Showing papers on "Hydrostatic equilibrium published in 2001"

Modeling of Coronal EUV Loops Observed with TRACE. I. Hydrostatic Solutions with Nonuniform Heating

Abstract: Recent observations of coronal loops in EUV wavelengths with the Transition Region and Coronal Explorer (TRACE) and the Extreme-Ultraviolet Imaging Telescope (EIT) on the Solar and Heliospheric Observatory (SOHO) demonstrated three new results that cannot be explained by most of the existing loop models: (1) EUV loops are near-isothermal along their coronal segments, (2) they show an overpressure or overdensity compared with the requirements of steady state loops with uniform heating, and (3) the brightest EUV loops exhibit extended scale heights up to 4 times the hydrostatic scale height. These observations cannot be reconciled with the classical RTV (Rosner, Tucker, & Vaiana) model, they do not support models with uniform heating, and they even partially violate the requirements of hydrostatic equilibrium. In this study we are fitting for the first time steady state solutions of the hydrodynamic equations to observed intensity profiles, permitting a detailed consistency test of the observed temperature T(s) and density profiles ne(s) with steady state models, which was not possible in previous studies based on scaling laws. We calculate some 500 hydrostatic solutions, which cover a large parameter space of loop lengths (L ? 4-300 Mm), of nonuniform heating functions (with heating scale heights in the range of ?H ? 1-300 Mm), approaching also the limit of uniform heating (?H L). The parameter space can be subdivided into three regimes, which contain (1) solutions of stably stratified loops, (2) solutions of unstably stratified loops (in the case of short heating scale heights, ?H,Mm ? ), and (3) a regime in which we find no numerical solutions (when ?H,Mm ). Fitting the hydrostatic solutions to 41 EUV loops observed with TRACE (selected by the criterion of detectability over their entire length), we find that only 30% of the loops are consistent with hydrostatic steady state solutions. None of the observed EUV loops is consistent with a uniform heating function while in quasi-steady state. Those loops compatible with a steady state are found to be heated near the footpoints, with a heating scale height of ?H = 12 ? 5 Mm, covering a fraction ?H/L = 0.2 ? 0.1 of the loop length. These results support coronal heating mechanisms operating in or near the chromosphere and transition region.

Nonhydrostatic Gas in the Core of the Relaxed Galaxy Cluster A1795

Abstract: Chandra data on A1795 reveal a mild edge-shaped discontinuity in the gas density and temperature in the southern sector of the cluster at r = 60 h-1 kpc. The gas inside the edge is 1.3-1.5 times denser and cooler than outside, while the pressure is continuous, indicating that this is a "cold front," the surface of contact between two moving gases. The continuity of the pressure indicates that the current relative velocity of the gases is near zero, making the edge appear to be in hydrostatic equilibrium. However, a total mass profile, derived from the data in this sector under the equilibrium assumption, exhibits an unphysical jump by a factor of 2, with the mass inside the edge being lower. We propose that the cooler gas is "sloshing" in the cluster gravitational potential well and is now near the point of maximum displacement, where it has zero velocity but nonzero centripetal acceleration. The distribution of this nonhydrostatic gas should reflect the reduced gravity force in the accelerating reference frame, resulting in the apparent mass discontinuity. Assuming that the gas outside the edge is hydrostatic, the acceleration of the moving gas can be estimated from the mass jump, a ~ 800 h km s-1 (10 8 yr)-1. The gravitational potential energy of this gas that is available for dissipation is about half of its current thermal energy. The length of the cool filament extending from the cD galaxy (Fabian et al.) may give the amplitude of the gas sloshing, 30-40 h-1 kpc. Such gas bulk motion might be caused by a disturbance of the central gravitational potential by past subcluster infall.

