estimate. Both corrections slightly but significantly reduce the hydrostatic J2 value: the dynamical flattening of the Earth is even further from hydrostaticity than previously thought. The difference between the polar and equatorial radii appears to be 113 ± 1 m (instead of 98 m) larger than the hydrostatic value. Moreover, uncertainties upon the hydrostatic parameters are estimated.

Theoretical investigation of the high pressure structure, lattice dynamics, phase transition, and thermal equation of state of titanium metal

Abstract: We report a detailed first-principles calculation to investigate the structures, elastic constants, and phase transition of Ti. The axial ratios of both alpha-Ti and omega-Ti are nearly constant under hydrostatic compression, which confirms the latest experimental results. From the high pressure elastic constants, we find that the alpha-Ti is unstable when the applied pressures are larger than 24.2 GPa, but the omega-Ti is mechanically stable at all range of calculated pressure. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening around Gamma point of alpha-Ti. When the pressure is raised to 35.9 GPa, the frequencies around the Gamma point along Gamma-M-K and Gamma-A in transverse acoustical branches become imaginary, indicating a structural instability. Within quasiharmonic approximation, we obtained the full phase diagram and accurate thermal equations of state of Ti. The phase transition omega-Ti ->alpha-Ti ->beta-Ti at zero pressure occurs at 146 K and 1143 K, respectively. The predicted triple point is at 9.78 GPa, 931 K, which is close to the experimental data. Our thermal equations of state confirm the available experimental results and are extended to a wider pressure and temperature range. (C) 2010 American Institute of Physics. [doi:10.1063/1.3407560]

Shapes of Gas, Gravitational Potential and Dark Matter in Lambda-CDM Clusters

Abstract: We present analysis of the three-dimensional shape of intracluster gas in clusters formed in cosmological simulations of the Lambda-CDM cosmology and compare it to the shape of dark matter distribution and the shape of the overall isopotential surfaces. We find that in simulations with radiative cooling, star formation and stellar feedback (CSF), intracluster gas outside the cluster core is more spherical compared to non-radiative (NR) simulations, while in the core the gas in the CSF runs is more triaxial and has a distinctly oblate shape. The latter reflects the ongoing cooling of gas, which settles into a thick oblate ellipsoid as it loses thermal energy. The shape of the gas in the inner regions of clusters can therefore be a useful diagnostic of gas cooling. We find that gas traces the shape of the underlying potential rather well outside the core, as expected in hydrostatic equilibrium. At smaller radii, however, the gas and potential shapes differ significantly. In the CSF runs, the difference reflects the fact that gas is partly rotationally supported. Interestingly, we find that in NR simulations the difference between gas and potential shape at small radii is due to random gas motions, which make the gas distribution more spherical than the equipotential surfaces. Finally, we use mock Chandra X-ray maps to show that the differences in shapes observed in three-dimensional distribution of gas are discernible in the ellipticity of X-ray isophotes. Contrasting the ellipticities measured in simulated clusters against observations can therefore constrain the amount of cooling of the intracluster medium and the presence of random gas motions in cluster cores.

Gravity waves, scale asymptotics and the pseudo-incompressible equations

Abstract: Multiple-scale asymptotics is used to analyse the Euler equations for the dynamical situation of a gravity wave (GW) near breaking level. A simple saturation argument in combination with linear theory is used to obtain the relevant dynamical scales. As a small expansion parameter, the ratio of the inverse of the vertical wavenumber and potential temperature and pressure scale heights is used, which we allow to be of the same order of magnitude here. It is shown that the resulting equation hierarchy is consistent with that obtained from the pseudo-incompressible equations, both for non-hydrostatic and hydrostatic GWs, while this is not the case for the anelastic equations unless the additional assumption of sufficiently weak stratification is adopted. To describe vertical propagation of wavepackets over several atmospheric-scale heights, Wentzel–Kramers–Brillouin (WKB) theory is used to show that the pseudo-incompressible flow divergence generates the same amplitude equation that also obtains from the full Euler equations. This gives a mathematical justification for the use of the pseudo-incompressible equations in the study of GW breaking in the atmosphere for arbitrary background stratification. The WKB theory interestingly even holds at wave amplitudes close to static instability. In the mean-flow equations, we obtain in addition to the classic wave-induced momentum-flux divergences a wave-induced correction of hydrostatic balance in the vertical momentum equation, which cannot be obtained from Boussinesq or anelastic dynamics.

