Showing papers on "Hydrostatic equilibrium published in 2012"
TL;DR: A new formulation of the boundary condition at static and moving solid walls in SPH simulations based on a local force balance between wall and fluid particles and applies a pressure boundary condition on the solid particles to prevent wall penetration.
539 citations
TL;DR: In this paper, the authors examined the effects of mergers on the hydrostatic mass estimate of galaxy clusters using high-resolution Eulerian cosmological simulations and found that during a merger, a shock propagates outward from the parent cluster, resulting in an overestimate in the hydrolastic mass bias.
Abstract: In this work, we examine the effects of mergers on the hydrostatic mass estimate of galaxy clusters using high-resolution Eulerian cosmological simulations. We utilize merger trees to isolate the last merger for each cluster in our sample and follow the time evolution of the hydrostatic mass bias as the systems relax. We find that during a merger, a shock propagates outward from the parent cluster, resulting in an overestimate in the hydrostatic mass bias. After the merger, as a cluster relaxes, the bias in hydrostatic mass estimate decreases but remains at a level of ?5%-10% with 15%-20% scatter within r 500. We also investigate the post-merger evolution of the pressure support from bulk motions, a dominant cause of this residual mass bias. At r 500, the contribution from random motions peaks at 30% of the total pressure during the merger and quickly decays to ~10%-15% as a cluster relaxes. Additionally, we use a measure of the random motion pressure to correct the hydrostatic mass estimate. We discover that 4?Gyr after mergers, the direct effects of the merger event on the hydrostatic mass bias have become negligible. Thereafter, the mass bias is primarily due to residual bulk motions in the gas which are not accounted for in the hydrostatic equilibrium equation. We present a hydrostatic mass bias correction method that can recover the unbiased cluster mass for relaxed clusters with 9% scatter at r 500 and 11% scatter in the outskirts, within r 200.
105 citations
TL;DR: In this article, the basic dynamics of Earth's core and their impact on various mechanisms of core-mantle coupling are surveyed. And the implications of the resulting "adiabatic torques" on topographic and gravitational coupling are considered.
Abstract: This article commences by surveying the basic dynamics of Earth's core and their impact on various mechanisms of core-mantle coupling. The physics governing core convection and magnetic field production in the Earth is briefly reviewed. Convection is taken to be a small perturbation from a hydrostatic, “adiabatic reference state” of uniform composition and specific entropy, in which thermodynamic variables depend only on the gravitational potential. The four principal processes coupling the rotation of the mantle to the rotations of the inner and outer cores are analyzed: viscosity, topography, gravity and magnetic field. The gravitational potential of density anomalies in the mantle and inner core creates density differences in the fluid core that greatly exceed those associated with convection. The implications of the resulting “adiabatic torques” on topographic and gravitational coupling are considered. A new approach to the gravitational interaction between the inner core and the mantle, and the assoc...
89 citations
TL;DR: In this paper, an analytic one-dimensional radiative-convective model of the thermal structure of planetary atmospheres is presented, which assumes that thermal radiative transfer is gray and can be represented by the twostream approximation.
Abstract: We present an analytic one-dimensional radiative‐convective model of the thermal structure of planetary atmospheres. Our model assumes that thermal radiative transfer is gray and can be represented by the twostream approximation. Model atmospheres are assumed to be in hydrostatic equilibrium, with a power-law scaling between the atmospheric pressure and the gray thermal optical depth. The convective portions of our models are taken to follow adiabats that account for condensation of volatiles through a scaling parameter to the dry adiabat. By combining these assumptions, we produce simple, analytic expressions that allow calculations of the atmosphericpressure‐temperature profile, as well as expressions for the profiles of thermal radiative flux and convective flux. We explore the general behaviors of our model. These investigations encompass (1) worlds where atmospheric attenuation of sunlight is weak, which we show tend to have relatively high radiative‐convective boundaries; (2) worlds with some attenuation of sunlight throughout the atmosphere, which we show can produce either shallow or deep radiative‐convective boundaries, depending on the strength of sunlight attenuation; and (3) strongly irradiated giant planets (including hot Jupiters), where we explore the conditions under which these worlds acquire detached convective regions in their mid-tropospheres. Finally, we validate our model and demonstrate its utility through comparisons to the average observed thermal structure of Venus, Jupiter, and Titan, and by comparing computed flux profiles to more complex models.