Non-hydrostatic gas in the core of the relaxed galaxy cluster A1795

Abstract: Chandra data on A1795 reveal a mild edge-shaped discontinuity in the gas density and temperature in the southern sector of the cluster at r=60/h kpc. The gas inside the edge is 1.3-1.5 times denser and cooler than outside, while the pressure is continuous, indicating that this is a "cold front", the surface of contact between two moving gases. The continuity of the pressure indicates that the current relative velocity of the gases is near zero, making the edge appear to be in hydrostatic equilibrium. However, a total mass profile derived from the data in this sector under the equilibrium assumption, exhibits an unphysical jump by a factor of 2, with the mass inside the edge being lower. We propose that the cooler gas is "sloshing" in the cluster gravitational potential well and is now near the point of maximum displacement, where it has zero velocity but nonzero centripetal acceleration. The distribution of this non-hydrostatic gas should reflect the reduced gravity force in the accelerating reference frame, resulting in the apparent mass discontinuity. Assuming that the gas outside the edge is hydrostatic, the acceleration of the moving gas can be estimated from the mass jump, a ~ 800 h km/s/(10^8 yr). The gravitational potential energy of this gas that is available for dissipation is about half of its current thermal energy. The length of the cool filament extending from the cD galaxy (Fabian et al.) may give the amplitude of the gas sloshing, 30-40/h kpc. Such gas bulk motion might be caused by a disturbance of the central gravitational potential by past subcluster infall.

Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics

Abstract: Geophysical fluids all exhibit a common feature: their aspect ratio (depth to hori- zontal width) is very small. This leads to an asymptotic model widely used in meteorology, oceanog- raphy, and limnology, namely the hydrostatic approximation of the time-dependent incompressible Navier-Stokes equations. It relies on the hypothesis that pressure increases linearly in the vertical direction. In the following, we prove a convergence and existence theorem for this model by means of anisotropic estimates and a new time-compactness criterium.

Experimental analysis of compaction of concrete and mortar

Abstract: Compaction of concrete is physically a collapse of the material porous microstructure. It produces plastic strains in the material and, at the same time, an increase of its bulk modulus. This paper presents two experimental techniques aimed at obtaining the hydrostatic response of concrete and mortar. The first one is a uniaxial confined compression test which is quite simple to implement and allows to reach hydrostatic pressures of about 600 MPa. The specimen size is large enough so that concrete with aggregate sizes up to 16 nam can be tested. The second one is a true hydrostatic test performed on smaller (mortar) specimens. Test results show that the hydrostatic response of the material is elasto-plastic with a stiffening effect on both the tangent and unloading bulk moduli. The magnitude of the irreversible volumetric strains depends on the initial porosity of the material. This porosity can be related in a first approximation to the water/cement ratio. A comparison of the hydrostatic responses obtained from the two testing techniques on the same material show that the hydrostatic response of cementitious materials cannot be uncoupled from the deviatoric response, as opposed to the standard assumption in constitutive relations for metal alloys. This feature should be taken into account in the development of constitutive relations for concrete subjected to high confinement pressures which are needed in the modelling of impact problems.

Transport of Magnetic Fields in Convective, Accreting Supernova Cores

Abstract: We consider the amplification and transport of a magnetic field in the collapsed core of a massive star, including both the region between the neutrinosphere and the shock, and the central, opaque core. An analytical argument explains why rapid convective overturns persist within a newly formed neutron star for roughly 10 s (>103 overturns), consistent with recent numerical models. A dynamical balance between turbulent and magnetic stresses within this convective layer corresponds to flux densities in excess of 1015 G. Material accreting onto the core is heated by neutrinos and also becomes strongly convective. We compare the expected magnetic stresses in this convective "gain layer" with those deep inside the neutron core. Buoyant motions of magnetized fluid are greatly aided by the intense neutrino flux. We calculate the transport rate through a medium containing free neutrons, protons, and electrons, in the limiting cases of degenerate or nondegenerate nucleons. Fields stronger than ~1013 G are able to rise through the outer degenerate layers of the neutron core during the last stages of Kelvin-Helmholtz cooling (up to 10 s postcollapse), even though these layers have become stable to convection. We also find the equilibrium shape of a thin magnetic flux rope in the dense hydrostatic atmosphere of the neutron star, along with the critical separation of the footpoints above which the rope undergoes unlimited expansion against gravity. The implications of these results for pulsar magnetism are summarized, and applied to the case of late fallback over the first 103-104 s of the life of a neutron star.

