Showing papers on "Hydrostatic equilibrium published in 2011"

Hot jupiter magnetospheres

Abstract: The upper atmospheres of close-in gas giant exoplanets (hot Jupiters) are subjected to intense heating and tidal forces from their parent stars. The atomic (H) and ionized (H+) hydrogen layers are sufficiently rarefied that magnetic pressure may dominate gas pressure for expected planetary magnetic field strength. We examine the structure of the magnetosphere using a 3D isothermal magnetohydrodynamic model that includes a static dead zone near the magnetic equator containing gas confined by the magnetic field, a wind zone outside the magnetic equator in which thermal pressure gradients and the magneto-centrifugal-tidal effect give rise to a transonic outflow, and a region near the poles where sufficiently strong tidal forces may suppress transonic outflow. Using dipole field geometry, we estimate the size of the dead zone to be several to tens of planetary radii for a range of parameters. Tides decrease the size of the dead zone, while allowing the gas density to increase outward where the effective gravity is outward. In the wind zone, the rapid decrease of density beyond the sonic point leads to smaller densities relative to the neighboring dead zone, which is in hydrostatic equilibrium. To understand the appropriate base conditions for the 3D isothermal model, we compute a simple 1D thermal model in which photoelectric heating from the stellar Lyman continuum is balanced by collisionally excited Lyα cooling. This 1D model exhibits a H layer with temperature T 5000-10,000 K down to a pressure P ~ 10-100 nbar. Using the 3D isothermal model, we compute maps of the H column density as well as the Lyα transmission spectra for parameters appropriate for HD 209458b. Line-integrated transit depths 5%-10% can be achieved for the above base conditions, in agreement with the results of Koskinen et al. A deep, warm H layer results in a higher mass-loss rate relative to that for a more shallow layer, roughly in proportion to the base pressure. Strong magnetic fields have the effect of increasing the transit signal while decreasing the mass loss, due to higher covering fraction and density of the dead zone. Absorption due to bulk fluid velocity is negligible at linewidths 100 km s-1 from line center. In our model, most of the transit signal arises from magnetically confined gas, some of which may be outside the L1 equipotential. Hence, the presence of gas outside the L1 equipotential does not directly imply mass loss. We verify a posteriori that particle mean free paths and ion-neutral drift are small in the region of interest in the atmosphere, and that flux freezing is a good approximation. We suggest that resonant scattering of Lyα by the magnetosphere may be observable due to the Doppler shift from the planet's orbital motion, and may provide a complementary probe of the magnetosphere. Lastly, we discuss the domain of applicability for the magnetic wind model described in this paper as well as the Roche-lobe overflow model.

Heating and cooling protostellar disks

Abstract: We examine heating and cooling in protostellar disks using three-dimensional radiation-MHD calculations of a patch of the Solar nebula at 1 AU, employing the shearing-box and flux-limited radiation diffusion approximations. The disk atmosphere is ionized by stellar X-rays, well coupled to magnetic fields, and sustains a turbulent accretion flow driven by magnetorotational instability, while the interior is resistive and magnetically dead. The turbulent layers are heated by absorbing the light from the central star and by dissipating the magnetic fields. They are optically thin to their own radiation and cool inefficiently. The optically thick interior in contrast is heated only weakly, by re-emission from the atmosphere. The interior is colder than a classical viscous model and isothermal. The magnetic fields support an extended atmosphere that absorbs the starlight 1.5 times higher than the hydrostatic viscous model. The disk thickness thus measures not the internal temperature, but the magnetic field strength. Fluctuations in the fields move the starlight-absorbing surface up and down. The height ranges between 13% and 24% of the radius over timescales of several orbits, with implications for infrared variability. The fields are buoyant, so the accretion heating occurs higher in the atmosphere than the stresses. The heating is localized around current sheets, caused by magnetorotational instability at lower elevations and by Parker instability at higher elevations. Gas in the sheets is heated above the stellar irradiation temperature, even though accretion is much less than irradiation power when volume averaged. The hot optically thin current sheets might be detectable through their line emission.

Shapes of Gas, Gravitational Potential, and Dark Matter in ΛCDM 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 (r >= 0.1r(500)) is more spherical compared to non-radiative (NR) simulations, while in the core the gas in the CSF runs is moretriaxial 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 a 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 in the intracluster medium and the presence of random gas motions in cluster cores.