83 citations
TL;DR: In this article, the spectral energy distribution of the first hydrostatic core was derived from high-resolution radiation-magneto-hydrodynamic calculations using the RAMSES code.
Abstract: Context. The low-mass star formation evolutionary sequence is relatively well-defined both from observations and theoretical considerations. The first hydrostatic core is the first protostellar equilibrium object that is formed during the star formation process.Aims. Using state-of-the-art radiation-magneto-hydrodynamic 3D adaptive mesh refinement calculations, we aim to provide predictions for the dust continuum emission from first hydrostatic cores.Methods. We investigated the collapse and the fragmentation of magnetized 1 M ⊙ prestellar dense cores and the formation and evolution of first hydrostatic cores using the RAMSES code. We used three different magnetization levels for the initial conditions, which cover a wide variety of early evolutionary morphology, e.g., the formation of a disk or a pseudo-disk, outflow launching, and fragmentation. We post-processed the dynamical calculations using the 3D radiative transfer code RADMC-3D. We computed spectral energy distributions and usual evolutionary stage indicators such as bolometric luminosity and temperature.Results. We find that the first hydrostatic core lifetimes depend strongly on the initial magnetization level of the parent dense core. We derive, for the first time, spectral energy distribution evolutionary sequences from high-resolution radiation-magneto-hydrodynamic calculations. We show that under certain conditions, first hydrostatic cores can be identified from dust continuum emission at 24 μ m and 70 μ m. We also show that single spectral energy distributions cannot help in distinguishing between the formation scenarios of the first hydrostatic core, i.e., between the magnetized and non-magnetized models. Conclusions. Spectral energy distributions are a first useful and direct way to target first hydrostatic core candidates but high-resolution interferometry is definitively needed to determine the evolutionary stage of the observed sources.
70 citations
TL;DR: In this paper, the propagation of plane waves in fiber-reinforced, anisotropic thermoelastic half-space under hydrostatic initial stress is discussed and the problem has been solved numerically using a finite element method.
Abstract: The propagation of plane waves in fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord-Shulman under hydrostatic initial stress is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of pressure. It is found that the hydrostatic initial stress has a great effect on the distribution of field quantities.
66 citations
TL;DR: In this article, an analytic 1-D radiative-convective model of the thermal structure of planetary atmospheres is presented, which assumes that thermal radiative transfer is gray and can be represented by the two-stream approximation.
Abstract: We present an analytic 1-D radiative-convective model of the thermal structure of planetary atmospheres. Our model assumes that thermal radiative transfer is gray and can be represented by the two-stream approximation. Model atmospheres are assumed to be in hydrostatic equilibrium, with a power law scaling between the atmospheric pressure and the gray thermal optical depth. The convective portions of our models are taken to follow adiabats that account for condensation of volatiles through a scaling parameter to the dry adiabat. By combining these assumptions, we produce simple, analytic expressions that allow calculations of the atmospheric pressure-temperature profile, as well as expressions for the profiles of thermal radiative flux and convective flux. We explore the general behaviors of our model. These investigations encompass (1) worlds where atmospheric attenuation of sunlight is weak, which we show tend to have relatively high radiative-convective boundaries, (2) worlds with some attenuation of sunlight throughout the atmosphere, which we show can produce either shallow or deep radiative-convective boundaries, depending on the strength of sunlight attenuation, and (3) strongly irradiated giant planets (including Hot Jupiters), where we explore the conditions under which these worlds acquire detached convective regions in their mid-tropospheres. Finally, we validate our model and demonstrate its utility through comparisons to the average observed thermal structure of Venus, Jupiter, and Titan, and by comparing computed flux profiles to more complex models.
57 citations
TL;DR: In this article, Audusse et al. showed that this method exhibits an abnormal behavior for some combinations of slope, mesh size, and water height, and they proposed a well-balanced scheme for shallow water equations with a positive numerical flux.