Boyle's law and gravitational instability

Abstract: We have re-examined the classical problem of the macroscopic equation of state for a hydrostatic isothermal self-gravitating gas cloud bounded by an external medium at constant pressure. We have obtained analytical conditions for its equilibrium and stability without imposing any specific shape and symmetry to the cloud density distribution. The equilibrium condition can be stated in the form of an upper limit to the cloud mass; this is found to be inversely proportional to the power $3/2$ of a form factor μ characterizing the shape of the cloud. In this respect, the spherical solution, associated with the maximum value of the form factor, $\mu = 1$, turns out to correspond to the shape that is most difficult to realize. Surprisingly, the condition that defines the onset of the Bonnor instability (or gravothermal catastrophe) can be cast in the form of an upper limit to the density contrast within the cloud that is independent of the cloud shape. We have then carried out a similar analysis in the two-dimensional case of infinite cylinders, without assuming axisymmetry. The results obtained in this paper generalize well-known results available for spherical or axisymmetric cylindrical isothermal clouds that have had wide astrophysical applications, especially in the study of the interstellar medium.

Chemical abundances from inversions of stellar spectra: Analysis of solar-type stars with homogeneous and static model atmospheres

Abstract: Spectra of late-type stars are usually analyzed with static model atmospheres in local thermodynamic equilibrium (LTE) and a homogeneous plane-parallel or spherically symmetric geometry. The energy balance requires particular attention, as two elements that are particularly difficult to model play an important role: line blanketing and convection. Inversion techniques are able to bypass the difficulties of a detailed description of the energy balance. Assuming that the atmosphere is in hydrostatic equilibrium and LTE, it is possible to constrain its structure from spectroscopic observations. Among the most serious approximations still implicit in the method is a static and homogeneous geometry. In this paper, we take advantage of a realistic three-dimensional radiative hydrodynamical simulation of the solar surface to check the systematic errors incurred by an inversion assuming a plane-parallel horizontally-homogeneous atmosphere. The thermal structure recovered resembles the spatial and time average of the three-dimensional atmosphere. Furthermore, the abundances retrieved are typically within 10% (0.04 dex) of the abundances used to construct the simulation. The application to a fairly complete data set from the solar spectrum provides further confidence in previous analyses of the solar composition. There is only a narrow range of one-dimensional thermal structures able to fit the absorption lines in the spectrum of the Sun. With our carefully selected data set, random errors are about a factor of 2 smaller than systematic errors. A small number of strong metal lines can provide very reliable results. We foresee no major difficulties in applying the technique to other similar stars, and obtaining similar accuracies, using spectra with λ/δλ ~ 5 × 104 and a signal-to-noise ratio as low as 30.

A New Static Failure Criterion for Isotropic Polymers

Abstract: A new static failure criterion for isotropic polymers with different strengths in tension and compression based on exponential dependence between the mean stress and the von Mises equivalent stress is proposed. The two material parameters introduced can be determined by two simple tests - the uniaxial tension and compression. The locus of the criterion is nearly conical for low hydrostatic pressures and tends to a cylindrical form if an increased hydrostatic pressure is applied. The validity of the criterion is demonstrated by experimental strength data taken from the literature for several polymers in the case of superimposed hydrostatic pressure.

Radiation pressure acceleration by X-rays in active galactic nuclei

Abstract: We present calculations of the dynamics of highly ionized gas (HIG) clouds that are confined by external pressure, and are photoionized by AGN continuum. We focus on the gas that is seen, in absorption, in the X-ray spectrum of many AGN and show that such gas can reach hydrostatic equilibrium under various conditions. The principal conclusion is that the clouds can be accelerated to high velocities by the central X-ray source. The dynamical problem can be reduced to the calculation of a single parameter, the average force multiplier, 〈M〉. The typical value of 〈M〉 is ∼10 suggesting that radiation pressure acceleration by X-rays is efficient for L/LEdd≳0.1. The terminal velocity scales with the escape velocity at the base of the flow and can exceed it by a large factor. The typical velocity for a HIG flow that originates at R=1017 cm in a source with Lx=1044 erg s−1 is ∼1000 km s−1, i.e. similar to the velocities observed in several X-ray and UV absorption systems. Highly ionized AGN clouds are driven mainly by bound–free absorption, and bound–bound processes are less important unless the lines are significantly broadened or the column density is very small. Pressure laws that result in constant or outward decreasing ionization parameters are most effective in accelerating the flow.