On the influence of non-thermal pressure on the mass determination of galaxy clusters

Abstract: Aims. Given that in most cases just thermal pressure is taken into account in the hydrostatic equilibrium equation to estimate galaxy cluster mass, the main purpose of this paper is to consider the contribution of all three non-thermal components to total mass measurements. The non-thermal pressure is composed by cosmic rays, turbulence and magnetic pressures. Methods. To estimate the thermal pressure we used public XMM-Newton archival data of five Abell clusters to derive temperature and density profiles. To describe the magnetic pressure, we assume a radial distribution for the magnetic field, B(r) ∝ ρ α . To seek generality we assume α within the range of 0.5 to 0.9, as indicated by observations and numerical simulations. Turbulent motions and bulk velocities add a turbulent pressure, which is considered using an estimate from numerical simulations. For this component, we assume an isotropic pressure, Pturb = 1 ρg(σ 2 + σ 2 ). We also consider the contribution of cosmic ray pressure, Pcr ∝ r −0.5 . Thus, besides the gas (thermal) pressure, we include these three non-thermal components in the magnetohydrostatic equilibrium equation and compare the total mass estimates with the values obtained without them. Results. A consistent description for the non-thermal component could yield a variation in mass estimates that extends from 10% to ∼30%. We verified that in the inner parts of cool core clusters the cosmic ray component is comparable to the magnetic pressure, while in non-cool core clusters the cosmic ray component is dominant. For cool core clusters the magnetic pressure is the dominant component, contributing more than 50% of the total mass variation due to non-thermal pressure components. However, for non-cool core clusters, the major influence comes from the cosmic ray pressure that accounts for more than 80% of the total mass variation due to non-thermal pressure effects. For our sample, the maximum influence of the turbulent component to the total mass variation can be almost 20%. Although all of the assumptions agree with previous works, it is important to notice that our results rely on the specific parametrization adopted in this work. We show that this analysis can be regarded as a starting point for a more detailed and refined exploration of the influence of non-thermal pressure in the intra-cluster medium (ICM).

Equilibrium initialization and stability of three-dimensional gas discs

Abstract: We present a new systematic way of setting up galactic gas discs based on the assumption of detailed hydrodynamic equilibrium. To do this, we need to specify the density distribution and the velocity field which supports the disc. We first show that the required circular velocity has no dependence on the height above or below the mid-plane so long as the gas pressure is a function of density only. The assumption of discs being very thin enables us to decouple the vertical structure from the radial direction. Based on that, the equation of hydrostatic equilibrium together with the reduced Poisson equation leads to two sets of second-order non-linear differential equations, which are easily integrated to set up a stable disc. We call one approach ‘density method’ and the other one ‘potential method’. Gas discs in detailed balance are especially suitable for investigating the onset of the gravitational instability. We revisit the question of global, axisymmetric instability using fully three-dimensional disc simulations. The impact of disc thickness on the disc instability and the formation of spontaneously induced spirals is studied systematically with or without the presence of the stellar potential. In our models, the numerical results show that the threshold value for disc instability is shifted from unity to 0.69 for self-gravitating thick discs and to 0.75 for combined stellar and gas thick discs. The simulations also show that self-induced spirals occur in the correct regions and with the right numbers as predicted by the analytic theory.

The axis ratio distribution of x-ray clusters observed by xmm-newton

Abstract: We derive the axis ratio distribution of X-ray clusters using the XMM-Newton catalog. By fitting the contour lines of the X-ray image by ellipses, we confirm that the X-ray distribution is well approximated by the elliptic distribution with a constant axis ratio and direction. We construct a simple model describing the axis ratio of the X-ray gas assuming the hydrostatic equilibrium embedded in the triaxial dark matter halo model proposed by Jing & Suto and the hydrostatic equilibrium. We find that the observed probability density function of the axis ratio is consistent with this model prediction.