The Dawn Gravity Investigation at Vesta and Ceres

Abstract: The objective of the Dawn gravity investigation is to use high precision X-band Doppler tracking and landmark tracking from optical images to measure the gravity fields of Vesta and Ceres to a half-wavelength surface resolution better than 90-km and 300-km, respectively. Depending on the Doppler tracking assumptions, the gravity field will be determined to somewhere between harmonic degrees 15 and 25 for Vesta and about degree 10 for Ceres. The gravity fields together with shape models determined from Dawn’s framing camera constrain models of the interior from the core to the crust. The gravity field is determined jointly with the spin pole location. The second degree harmonics together with assumptions on obliquity or hydrostatic equilibrium may determine the moments of inertia.

Hot Jupiter Magnetospheres

Abstract: The upper atmospheres of close-in gas giant exoplanets (hot Jupiters) are subjected to intense heating and tidal forces from their parent stars. The atomic (H) and ionized (H+) hydrogen layers are sufficiently rarefied that magnetic pressure may dominate gas pressure for expected planetary magnetic field strength. We examine the structure of the magnetosphere using a 3D isothermal magnetohydrodynamic model that includes a static dead zone near the magnetic equator containing gas confined by the magnetic field, a wind zone outside the magnetic equator in which thermal pressure gradients and the magneto-centrifugal-tidal effect give rise to a transonic outflow, and a region near the poles where sufficiently strong tidal forces may suppress transonic outflow. Using dipole field geometry, we estimate the size of the dead zone to be several to tens of planetary radii for a range of parameters. Tides decrease the size of the dead zone, while allowing the gas density to increase outward where the effective gravity is outward. In the wind zone, the rapid decrease of density beyond the sonic point leads to smaller densities relative to the neighboring dead zone, which is in hydrostatic equilibrium. To understand the appropriate base conditions for the 3D isothermal model, we compute a simple 1D thermal model in which photoelectric heating from the stellar Lyman continuum is balanced by collisionally excited Lyα cooling. This 1D model exhibits a H layer with temperature T 5000-10,000 K down to a pressure P ~ 10-100 nbar. Using the 3D isothermal model, we compute maps of the H column density as well as the Lyα transmission spectra for parameters appropriate for HD 209458b. Line-integrated transit depths 5%-10% can be achieved for the above base conditions, in agreement with the results of Koskinen et al. A deep, warm H layer results in a higher mass-loss rate relative to that for a more shallow layer, roughly in proportion to the base pressure. Strong magnetic fields have the effect of increasing the transit signal while decreasing the mass loss, due to higher covering fraction and density of the dead zone. Absorption due to bulk fluid velocity is negligible at linewidths 100 km s-1 from line center. In our model, most of the transit signal arises from magnetically confined gas, some of which may be outside the L1 equipotential. Hence, the presence of gas outside the L1 equipotential does not directly imply mass loss. We verify a posteriori that particle mean free paths and ion-neutral drift are small in the region of interest in the atmosphere, and that flux freezing is a good approximation. We suggest that resonant scattering of Lyα by the magnetosphere may be observable due to the Doppler shift from the planet's orbital motion, and may provide a complementary probe of the magnetosphere. Lastly, we discuss the domain of applicability for the magnetic wind model described in this paper as well as the Roche-lobe overflow model.

Detection of a bipolar molecular outflow driven by a candidate first hydrostatic core

Abstract: We present new 230 GHz Submillimeter Array observations of the candidate first hydrostatic core Per-Bolo 58. We report the detection of a 1.3 mm continuum source and a bipolar molecular outflow, both centered on the position of the candidate first hydrostatic core. The continuum detection has a total flux density of 26.6 ± 4.0 mJy, from which we calculate a total (gas and dust) mass of 0.11 ± 0.05 Mand a mean number density of 2.0 ± 1.6 × 10 7 cm −3 . There is some evidence for the existence of an unresolved component in the continuum detection, but longer-baseline observations are required in order to confirm the presence of this component and determine whether its origin lies in a circumstellar disk or in the dense inner envelope. The bipolar molecular outflow is observed along a nearly due east-west axis. The outflow is slow (characteristic velocity of 2.9 km s −1 ), shows a jet-like morphology (opening semi-angles ∼8 ◦ for both lobes), and extends to the edges of the primary beam. We calculate the kinematic and dynamic properties of the outflow in the standard manner and compare them to several other protostars and candidate first hydrostatic cores with similarly low luminosities. We discuss the evidence both in support of and against the possibility that Per-Bolo 58 is a first hydrostatic core, and we outline future work needed to further evaluate the evolutionary status of this object.