56 citations
TL;DR: In this article, the authors investigated the transverse response of a magnetic field to the independent relaxation of its flux tubes of fluid seeking hydrostatic and energy balance, under the frozen-in condition and suppression of cross-field thermal conduction.
Abstract: This second paper of the series investigates the transverse response of a magnetic field to the independent relaxation of its flux tubes of fluid seeking hydrostatic and energy balance, under the frozen-in condition and suppression of cross-field thermal conduction. The temperature, density, and pressure naturally develop discontinuities across the magnetic flux surfaces separating the tubes, requiring the finite pressure jumps to be compensated by magnetic-pressure jumps in cross-field force balance. The tangentially discontinuous fields are due to discrete currents in these surfaces, δ-function singularities in the current density that are fully admissible under the rigorous frozen-in condition but must dissipate resistively if the electrical conductivity is high but finite. The magnetic field and fluid must thus endlessly evolve by this spontaneous formation and resistive dissipation of discrete currents taking place intermittently in spacetime, even in a low-β environment. This is a multi-dimensional effect in which the field plays a central role suppressed in the one-dimensional (1D) slab model of the first paper. The study begins with an order-of-magnitude demonstration that of the weak resistive and cross-field thermal diffusivities in the corona, the latter is significantly weaker for small β. This case for spontaneous discrete currents, as an important example of the general theory of Parker, is illustrated with an analysis of singularity formation in three families of two-dimensional generalizations of the 1D slab model. The physical picture emerging completes the hypothesis formulated in Paper I that this intermittent process is the origin of the dynamic interiors of a class of quiescent prominences revealed by recent Hinode/SOT and SDO/AIA high-resolution observations.
56 citations
Book•
16 Jan 2012Abstract: 1. The Earth-atmosphere system 2. Thermodynamics of gases 3. The second law and its implications 4. Heterogeneous systems 5. Transformations of moist air 6. Hydrostatic equilibrium 7. Static stability 8. Radiative transfer 9. Aerosol and cloud 10. Atmospheric motion 11. Atmospheric equations of motion 12. Large-scale motion 13. The planetary boundary layer 14. Atmospheric waves 15. The general circulation 16. Dynamic stability 17. Influence of the ocean 18. Interaction with the stratosphere.
51 citations
TL;DR: In this paper, three-dimensional finite element (FE) simulations of double SAW and hydrostatic test processes of spiral welded pipes are carried out in two simulation steps using the ANSYS commercial software.
TL;DR: In this article, the authors investigated the extent to which an exoplanet's interior can be constrained in terms of core mass and envelope metallicity by taking the tidal Love number k2 into account as an additional, possibly observable parameter.
Abstract: Context. Transit and radial velocity observations continuously discover an increasing number of exoplanets. However, when it comes to the composition of the observed planets the data are compatible with several interior structure models. Thus, a planetary parameter sensitive to the planet’s density distribution could help constrain this large number of possible models even further. Aims. We aim to investigate to what extent an exoplanet’s interior can be constrained in terms of core mass and envelope metallicity by taking the tidal Love number k2 into account as an additional, possibly observable parameter. Methods. Because it is the only planet with an observationally determined k2, we constructed interior models for the Hot Jupiter exoplanet HAT-P-13b by solving the equations of hydrostatic equilibrium and mass conservation for different boundary conditions. In particular, we varied the surface temperature and the outer temperature profile, as well as the envelope metallicity within the widest possible parameter range. We also considered atmospheric conditions that are consistent with nongray atmosphere models. For all these models we calculated the Love number k2 and compared it to the allowed range of k2 values that could be obtained from eccentricity measurements of HAT-P-13b. Results. We use the example of HAT-P-13b to show the general relationships between the quantities temperature, envelope metallicity, core mass, and Love number of a planet. For any given k2 value a maximum possible core mass can be determined. For HAT-P-13b we find Mcore < 27 M⊕, based on the latest eccentricity measurement. We favor models that are consistent with our model atmosphere, which gives us the temperature of the isothermal region as ∼2100 K. With this external boundary condition and our new k2-interval we are able to constrain both the envelope and bulk metallicity of HAT-P-13b to 1−11 times stellar metallicity and the extension of the isothermal layer in the planet’s atmosphere to 3−44 bar. Assuming equilibrium tidal theory, we find lower limits on the tidal Q consistent with 10 3 −10 5 . Conclusions. Our analysis shows that the tidal Love number k2 is a very useful parameter for studying the interior of exoplanets. It allows one to place limits on the core mass and estimate the metallicity of a planet’s envelope.