Equilibrium Initialization and Stability of Three-Dimensional Gas Disks

Abstract: We present a new systematic way of setting up galactic gas disks based on the assumption of detailed hydrodynamic equilibrium. To do this, we need to specify the density distribution and the velocity field which supports the disk. We first show that the required circular velocity has no dependence on the height above or below the midplane so long as the gas pressure is a function of density only. The assumption of disks being very thin enables us to decouple the vertical structure from the radial direction. Based on that, the equation of hydrostatic equilibrium together with the reduced Poisson equation leads to two sets of second-order non-linear differential equation, which are easily integrated to set-up a stable disk. We call one approach `density method' and the other one `potential method'. Gas disks in detailed balance are especially suitable for investigating the onset of the gravitational instability. We revisit the question of global, axisymmetric instability using fully three-dimensional disk simulations. The impact of disk thickness on the disk instability and the formation of spontaneously induced spirals is studied systematically with or without the presence of the stellar potential. In our models, the numerical results show that the threshold value for disk instability is shifted from unity to 0.69 for self-gravitating thick disks and to 0.75 for combined stellar and gas thick disks. The simulations also show that self-induced spirals occur in the correct regions and with the right numbers as predicted by the analytic theory.

Testing strict hydrostatic equilibrium in simulated clusters of galaxies: Implications for A1689

Abstract: Accurate mass determination of clusters of galaxies is crucial if they are to be used as cosmological probes. However, there are some discrepancies between cluster masses determined based on gravitational lensing and X-ray observations assuming strict hydrostatic equilibrium (i.e., the equilibrium gas pressure is provided entirely by thermal pressure). Cosmological simulations suggest that turbulent gas motions remaining from hierarchical structure formation may provide a significant contribution to the equilibrium pressure in clusters. We analyze a sample of massive clusters of galaxies drawn from high-resolution cosmological simulations and find a significant contribution (20%-45%) from non-thermal pressure near the center of relaxed clusters, and, in accord with previous studies, a minimum contribution at about 0.1 R vir, growing to about 30%-45% at the virial radius, R vir. Our results strongly suggest that relaxed clusters should have significant non-thermal support in their core region. As an example, we test the validity of strict hydrostatic equilibrium in the well-studied massive galaxy cluster A1689 using the latest high-resolution gravitational lensing and X-ray observations. We find a contribution of about 40% from non-thermal pressure within the core region of A1689, suggesting an alternate explanation for the mass discrepancy: the strict hydrostatic equilibrium is not valid in this region.

EFFECTS OF f(R) DARK ENERGY ON DISSIPATIVE ANISOTROPIC COLLAPSING FLUID

Abstract: The purpose of this paper is to study the effects of dark energy on dynamics of the collapsing fluid within the framework of metric f(R) gravity. The fluid distribution is assumed to be locally anisotropic and undergoing dissipation in the form of heat flow, null radiations and shear viscosity. For this purpose, we take general spherical symmetric spacetime. Dynamical equations are obtained and also some special solutions are found by considering shearing expansion-free evolution of the fluid. It is found that dark energy affects the mass of the collapsing matter and rate of collapse but does not affect the hydrostatic equilibrium.

Testing Strict Hydrostatic Equilibrium in Simulated Clusters of Galaxies: Implications to Abell 1689

Abstract: Accurate mass determination of clusters of galaxies is crucial if they are to be used as cosmological probes. However, there are some discrepancies between cluster masses determined based on gravitational lensing, and X-ray observations assuming strict hydrostatic equilibirium (i.e., the equilibrium gas pressure is provided entirely by thermal pressure). Cosmological simulations suggest that turbulent gas motions remaining from hierarchical structure formation may provide a significant contribution to the equilibrium pressure in clusters. We analyze a sample of massive clusters of galaxies drawn from high resolution cosmological simulations, and find a significant contribution (20%-45%) from non-thermal pressure near the center of relaxed clusters, and, in accord with previous studies, a minimum contribution at about 0.1 Rvir, growing to about 30%-45% at the virial radius, Rvir. Our results strongly suggest that relaxed clusters should have significant non-thermal support in their core region. As an example, we test the validity of strict hydrostatic equilibirium in the well-studied massive galaxy cluster Abell 1689 using the latest high resolution gravitational lensing and X-ray observations. We find a contribution of about 40% from non-thermal pressure within the core region of A1689, suggesting an alternate explanation for the mass discrepancy: the strict hydrostatic equilibirium is not valid in this region.