Evolution of the Merger Induced Hydrostatic Mass Bias in Galaxy Clusters

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 r500. We also investigate the post-merger evolution of the pressure support from bulk motions, a dominant cause of this residual mass bias. At r500, the contribution from random motions peaks at 30% of the total pressure during the merger and quickly decays to \sim 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 r500 and 11% scatter in the outskirts, within r200.

Heating and Cooling Protostellar Disks

Abstract: We examine heating and cooling in protostellar disks using 3-D radiation-MHD calculations of a patch of the Solar nebula at 1 AU, employing the shearing-box and flux-limited radiation diffusion approximations. The disk atmosphere is ionized by stellar X-rays, well-coupled to magnetic fields, and sustains a turbulent accretion flow driven by magneto-rotational instability, while the interior is resistive and magnetically dead. The turbulent layers heat by absorbing the light from the central star and by dissipating the magnetic fields. They are optically-thin to their own radiation and cool inefficiently. The optically-thick interior in contrast is heated only weakly, by re-emission from the atmosphere. The interior is colder than a classical viscous model, and isothermal. The magnetic fields support an extended atmosphere that absorbs the starlight 1.5 times higher than the hydrostatic viscous model. The disk thickness thus measures not the internal temperature, but the magnetic field strength. Fluctuations in the fields move the starlight-absorbing surface up and down. The height ranges between 13% and 24% of the radius over timescales of several orbits, with implications for infrared variability. The fields are buoyant, so the accretion heating occurs higher in the atmosphere than the stresses. The heating is localized around current sheets, caused by magneto-rotational instability at lower elevations and by Parker instability at higher elevations. Gas in the sheets is heated above the stellar irradiation temperature, even though accretion is much less than irradiation power when volume-averaged. The hot optically-thin current sheets might be detectable through their line emission.

Gravity, the hydrostatic indifference concept and the cardiovascular system

Abstract: Gravity, like any acceleration, causes a hydrostatic pressure gradient in fluid-filled bodily compartments. At a force of 1G, this pressure gradient amounts to 10 kPa/m. Postural changes alter the distribution of hydrostatic pressure patterns according to the body’s alignment to the acceleration field. At a certain location—referred to as hydrostatically indifferent—within any given fluid compartment, pressure remains constant during a given change of position relative to the acceleration force acting upon the body. At this specific location, there is probably little change in vessel volume, wall tension, and the balance of Starling forces after a positional manoeuvre. In terms of cardiac function, this is important because arterial and venous hydrostatic indifference locations determine postural cardiac preload and afterload changes. Baroreceptors pick up pressure signals that depend on their respective distance to hydrostatic indifference locations with any change of body position. Vascular shape, filling volume, and compliance, as well as temperature, nervous and endocrine factors, drugs, and time all influence hydrostatic indifference locations. This paper reviews the physiology of pressure gradients in the cardiovascular system that are operational in a gravitational/acceleration field, offers a broadened hydrostatic indifference concept, and discusses implications that are relevant in physiological and clinical terms.

Radiation thermo-chemical models of protoplanetary discs – III. Impact of inner rims on spectral energy distributions

Abstract: We study the hydrostatic density structure of the inner disc rim around Herbig Ae stars using the thermo-chemical hydrostatic code prodimo. We compare the spectral energy distributions (SEDs) and images from our hydrostatic disc models to that from prescribed density structure discs. The 2D continuum radiative transfer in prodimo includes isotropic scattering. The dust temperature is set by the condition of radiative equilibrium. In the thermal-decoupled case, the gas temperature is governed by the balance between various heating and cooling processes. The gas and dust interact thermally via photoelectrons, radiatively, and via gas accommodation on grain surfaces. As a result, the gas is much hotter than in the thermo-coupled case, where the gas and dust temperatures are equal, reaching a few thousands K in the upper disc layers and making the inner rim higher. A physically motivated density drop at the inner radius ('soft-edge') results in rounded inner rims, which appear ring-like in near-infrared images. The combination of lower gravity pull and hot gas beyond similar to 1 au results in a disc atmosphere that reaches a height over radius ratio z/r of 0.2, while this ratio is 0.1 only in the thermo-coupled case. This puffed-up disc atmosphere intercepts larger amount of stellar radiation, which translates into enhanced continuum emission in the 3-30 mu m wavelength region from hotter grains at similar to 500 K. We also consider the effect of disc mass and grain size distribution on the SEDs self-consistently feeding those quantities back into the gas temperature, chemistry and hydrostatic equilibrium computation.