Patent•
11 Oct 2012TL;DR: In this paper, a hydrostatic actuator and an arrangement for attaching it to a receiving component are provided. But they do not specify an arrangement to attach the actuator to the receiving component.
Abstract: A hydrostatic actuator and an arrangement for attaching it to a receiving component are provided. The hydrostatic actuator has a master cylinder containing a housing and a piston movable axially within the housing which acts on a pressure chamber filled with a pressurizing agent. The piston is driven by a rotary-driven electric motor having a stator and a rotor, by a rolling planetary transmission that converts the rotary drive to an axial motion. In order to be able to produce such a hydrostatic actuator with little need for construction space, cost-effectively and with better quality, a supporting of the rolling planetary transmission is simplified, and the cooling and shielding of an electronic controller and the pressure behavior of the hydrostatic actuator is improved.
TL;DR: In this paper, it was shown that nonmonotone saturation profiles might occur even at zero flux, when both fluids are at rest, and that hysteresis suffices to explain the effect.
Abstract: Nonmonotonic saturation profiles (saturation overshoot) occur as travelling waves in gravity driven fingering. They seem important for preferential flow mechanisms and have found much attention recently. Here, we predict them even for hydrostatic equilibrium when all velocities vanish. We suggest that hysteresis suffices to explain the effect. Recently, the observation of nonmonotonicity of traveling wave solutions for saturation profiles during constant-flux infiltration experiments has highlighted the shortcomings of the traditional, seventy year old mathematical model for immiscible displacement in porous media. Several recent modifications have been proposed to explain these observations. The present paper suggests that nonmonotone saturation profiles might occur even at zero flux. Specifically, nonmonotonicity of saturation profiles is predicted for hydrostatic equilibrium, when both fluids are at rest. It is argued that in traditional theories with the widely used single-valued monotone constitutive functions, nonmonotone profiles should not exist in hydrostatic equilibrium. The same applies to some modifications of the traditional theory. Nonmonotone saturation profiles in hydrostatic equilibrium arise within a generalized theory that contains the traditional theory as a special case. The physical origin of the phenomenon is simultaneous occurrence of imbibition and drainage. It is argued that indications for nonmonotone saturation profiles in hydrostatic equilibrium might have been observed in past experiments and could become clearly observable in a closed column experiment.
TL;DR: In this article, the authors consider the case of a body floating freely on a liquid and show that under the influence of gravitational and capillary forces there exists an equilibrium solution with contact angle π/2, which is the minimizer of a variational problem with an obstacle condition.
Abstract: We consider the hydrostatic configuration of a body floating freely on a liquid. Under the influence of gravitational and capillary forces there exists an equilibrium solution with contact angle π/2. This solution is the minimizer of a variational problem with an obstacle condition; the corresponding free boundary consists of the curve where the capillary surface meets the floating body.
TL;DR: In this paper, the authors analyzed Robe's restricted three-body problem with an oblate spheroid and the shape of the second primary as a triaxial rigid body, and the full buoyancy force of the fluid was considered.
Abstract: This paper analyzes Robe’s circular restricted three-body problem when the hydrostatic equilibrium figure of the first primary is assumed to be an oblate spheroid, the shape of the second primary is considered as a triaxial rigid body, and the full buoyancy force of the fluid is taken into account. It is found that there is an equilibrium point near the center of the first primary, another equilibrium point exists on the line joining the centers of the primaries and there exist infinite number of equilibrium points on an ellipse in the orbital plane of the second primary. It is also observed that under certain conditions, all these equilibrium points can be stable. The most interesting and distinguishable results of this study are the existence of elliptical points and their stability.
TL;DR: In this article, the authors derived the exact solution of the problem using oblate spheroidal coordinates, allowing them to compute the value of its zonal gravity coefficients¯ J2n,n = 1,2,3,, without making any approximation when the deep zonal flow is sufficiently strong.