The fragmentation of expanding shells – II. Thickness matters

Abstract: We study analytically the development of gravitational instability in an expanding shell having finite thickness. We consider three models for the radial density profile of the shell: (i) an analytic uniform-density model, (ii) a semi-analytic model obtained by numerical solution of the hydrostatic equilibrium equation and (iii) a 3D hydrodynamic simulation. We show that all three profiles are in close agreement, and this allows us to use the first model to describe fragments in the radial direction of the shell. We then use non-linear equations describing the time-evolution of a uniform oblate spheroid to derive the growth rates of shell fragments having different sizes. This yields a dispersion relation which depends on the shell thickness, and hence on the pressure confining the shell. We compare this dispersion relation with the dispersion relation obtained using the standard thin-shell analysis, and show that, if the confining pressure is low, only large fragments are unstable. On the other hand, if the confining pressure is high, fragments smaller than predicted by the thin-shell analysis become unstable. Finally, we compare the new dispersion relation with the results of 3D hydrodynamic simulations, and show that the two are in good agreement.

Galactic spiral shocks with thermal instability in vertically stratified galactic disks

Abstract: Galactic spiral shocks are dominant morphological features and believed to be responsible for substructure formation within spiral arms in disk galaxies. They can also contribute a substantial amount of kinetic energy to the interstellar gas by tapping the (differential) rotational motion. We use numerical hydrodynamic simulations to investigate dynamics and structure of spiral shocks with thermal instability (TI) in vertically stratified galactic disks, focusing on environmental conditions (of heating and the galactic potential) similar to the Solar neighborhood. We initially consider an isothermal disk in vertical hydrostatic equilibrium and let it evolve subject to interstellar cooling and heating as well as a stellar spiral potential. Due to TI, a disk with surface density Σ0 ≥ 6.7 M ☉ pc–2 rapidly turns to a thin dense slab near the midplane sandwiched between layers of rarefied gas. The imposed spiral potential leads to a vertically curved shock that exhibits strong flapping motions in the plane perpendicular to the arm. The overall flow structure at saturation is comprised of the arm, postshock expansion zone, and interarm regions that occupy typically 10%, 20%, and 70% of the arm-to-arm distance, in which the gas resides for 15%, 30%, and 55% of the arm-to-arm crossing time, respectively. The flows are characterized by transitions from rarefied to dense phases at the shock and from dense to rarefied phases in the postshock expansion zone, although gas with too-large postshock-density does not undergo this return phase transition, instead forming dense condensations. If self-gravity is omitted, the shock flapping drives random motions in the gas, but only up to ~2-3 km s-1 in the in-plane direction and less than 2 km s-1 in the vertical direction. Time-averaged shock profiles show that the spiral arms in stratified disks are broader and less dense compared to those in unstratified models, and that the vertical density distribution is overall consistent with local effective hydrostatic equilibrium. Inclusion of self-gravity increases the dense gas fraction by a factor of ~2 and raises the in-plane velocity dispersion to ~5-7 km s-1. When the disks are massive enough, with Σ0 ≥ 5 M ☉ pc–2, self-gravity promotes formation of bound clouds that repeatedly collide with each other in the arm and break up in the postshock expansion zone.