Nonhydrostatic Model for Surf Zone Simulation

Abstract: A previously developed model for nonhydrostatic free surface flow is adapted to simulate breaking waves in the surf zone. The model solves the Reynolds-averaged Navier-Stokes equations in a fraction step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver. This approach is particularly well suited for simulating discontinuous flow associated with breaking waves because the model prediction converges to the classical solution for a turbulent bore, which closely resembles breaking waves in the surf zone. The hydrostatic solution is then corrected by including the nonhydrostatic pressure. The model uses a sigma coordinate discretization in the vertical direction, which has been previously demonstrated to yield significant truncation errors with highly skewed grids over large bottom slopes. This potential problem is investigated in the context of highly skewed (but transient) grids that occur with steep br...

Dispersive and Nonhydrostatic Pressure Effects at the Front of Surge

Abstract: Undular bores and shocks generated by dam-break flows or tsunamis are examined considering nonhydrostatic pressure and dispersive effects in one- and two-horizontal-dimensional space. The fully nonlinear Boussinesq-type equations based on a weakly nonhydrostatic pressure assumption are chosen as the governing equations. The equation set is solved by a fourth-order accurate finite-volume method with an approximate Riemann solver. Several typical benchmark problems such as dam-break flows and tsunami wave fission are tested in one- and two-horizontal-dimensional space. The computed results by the Boussinesq-type model are at least as accurate as the results by the hydrostatic shallow water equations. This is particularly evident near the steep front of the wave, where frequency dispersion can play an important role. The magnitude of this nonhydrostatic pressure and dispersive effect near the front is quantified, and the engineering implications of neglecting these physics, as would be done through the use of a hydrostatic model, are discussed.

Triaxiality and non-thermal gas pressure in Abell 1689

Abstract: Clusters of galaxies are uniquely important cosmological probes of the evolution of the large-scale structure, whose diagnostic power depends quite significantly on the ability to reliably determine their masses. Clusters are typically modelled as spherical systems whose intracluster gas is in strict hydrostatic equilibrium (i.e. the equilibrium gas pressure is provided entirely by thermal pressure), with the gravitational field dominated by dark matter, assumptions that are only rough approximations. In fact, numerical simulations indicate that galaxy clusters are typically triaxial, rather than spherical, and that turbulent gas motions (induced during hierarchical merger events) provide an appreciable pressure component. Extending our previous work, we present results of a joint analysis of X-ray, weak-and strong-lensing measurements of Abell 1689. The quality of the data allows us to determine both the triaxial shape of the cluster and the level of non-thermal pressure that is required if the intracluster gas is in hydrostatic equilibrium. We find that the dark matter axial ratios are 1.24 +/- 0.13 and 2.02 +/- 0.01 on the plane of the sky and along the line of sight, respectively, and that about 20 per cent of the pressure is non-thermal. Our treatment demonstrates that the dynamical properties of clusters can be determined in a (mostly) bias-free way, enhancing the use of clusters as more precise cosmological probes.