Abstract: Rapidly rotating giant planets are usually marked by the existence of strong zonal flows at the cloud level If the zonal flow is sufficiently deep and strong, it can produce hydrostatic-related gravitational anomalies through distortion of the planet’s shape This paper determines the zonal gravity coefficients, J2n ,n = 1,2,3 ,, via an analytical method taking into account rotation-induced shape changes by assuming that a planet has an effective uniform density and that the zonal flows arise from deep convection and extend along cylinders parallel to the rotation axis Two different but related hydrostatic models are considered When a giant planet is in rigid-body rotation, the exact solution of the problem using oblate spheroidal coordinates is derived, allowing us to compute the value of its zonal gravity coefficients ¯ J2n ,n = 1,2,3 , , without making any approximation When the deep zonal flow is sufficiently strong, we develop a general perturbation theory for estimating the variation of the zonal gravity coefficients, ΔJ2n = J2n − ¯ J2n ,n = 1,2,3 , , caused by the effect of the deep zonalflows for an arbitrarily rapidly rotating planet Applying the general theory to Jupiter, we find that the deep zonal flow could contribute up to 03% of the J2 coefficient and 07% of J4 It is also found that the shape-driven harmonics at the 10th zonal gravity coefficient become dominant, ie, ΔJ2n ¯ J2n for n5
TL;DR: In this article, the assumption of strict hydrostatic equilibrium in galaxy cluster MS2137 was tested using the latest CHANDRA X-ray observations and results from a combined strong and weak lensing analysis based on optical observations.
Abstract: We test the assumption of strict hydrostatic equilibrium in galaxy cluster MS2137.3-2353 (MS 2137) using the latest CHANDRA X-ray observations and results from a combined strong and weak lensing analysis based on optical observations. We deproject the two-dimensional X-ray surface brightness and mass surface density maps assuming spherical and spheroidal dark matter distributions. We find a significant, 40%-50%, contribution from non-thermal pressure in the core assuming a spherical model. This non-thermal pressure support is similar to what was found by Molnar et al. (2010) using a sample of massive relaxed clusters drawn from high resolution cosmological simulations. We have studied hydrostatic equilibrium in MS 2137 under the assumption of elliptical cluster geometry adopting prolate models for the dark matter density distribution with different axis ratios. Our results suggest that the main effect of ellipticity (compared to spherical models) is to decrease the non-thermal pressure support required for equilibrium at all radii without changing the distribution qualitatively. We find that a prolate model with an axis ratio of 1.25 (axis in the line of sight over perpendicular to it) provides a physically acceptable model implying that MS 2137 is close to hydrostatic equilibrium at about 0.04-0.15 Rvir and have an about 25% contribution from non-thermal pressure at the center. Our results provide further evidence that there is a significant contribution from non-thermal pressure in the core region of even relaxed clusters, i.e., the assumption of hydrostatic equilibrium is not valid in this region, independently of the assumed shape of the cluster.
TL;DR: In this paper, an analytic parametric model is presented to describe the baryonic and dark matter distributions in clusters of galaxies with spherical symmetry. But it is assumed that the dark matter density follows a Navarro-Frenk-White (NFW) profile and that the gas pressure is described by a generalized NFW profile.
Abstract: We present an analytic parametric model to describe the baryonic and dark matter distributions in clusters of galaxies with spherical symmetry. It is assumed that the dark matter density follows a Navarro–Frenk–White (NFW) profile and that the gas pressure is described by a generalized NFW profile. By further demanding hydrostatic equilibrium and that the local gas fraction is small throughout the cluster, one obtains unique functional forms, dependent on basic cluster parameters, for the radial profiles of all the properties of interest in the cluster. We show that these profiles are consistent with both numerical simulations and multiwavelength observations of clusters. We also use our model to analyse six simulated Sunyaev–Zel’dovich (SZ) clusters as well as A611 SZ data from the Arcminute Microkelvin Imager. In each case, we derive the radial profile of the enclosed total mass and the gas pressure and show that the results are in good agreement with our model prediction.