Model-independent X-ray Mass Determinations

Abstract: A new method is introduced for making X-ray mass determinations of spherical clusters of galaxies. Treating the distribution of gravitating matter as piecewise constant and the cluster atmosphere as piecewise isothermal, X-ray spectra of a hydrostatic atmosphere are determined up to a single overall normalizing factor. In contrast to more conventional approaches, this method relies on the minimum of assumptions, apart from the conditions of hydrostatic equilibrium and spherical symmetry. The method has been implemented as an XSPEC mixing model called CLMASS, which was used to determine masses for a sample of nine relaxed X-ray clusters. Compared to conventional mass determinations, CLMASS provides weak constraints on values of M 500, reflecting the quality of current X-ray data for cluster regions beyond r 500. At smaller radii, where there are high quality X-ray spectra inside and outside the radius of interest to constrain the mass, CLMASS gives confidence ranges for M 2500 that are only moderately less restrictive than those from more familiar mass determination methods. The CLMASS model provides some advantages over other methods and should prove useful for mass determinations in regions where there are high quality X-ray data.

Influence of Magnetic Field and Hydrostatic Initial Stress on Wave Reflection from a Generalized Thermoelastic Solid Half-space

Abstract: Using a generalized thermoelastic solid half-space, we estimate the impact of magnetic field, initial pressure and hydrostatic initial stress on reflection of P and SV waves. We consider a Green Lindsay model and present the governing equations for an isotropic homogeneous generalized thermoelastic solid under a magnetic field and hydrostatic initial stress. Lame’s potentials are used in two dimensions that tend to separate the governing equations into three equations that are sought in harmonic travelling wave form. We introduce the equations of the velocity of the P wave, thermal wave and SV wave. The boundary conditions for mechanical and Maxwell’s stresses and thermal insulation are applied to determine the reflection coefficients for the P wave, thermal wave and SV wave. Some new aspects are obtained of the reflection coefficients and displayed graphically and new conclusions are presented. Finally, it is shown that, under some conditions, previous results are special cases of our results.

Effect of nonhydrostatic stresses on solid-fluid equilibrium. I. Bulk thermodynamics

Abstract: We present a thermodynamic analysis of the effect of nonhydrostatic stresses on solid-fluid equilibrium in single-component systems. The solid is treated in the small-strain approximation and anisotropic linear elasticity. If the latent heat of the solid-fluid transformation is nonzero and pressure in the fluid is fixed, the shift of the equilibrium temperature relative to hydrostatic equilibrium is shown to be quadratic in nonhydrostatic components of the stress. If atomic volumes of the phases are different and temperature is fixed, the shift of the equilibrium liquid pressure relative to a hydrostatic state is quadratic in nonhydrostatic components of the stress in the solid. The stress effects at special points, at which either the latent heat or the volume difference turn to zero, have also been analyzed. Our theoretical predictions for the temperature and pressure shifts are quantitatively verified by atomistic computer simulations of solid-liquid equilibrium in copper using molecular dynamics with an embedded-atom potential. The simulations also demonstrate spontaneous crystallization of liquid on the surface of a stressed solid with the formation of solid-solid interfaces with the same crystallographic orientation of the solid layers. The lattice mismatch between the stressed and unstressed regions is accommodated by misfit dislocations dissociated in a zigzag pattern.

Hydrostatic levelling systems: Measuring at the system limits

Abstract: SUMMARY Three hydrostatic displacement monitoring system applications in Switzerland are discussed; the first concerns experience gained monitoring the foundation of the Albigna dam, the second relating to the underground stability of the Swiss Light Source synchrotron and the third concerning the deformation of a bridge near the city of Lucerne. Two different principles were applied, the Hydrostatic Leveling System (HLS) using the “half-filled pipe principle” which was developed for the Paul Scherrer Institute (PSI) and the Large Area Settlement System (LAS) using the “differential pressure principle”. With both principles deformations down to ground deformations induced by tidal forces can be seen. However, high accuracy of single sensors is not sufficient. A well-considered configuration of the complete system is equally important. On the other hand there are also limits given by the feasible installation or by the environmental conditions. Such an example is shown in the measurement task of the bridge, where the acceleration along the bridge due to the pass over of heavy trucks is limiting the feasibility of hydrostatic leveling measurements.