The interstellar medium and star formation in edge-on galaxies. i. ngc 891

Abstract: We analyze images of BIMA (CO)-C-12 (J = 1 -> 0), Very Large Array H I, and Spitzer 3.6 and 24 mu m emission toward the edge-on galaxy NGC 891 and derive the radial and vertical distributions of gas and the radial distributions of stellar mass and recent star formation. We describe our method of deriving radial profiles for edge-on galaxies, assuming circular motion, and verify basic relationships between star formation rate (SFR) and gas and stellar content, and between the molecular-to-atomic ratio and hydrostatic midplane pressure that have been found in other galaxy samples. The Schmidt law index we find for the total gas (H-2 + H I) is 0.85 +/- 0.55, but the Schmidt law provides a poor description of the SFR in comparison to a model that includes the influence of the stellar disk. Using our measurements of the thickness of the gas disk and the assumption of hydrostatic equilibrium, we estimate volume densities and pressures as a function of radius and height in order to test the importance of pressure in controlling the rho H-2/rho H-I ratio. The gas pressure in two dimensions P(r, z) using constant velocity dispersion does not seem to correlate with the rho H-2/rho H-I ratio, but the pressure using varying velocity dispersion appears to correlate with the ratio. We test the importance of gravitational instability in determining the sites of massive star formation and find that the Q parameter using a radially varying gas velocity dispersion is consistent with self-regulation (Q similar to 1) over a large part of the disk.

The structure and evolution of quasi-stars

Abstract: The existence of bright quasars at high redshifts implies that supermassive black holes were able to form in the early Universe. Though a number of mechanisms to achieve this have been proposed, none yet stands out. A recent suggestion is the formation of quasi-stars, initially stellar-mass black holes accreting from hydrostatic giant-like envelopes of gas, formed from the monolithic collapse of pre-galactic gas clouds. In this work, we modify the Cambridge STARS stellar evolution package to construct detailed models of the evolution of these objects. We find that, in all of our models, the black hole inside the envelope is able to reach slightly more than one-tenth of the total mass of the system before hydrostatic equilibrium breaks down. This breakdown occurs after a few million years of evolution. We show that the mechanism which causes the hydrostatic evolution to end is present in polytropic models. We also show that the solutions are highly sensitive to the size of the inner boundary radius and that no physical solutions exist if the inner boundary is chosen to be less than about 0.3 of the Bondi radius.

Constructing and characterising solar structure models for computational helioseismology

Abstract: In local helioseismology, numerical simulations of wave propagation are useful to model the interaction of solar waves with perturbations to a background solar model. However, the solution to the linearised equations of motion include convective modes that can swamp the helioseismic waves that we are interested in. In this article, we construct background solar models that are stable against convection, by modifying the vertical pressure gradient of Model S (Christensen-Dalsgaard et al., 1996, Science272, 1286) relinquishing hydrostatic equilibrium. However, the stabilisation affects the eigenmodes that we wish to remain as close to Model S as possible. In a bid to recover the Model S eigenmodes, we choose to make additional corrections to the sound speed of Model S before stabilisation. No stabilised model can be perfectly solar-like, so we present three stabilised models with slightly different eigenmodes. The models are appropriate to study the f and p1 to p4 modes with spherical harmonic degrees in the range from 400 to 900. Background model CSM has a modified pressure gradient for stabilisation and has eigenfrequencies within 2% of Model S. Model CSM_A has an additional 10% increase in sound speed in the top 1 Mm resulting in eigenfrequencies within 2% of Model S and eigenfunctions that are, in comparison with CSM, closest to those of Model S. Model CSM_B has a 3% decrease in sound speed in the top 5 Mm resulting in eigenfrequencies within 1% of Model S and eigenfunctions that are only marginally adversely affected. These models are useful to study the interaction of solar waves with embedded three-dimensional heterogeneities, such as convective flows and model sunspots. We have also calculated the response of the stabilised models to excitation by random near-surface sources, using simulations of the propagation of linear waves. We find that the simulated power spectra of wave motion are in good agreement with an observed SOHO/MDI power spectrum. Overall, our convectively stabilised background models provide a good basis for quantitative numerical local helioseismology. The models are available for download from http://www.mps.mpg.de/projects/seismo/NA4/.

Numerical simulations of dense water cascading on a steep slope

Abstract: The sinking of dense shelf waters down the continental slope (or "cascading") contributes to oceanic water mass formation and carbon cycling. Cascading over steep bottom topography is studied here in numerical experiments using POLCOMS, a 3-D ocean circulation model using a terrain-following s-coordinate system. The model setup is based on a laboratory experiment of a continuous dense water flow from a central source on a conical slope in a rotating tank. The governing parameters of the experiments are the density difference between plume and ambient water, the flow rate, the speed of rotation and (in the model) diffusivity and viscosity. The descent of the dense flow as characterized by the length of the plume as a function of time is studied for a range of parameters. Very good agreement between the model and the laboratory results is shown in dimensional and nondimensional variables. It is confirmed that a hydrostatic model is capable of reproducing the essential physics of cascading on a very steep slope if the model correctly resolves velocity veering in the bottom boundary layer. Experiments changing the height of the bottom Ekman layer (by changing viscosity) and modifying the plume from a 2-layer system to a stratified regime (by enhancing diapycnal diffusion) confirm previous theories, demonstrate their limitations and offer new insights into the dynamics of cascading outside of the controlled laboratory conditions