TL;DR: In this paper, the Schmidt-Kennicutt relation between surface densities of cold (neutral+molecular) gas and star formation rate of simulated galaxies is studied. But the authors only consider the case of isolated spiral galaxies in TreeSPH simulations run with the GADGET3 code and no chemical evolution is included in this version of the code.
Abstract: We study several versions of the Schmidt-Kennicutt (SK) relation obtained for isolated spiral galaxies in TreeSPH simulations run with the GADGET3 code including the novel MUlti-Phase Particle Integrator (MUPPI) algorithm for star formation and stellar feedback. This is based on a sub-resolution multi-phase treatment of gas particles, where star formation is explicitly related to molecular gas, and the fraction of gas in the molecular phase is computed from hydrodynamical pressure, following a phenomenological correlation. No chemical evolution is included in this version of the code. The standard SK relation between surface densities of cold (neutral+molecular) gas and star formation rate of simulated galaxies shows a steepening at low gas surface densities, starting from a knee whose position depends on disc gas fraction: for more gas-rich discs the steepening takes place at higher surface densities. Because gas fraction and metallicity are typically related, this environmental dependence mimics the predictions of models where the formation of H2 is modulated by metallicity. The cold gas surface density at which HI and molecular gas surface densities equate can range from 10 up to 34 M pc 2 . As expected, the SK relation obtained using molecular gas shows much smaller variations among simulations. We find that disc pressure is not well represented by the classical external pressure of a disc in vertical hydrostatic equilibrium. Instead is well fit by the expression Pt = cold cold= 6, where the three quantities on the right-hand side are cold gas surface density, vertical velocity dispersion and epicyclic frequency. When the “dynamical” SK relation, i.e. the relation that uses gas surface density divided by orbital time, is considered, we find that all of our simulations stay on the same relation. We interpret this as a manifestation of the equilibrium between energy injection and dissipation in stationary galaxy discs, when energetic feedback is effective and pressure is represented by the expression given above. These findings further support the idea that a realistic model of the structure of galaxy discs should take into account energy injection by SNe.
TL;DR: In this article, the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe's circular restricted three-body problem were investigated, and it was found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable.
Abstract: This paper investigates the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe’s circular restricted three-body problem, with assumptions that the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second primary is an oblate body as well. It is found that equilibrium point exists near the centre of the first primary. Further, there can be one more equilibrium point on the line joining the centers of both primaries. Points on the circle within the first primary are also equilibrium points under certain conditions and the existence of two out-of-plane points is also observed. The linear stability of this configuration is examined and it is found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable.
TL;DR: In this article, the authors investigated the GI of rotating, vertically stratified, pressure-confined, polytropic gas disks using a linear stability analysis as well as analytic approximations.
Abstract: We investigate the gravitational instability (GI) of rotating, vertically stratified, pressure-confined, polytropic gas disks using a linear stability analysis as well as analytic approximations. The disks are initially in vertical hydrostatic equilibrium and bounded by a constant external pressure. We find that the GI of a pressure-confined disk is in general a mixed mode of the conventional Jeans and distortional instabilities, and is thus an unstable version of acoustic-surface-gravity waves. The Jeans mode dominates in weakly confined disks or disks with rigid boundaries. On the other hand, when the disk has free boundaries and is strongly pressure confined, the mixed GI is dominated by the distortional mode that is surface-gravity waves driven unstable under their own gravity and thus incompressible. We demonstrate that the Jeans mode is gravity-modified acoustic waves rather than inertial waves and that inertial waves are almost unaffected by self-gravity. We derive an analytic expression for the effective sound speed c eff of acoustic-surface-gravity waves. We also find expressions for the gravity reduction factors relative to a razor-thin counterpart that are appropriate for the Jeans and distortional modes. The usual razor-thin dispersion relation, after correcting for c eff and the reduction factors, closely matches the numerical results obtained by solving a full set of linearized equations. The effective sound speed generalizes the Toomre stability parameter of the Jeans mode to allow for the mixed GI of vertically stratified, pressure-confined disks.
TL;DR: In this article, the authors investigate the force from finite-sized granular avalanches on a wall and find that the maximum force is equal to the kinetic force of the incoming flow at high slopes, whereas it scaled like hydrostatic force at lower slopes.