Computation of three-dimensional hydrostatic menisci

Abstract: A numerical method is developed for computing the shape of an infinite three-dimensional hydrostatic meniscus originating from interior contact lines whose projection in the horizontal plane has a specified shape. The Laplace-Young equation determining the meniscus shape is solved in orthogonal curvilinear coordinates generated by conformal mapping using a finite-difference method. The elevation of the contact lines is either prescribed or computed as part of the solution to ensure a specified contact angle. The method is applied to study the hydrostatic meniscus developing around an elliptical vertical cylinder using elliptic coordinates and between two parallel vertical circular cylinders using bipolar coordinates. The results illustrate variations in the contact angle or contact line distribution due to the boundary geometry and furnish numerical estimates for the capillary force and torque.

Gravity variations induced by core flows

Abstract: SUMMARY The temporal variation in the density structure associated with convective motions in the outer core causes a change in the Earth’s gravity field. Core flows also lead to a gravity change through the global elastic deformations that accompany changes in the non-hydrostatic pressure at the core–mantle boundary (CMB). In this work, we present predictions of the gravity changes from these two processes during the past century. These predictions are built on the basis of flows at the surface of the core that are reconstructed from the observed geomagnetic secular variation. The pressure-induced gravity variations can be reconstructed directly from surface core flows under the assumption of tangential geostrophy; predicted variations in the Stokes coefficients of degree 2, 3 and 4 are of the order of 10 −11 ,3 × 10 −12 and 10 −12 , respectively, with a typical timescale of a few decades. These correspond to changes in gravity of 70, 30 and 15 nGal, and to equivalent geoid height variations of 0.15, 0.05 and 0.02 mm, respectively. The density-induced gravity variations cannot be determined solely from surface core flows, though a partial recovery is possible if flows with important axial gradients dominate the dynamics at decadal timescales. If this is the case, the density-induced gravity signal is of similar amplitude and generally anti-correlated with the pressure-induced signal, thus reducing the overall amplitude of the gravity changes. However, because we expect decadal flows to be predominantly axially invariant, the amplitude of the density-induced gravity changes should be much smaller. Our prediction also allows to determine upper bounds in pressure change at the CMB and density change within the core that have taken place during the past 20 yr such that observed gravity variations are not exceeded; for harmonic degree 2, we find a maximum pressure change of approximately 350 Pa and a maximum departure from hydrostatic density of approximately 1 part in 10 7 . Although the predicted gravity changes from core flows are small, they are at the threshold of detectability with high-precision gravity measurements from satellite missions such as GRACE. The most important challenge to identifying a core signal will be the removal of interannual gravity variations caused by surface processes which are an order of magnitude larger and mask the core signal.

Gravity variations induced by core flows

Abstract: SUMMARY The temporal variation in the density structure associated with convective motions in the outer core causes a change in the Earth’s gravity field. Core flows also lead to a gravity change through the global elastic deformations that accompany changes in the non-hydrostatic pressure at the core–mantle boundary (CMB). In this work, we present predictions of the gravity changes from these two processes during the past century. These predictions are built on the basis of flows at the surface of the core that are reconstructed from the observed geomagnetic secular variation. The pressure-induced gravity variations can be reconstructed directly from surface core flows under the assumption of tangential geostrophy; predicted variations in the Stokes coefficients of degree 2, 3 and 4 are of the order of 10 −11 ,3 × 10 −12 and 10 −12 , respectively, with a typical timescale of a few decades. These correspond to changes in gravity of 70, 30 and 15 nGal, and to equivalent geoid height variations of 0.15, 0.05 and 0.02 mm, respectively. The density-induced gravity variations cannot be determined solely from surface core flows, though a partial recovery is possible if flows with important axial gradients dominate the dynamics at decadal timescales. If this is the case, the density-induced gravity signal is of similar amplitude and generally anti-correlated with the pressure-induced signal, thus reducing the overall amplitude of the gravity changes. However, because we expect decadal flows to be predominantly axially invariant, the amplitude of the density-induced gravity changes should be much smaller. Our prediction also allows to determine upper bounds in pressure change at the CMB and density change within the core that have taken place during the past 20 yr such that observed gravity variations are not exceeded; for harmonic degree 2, we find a maximum pressure change of approximately 350 Pa and a maximum departure from hydrostatic density of approximately 1 part in 10 7 . Although the predicted gravity changes from core flows are small, they are at the threshold of detectability with high-precision gravity measurements from satellite missions such as GRACE. The most important challenge to identifying a core signal will be the removal of interannual gravity variations caused by surface processes which are an order of magnitude larger and mask the core signal.