Reflection of P and SV waves from a stress-free surface thermoelastic half-space under the influence of a magnetic field and hydrostatic initial stress without energy dissipation

Abstract: The influence of the magnetic field and thermal field on the reflection of P and SV waves under hydrostatic initial stress is investigated. The basic governing equations for isotropic and homogeneous thermoelastic half-space under hydrostatic initial stress and Maxwell's stress are formulated in the context of the Green and Naghdi theory of type III. The governing equations are solved analytically in a two-dimensional xz-plane and then the velocities of reflected waves are obtained. It is shown that there exist three plane waves; P, thermal and SV waves. In addition, the reflection coefficients from stress-free surface for the incidence of P and SV waves are obtained. Finally, the influence of magnetic field and hydrostatic initial stress on the results obtained are computed numerically and displayed graphically.

The Effect of Oil Cavity Depth on Temperature Field in Heavy Hydrostatic Thrust Bearing

Abstract: For a heavy hydrostatic bearing with a high linear velocity, the results of numerical calculations often differ from practical conditions if the viscosity is considered as constant. In this article, the influence of the oil cavity depth on the temperature field in the heavy hydrostatic bearing is discussed in the context of variable viscosity. The viscosity-temperature relations for the gap oil film are first established by fitting B-Spline curves, then, numerical calculations for the temperature field in the heavy hydrostatic bearing of different oil cavity depths are carried out based on Finite Volume Method (FVM) under the same rotating speed, and the influence of the oil cavity depth on the temperature distribution in the gap oil film of the hydrostatic bearing is discussed. The results of numerical calculations provide the temperature distribution state inside the hydrostatic bearing, which would help the selection and the design of hydrostatic bearings in engineering practice.

Momentum Balance of the Wind-Driven and Meridional Overturning Circulation

Abstract: When a force is applied to the ocean, fluid parcels are accelerated both locally, by the applied force, and nonlocally, by the pressure gradient forces established to maintain continuity and satisfy the kinematic boundary condition. The net acceleration can be represented through a “rotational force” in the rotational component of the momentum equation. This approach elucidates the correspondence between momentum and vorticity descriptions of the large-scale ocean circulation: if two terms balance pointwise in the rotational momentum equation, then the equivalent two terms balance pointwise in the vorticity equation. The utility of the approach is illustrated for three classical problems: barotropic Rossby waves, wind-driven circulation in a homogeneous basin, and the meridional overturning circulation in an interhemispheric basin. In the hydrostatic limit, it is shown that the rotational forces further decompose into depth-integrated forces that drive the wind-driven gyres and overturning forces ...

Determination of coronal temperatures from electron density profiles

Abstract: The most popular method for determining coronal temperatures is the scale-height-method (shm). It is based on electron density profiles inferred from White Light (WL) brightness measurements of the corona during solar eclipses. This method has been applied to several published coronal electron density models. The calculated temperature distributions reach a maximum at r > 1.3 RS, and therefore do not satisfy one of the conditions for applying the shm method. Another method is the hydrostatic equilibrium method (hst), which enables coronal temperature distributions to be determined, providing solutions to the hydrostatic equilibrium equation. The temperature maximas using the hst method are almost equal to those obtained using the shm method, but the temperature peak is always at significantly lower altitude when the hst-method is used than when the shm-method is used. A third and more recently developed method, dyn, can be used for the same published electron density profiles. The temperature distributions obtained using the dyn method are regular solutions of the hydrodynamic equations. They depend on the expansion velocity of the coronal plasma considered as a free input parameter in the calculations. At the base of the solar corona, where the coronal bulk velocity is small (subsonic), the dyn and hst methods give similar temperature values. Larger differences are found at higher altitudes where the expansion velocity approaches and exceeds the velocity of sound. This paper shows also the effects of the flow tube geometry and ion temperatures on the electron temperature distributions. The dyn method is a generalization of the hst method, where the electron temperature distribution tends to zero at infinite radial distances. It is a new diagnostic tool for determining from WL coronal observations the range of radial distances where the coronal heating rate is at its maximum.