Abstract: Small-scale laboratory tests investigate the force from finite-sized granular avalanches on a wall. First, the reference flows, in absence of the wall, were analysed in a wide range of slopes from a minimum angle for which no flow is possible to a critical angle for which the flow becomes very dilute. The changes in thickness and velocity over time exhibit transitions at the minimum slope angle and at intermediate slopes. Then the normal force exerted on a wall spanning the flow was measured. It is notable that the transitions detected in reference flows had a direct effect on the force. The maximum force was equal to the kinetic force of the incoming flow at high slopes, whereas it scaled like hydrostatic force at lower slopes. This is the effect of the dense-to-dilute transition. Furthermore, the maximum force at low slopes was found to be several times greater than the hydrostatic force of the incoming flow. This finding is explained by the considerable contribution of the stagnant zone formed upstream of the wall. Furthermore, the jamming transition was highlighted at the avalanche standstill by the collapse of the residual force on the wall when approaching the minimum angle for which no flow is possible. These results are useful for the design of protection dams against rapid mass movements.
TL;DR: In this article, a linear analysis of the time-dependent energy equation together with the vertical hydrostatic equilibrium and the equation of state was proposed to study the fluctuations of thin accretion disks.
Abstract: We study the fluctuations of standard thin accretion disks by linear analysis of the time-dependent energy equation together with the vertical hydrostatic equilibrium and the equation of state. We show that some of the simulation results in Hirose et al., such as the time delay, the relationship of power spectra, and the correlation between magnetic energy and radiation energy, can be understood well by our analytic results.
TL;DR: In this article, the assumption of strict hydrostatic equilibrium in galaxy cluster MS2137 was tested using Chandra X-ray observations and results from a combined strong and weak lensing analysis based on optical observations.
Abstract: We test the assumption of strict hydrostatic equilibrium in galaxy cluster MS2137.3-2353 (MS 2137) using the latest Chandra X-ray observations and results from a combined strong and weak lensing analysis based on optical observations. We deproject the two-dimensional X-ray surface brightness and mass surface density maps assuming spherical and spheroidal dark matter distributions. We find a significant, 40%-50%, contribution from non-thermal pressure in the core assuming a spherical model. This non-thermal pressure support is similar to what was found by Molnar et?al. using a sample of massive relaxed clusters drawn from high-resolution cosmological simulations. We have studied hydrostatic equilibrium in MS?2137 under the assumption of elliptical cluster geometry adopting prolate models for the dark matter density distribution with different axis ratios. Our results suggest that the main effect of ellipticity (compared to spherical models) is to decrease the non-thermal pressure support required for equilibrium at all radii without changing the distribution qualitatively. We find that a prolate model with an axis ratio of 1.25 (axis in the line of sight over perpendicular to it) provides a physically acceptable model implying that MS?2137 is close to hydrostatic equilibrium at about 0.04-0.15 R vir and has an about 25% contribution from non-thermal pressure at the center. Our results provide further evidence that there is a significant contribution from non-thermal pressure in the core region of even relaxed clusters, i.e., the assumption of hydrostatic equilibrium is not valid in this region, independently of the assumed shape of the cluster.
TL;DR: In this paper, the influence of inaccuracies in density scaling on the structural evolution of physical analogue experiments of salt systems has been investigated considering a gravity spreading example, where a plane strain finite element numerical analysis was used to systematically evaluate the impact of changes in densities on buoyancy force, sediment strength, and pressure gradient.