The effect of hydrostatic pressure fields on the dispersion characteristics of fluid-shell coupled system

Abstract: The effect of hydrostatic pressure on the vibration dispersion characteristics of fluid-shell coupled structures was studied. Both fluid-loaded cylindrical shells and fluid-filled cylindrical shells were considered. Numerical analysis was applied to solve the dispersion equations for shells filled with or loaded with fluid at various hydrostatic pressures. The results for external pressure showed that non-dimensional axial wave numbers are nearly independent when the pressure is below the critical level. The influence of internal pressure on wave numbers was found significant for the real branch s=1 and the complex branches of dispersion curves. The presence of internal pressure increased the cut on frequencies for the branch s=1 for high order wave modes.

A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars

Abstract: Using the shape model of Mars GTM090AA in terms of spherical harmonics complete to degree and order 90 and gravitational field model of Mars GGM2BC80 in terms of spherical harmonics complete to degree and order 80, both from Mars Global Surveyor (MGS) mission, the geometry (shape) and gravity potential value of reference equipotential surface of Mars (Areoid) are computed based on a constrained optimization problem. In this paper, the Areoid is defined as a reference equipotential surface, which best fits to the shape of Mars in least squares sense. The estimated gravity potential value of the Areoid from this study, i.e. W0 = (12,654,875 ± 69) (m2/s2), is used as one of the four fundamental gravity parameters of Mars namely, {W0, GM, ω, J20}, i.e. {Areoid’s gravity potential, gravitational constant of Mars, angular velocity of Mars, second zonal spherical harmonic of gravitational field expansion of Mars}, to compute a bi-axial reference ellipsoid of Somigliana-Pizzetti type as the hydrostatic approximate figure of Mars. The estimated values of semi-major and semi-minor axis of the computed reference ellipsoid of Mars are (3,395,428 ± 19) (m), and (3,377,678 ± 19) (m), respectively. Finally the computed Areoid is presented with respect to the computed reference ellipsoid.

Theoretical Analysis and Numerical Simulation of the Static and Dynamic Characteristics of Hydrostatic Guides Based on Progressive Mengen Flow Controller

Abstract: The oil film thickness of oil hydrostatic guide with constant pressure supply based on capillary restrictor is greatly affected by load,and this kind of hydrostatic guide is usually applied to the machine tools with moderate load.The static and dynamic characteristics of the guide have been studied by using some theoretical,numerical and experimental approaches,and some methods and measures have been proposed to improve its performances.The hydrostatic guide based on progressive mengen(PM) flow controller is especially suitable for the heavy numerical control(NC) machine tools.However,few literatures about the research on the static and dynamic characteristics of the hydrostatic guides based on PM flow controller are reported.In this paper,the formulae are derived for analyzing the static and dynamic characteristics of hydrostatic guides with rectangle pockets and PM flow controller according to the theory of hydrostatic bearing.On the basis of the analysis of hydrostatic bearing with circular pocket,some equations are derived for solving the static pressure,volume pressure and squeezing pressure which influence the dynamic characteristics of hydrostatic guides with rectangle pocket.The function and the influencing factors of three pressures are clarified.The formulae of amplitude-frequency characteristics and dynamic stiffness of the hydrostatic guide system are derived.With the help of software MATLAB,programs are coded with C++ language to simulate numerically the static and dynamic characteristics of the hydrostatic guide based on PM flow controller.The simulation results indicate that the sensitive oil volume between the outlet of the PM flow controller and the guide pocket has the greatest influence on the characteristics of the guide,and it should be reduced as small as possible when the field working condition is met.Choosing the oil with a greater viscosity is also helpful in improving the dynamic performance of hydrostatic guides.The research work has instructing significance for analyzing and designing the guide with PM flow controller.