Effect of hydrostatic initial stress and rotation in green-naghdi (type iii) thermoelastic half-space with two temperature

Abstract: Green and Naghdi theory of thermoelasticity is employed to study the deformation of thermoelastic solid half-space under hydrostatic initial stress and rotation with two temperature. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, temperature distribution and conductive temperature. The numerical results are given and presented graphically when mechanical force is applied. Some particular cases are also discussed in context of the problem. Comparisons are made in the presence and absence of hydrostatic initial stress and rotation.

Preliminary design of dynamic framework for global non-hydrostatic spectral model

Abstract: Based on the global hydrostatic spectral model for operational run,referring to the upgrade and design idea of ECMWF from hydrostatic spectral model to the non-hydrostatic one,a preliminary dry dynamic framework is designed for global non-hydrostatic spectral model,with the consideration of the selection of the model equations,the linearization of the model equations,spectral representation in horizontal,finite difference in vertical,the scheme of integral in time,and the solution of the derived Helmholtz systems.The framework is provided for atmosphere with shallow approximation,and the Euler convection is exploited.Further,for the solution of the Helmholtz equations,a new computational scheme is provided based on the convection to the linear equations of block tri-diagonal form.The new scheme is clearly superior to the current one used in ECMWF for efficiency.

2D Magnetohydrodynamics simulations of induced plasma dynamics in the near‐core region of a galaxy cluster

Abstract: The mechanisms that maintain thermal balance in the intracluster medium (ICM) and produce the observed spatial distribution of the plasma density and temperature in galaxy clusters remain a subject of debate. We present results from numerical simulations of the cooling-core cluster A2199 produced by the two-dimensional (2-D) resistive magnetohydrodynamics (MHD) code MACH2. In our simulations we explore the effect of anisotropic thermal conduction on the energy balance of the system. The results from idealized cases in 2-D axisymmetric geometry underscore the importance of the initial plasma density in ICM simulations, especially the near-core values since the radiation cooling rate is proportional to ne 2 . Heat conduction is found to be noneffective in preventing catastrophic cooling in this cluster. In addition we performed 2-D planar MHD simulations starting from initial conditions deliberately violating both thermal balance and hydrostatic equilibrium in the ICM, to assess contributions of the convective terms in the energy balance of the system against anisotropic thermal conduction. We find that in this case work done by the pressure on the plasma can dominate the early evolution of the internal energy over anisotropic thermal conduction in the presence of subsonic flows, thereby reducing the impact of the magnetic field. Deviations from hydrostatic equilibrium near the cluster core may be associated with transient activity of a central active galactic nucleus and/or remnant dynamical activity in the ICM and warrant further study in three dimensions.

Detection of a Bipolar Molecular Outflow Driven by a Candidate First Hydrostatic Core

Abstract: We present new 230 GHz Submillimeter Array observations of the candidate first hydrostatic core Per-Bolo 58. We report the detection of a 1.3 mm continuum source and a bipolar molecular outflow, both centered on the position of the candidate first hydrostatic core. The continuum detection has a total flux density of 26.6 +/- 4.0 mJy, from which we calculate a total (gas and dust) mass of 0.11 +/- 0.05 Msun and a mean number density of 2.0 +/- 1.6 X 10^7 cm-3. There is some evidence for the existence of an unresolved component in the continuum detection, but longer-baseline observations are required in order to confirm the presence of this component and determine whether its origin lies in a circumstellar disk or in the dense inner envelope. The bipolar molecular outflow is observed along a nearly due east-west axis. The outflow is slow (characteristic velocity of 2.9 km/s), shows a jet-like morphology (opening semi-angles ~8 degrees for both lobes), and extends to the edges of the primary beam. We calculate the kinematic and dynamic properties of the outflow in the standard manner and compare them to several other protostars and candidate first hydrostatic cores with similarly low luminosities. We discuss the evidence both in support of and against the possibility that Per-Bolo 58 is a first hydrostatic core, and we outline future work needed to further evaluate the evolutionary status of this object.