Abstract: [1] The influence of inaccuracies in density scaling on the structural evolution of physical analogue experiments of salt systems has been debated, and is here investigated considering a gravity spreading example Plane strain finite element numerical analysis was used to systematically evaluate the impact of changes in density scaling on buoyancy force, sediment strength, and pressure gradient A range of densities typical of natural systems (including compacting sediment) and physical analogue experiments was included A fundamental shift in the structure of the salt-sediment system, from diapir-minibasin pairs to expulsion rollover, was observed when sediment and salt densities were altered from values typical of physical experiments (1600 and 990 kg/m3) to those most often found in nature (1900–2300 and 2150 kg/m3) Experiments equivalent to physical analogue models but with reduced sediment density showed diapir-minibasin pair geometry, persisting to sediment densities of ∼1300 kg/m3 Salt burial by pre-kinematic sediments was found to suppress diapir formation for thicknesses greater than ∼750 m (075 cm at the laboratory scale) The relative importance of disproportionately high buoyancy force, low sediment strength, and pressure gradient in physical experiments was investigated by isolating each of these scaling errors in turn Buoyancy was found to be most influential in the development of diapir-minibasin pairs versus expulsion rollover geometry Finally, we demonstrate that dry physical analogue experiments with sediment density reduced to ∼1140 kg/m3 (achievable through mixing with hollow glass beads) would provide a reasonable approximation of submarine salt systems in nature (including water load and hydrostatic pore fluid pressure)
TL;DR: In this article, it was shown that, for ideal magnetohydrodynamics, a magnetic field parallel to the flow direction can ensure well-posedness, and the only condition required is that the flow is subalfvenic.
Abstract: The well-posedness of the equations of fluid mechanics in the hydrostatic limit is well known to be a difficult problem. Partial results, both positive and negative, will be reviewed below. In this paper, it is shown that, for ideal magnetohydrodynamics, a magnetic field parallel to the flow direction can ensure well-posedness. The only condition required is that the flow is subalfvenic. The result has some relevance to viscoelastic flows of the upper convected Maxwell fluid, which, in the infinite Weissenberg number limit, is related to ideal MHD.
TL;DR: In this paper, a generalized Gibbs function is defined between the atmosphere and its equilibrium, which represents the maximum amount of total energy that can be converted into kinetic energy and hence the available energy of the atmosphere.
Abstract: The total potential energy of the atmosphere is the sum of its internal and gravitational energies. The portion of this total energy available to be converted into kinetic energy is determined relative to an isothermal, hydrostatic, equilibrium atmosphere that is convectively and dynamically “dead.” The temperature of this equilibrium state is determined by minimization of a generalized Gibbs function defined between the atmosphere and its equilibrium. Thus, this function represents the maximum amount of total energy that can be converted into kinetic energy and, hence, the available energy of the atmosphere. This general approach includes the effects of terrain, moisture, and hydrometeors. Applications are presented for both individual soundings and idealized baroclinic zones. An algorithm partitions the available energy into available baroclinic and available convective energies. Estimates of the available energetics of the general circulation suggest that atmospheric motions are primarily drive...
TL;DR: In this article, a gas thermal effect is modeled based on the energy equipartition principle and two independent state equations for an ideal gas are developed that provide a new way to analyze thermal effects in gas lubrication.
Abstract: In the present article, a gas thermal effect is modeled based on the energy equipartition principle. Two new independent state equations for an ideal gas are developed that provide a new way to analyze thermal effects in gas lubrication. Furthermore, the energy equation is derived for gas lubrication and the analysis of thermal effects is carried out on a gas spiral thrust bearing and a gas hydrostatic journal bearing. The results show that gas temperature increases significantly in the lubricated region at high speed for both the thrust and hydrostatic journal bearings, and the thermal effect positively influences the load capacity of the thrust bearing. The gas expansion effect makes the gas temperature decrease in the hydrostatic journal bearing, and the gas temperature decreases with an increase in the inlet pressure.
TL;DR: The uncertainty in the dynamical mass estimate caused by the substructure of the high velocity group is ∼14% as discussed by the authors, which can be partially explained by the ∼20% scatter in the 2D pressure map that can be propagated into the hydrostatic mass estimate.
Abstract: 500 = (1.18 ± 0.03) Mpc south-east of the cluster centroid, which is also indicated in the X-ray two-dimensional (2D) temperature, density, entropy, and pressure maps. The dynamical mass estimate is 80% of the hydrostatic mass estimate at r H.E. 500 . It can be partially explained by the ∼20% scatter in the 2D pressure map that can be propagated into the hydrostatic mass estimate. The uncertainty in the dynamical mass estimate caused by the substructure of the high velocity group is ∼14%. The dynamical mass estimate using blue members is 1.23 times that obtained using red members. The global properties of R1504 obey the observed scaling relations of nearby clusters, although its stellar-mass fraction is rather low.