Radiation Pressure Acceleration by X-rays in Active Galactic Nuclei

Abstract: We present calculations of the dynamics of highly ionized gas clouds that are confined by external pressure, and are ionized by AGN continuum. We focus on the gas that is seen in absorption in the X-ray spectrum of many AGN and show that such gas can reach hydrostatic equilibrium under various conditions. The principal conclusion is that the clouds can be accelerated to high velocities by the central X-ray source. The dynamical problem can be reduced to the calculation of a single parameter, the average force multiplier, . The typical value of is ~10 suggesting that radiation pressure acceleration by X-rays is efficient for L/L_Edd>0.1. The terminal velocity scales with the escape velocity at the base of the flow and can exceed it by a large factor. The typical velocity for a HIG flow that originates at R=1e17 cm in a source with L_x=1e44 erg/s is ~1000 km/s, i.e. similar to the velocities observed in several X-ray and UV absorption systems. Highly ionized AGN clouds are driven mainly by bound-free absorption and bound-bound processes are less important unless the lines are significantly broadened or the column density is very small. Pressure laws that result in constant or outward decreasing ionization parameters are most effective in accelerating the flow.

Hydrostatic Expansion and Spin Changes During Type I X-Ray Bursts

Abstract: We present calculations of the spin-down of a neutron star atmosphere due to hydrostatic expansion during a Type I X-ray burst. We show that (i) Cumming and Bildsten overestimated the spin-down of rigidly-rotating atmospheres by a factor of two, and (ii) general relativity has a small (5-10%) effect on the angular momentum conservation law. We rescale our results to different neutron star masses, rotation rates and equations of state, and present some detailed rotational profiles. Comparing with recent observations of large frequency shifts in MXB 1658-298 and 4U 1916-053, we find that the spin-down expected if the atmosphere rotates rigidly is a factor of two to three less than the observed values. If differential rotation is allowed to persist, we find that the upper layers of the atmosphere spin down by an amount comparable to the observed values; however, there is no compelling reason to expect the observed spin frequency to be that of only the outermost layers. We conclude that hydrostatic expansion and angular momentum conservation alone cannot account for the largest frequency shifts observed during Type I bursts.

Hydrostatic equilibrium in a magnetized, warped Galactic disc

Abstract: Hydrostatic equilibrium of the multiphase interstellar medium in the solar vicinity is reconsidered, with the regular and turbulent magnetic fields treated separately. The regular magnetic field strength required to support the gas is consistent with independent estimates provided energy equipartition is maintained between turbulence and random magnetic fields. Our results indicate that a midplane value of B0 = 4 � G for the regular magnetic field near the Sun leads to more attractive models than B0 = 2 � G. The vertical profiles of both the regular and random magnetic fields contain disc and halo components whose parameters we have determined. The layer at 1 < |z| < 4kpc can be overpressured and an outflow at a speed of about 50kms 1 may occur there, presumably associated with a Galactic fountain flow, if B0 ≃ 2 � G. We show that hydrostatic equilibrium in a warped disc must produce asymmetric density distributions in z, in rough agreement with H i observations in the outer Galaxy. This asymmetry may be a useful diagnostic of the details of the warping mechanism in the Milky Way and other galaxies. We find indications that gas and magnetic field pressures are different above and below the warped midplane in the outer Galaxy and quantify the difference in terms of turbulent velocity and/or magnetic field strength.

Atomistic simulations of the pressure-induced phase transitions in BaF2 crystals

Abstract: The pressure-induced sequence of phase transitions of the BaF2 fluorite was studied within the shell-model approach. This fluorite crystal presents two pressure-induced phase transitions at approximately 3 and 15 GPa. The interatomic potentials were calculated by using relevant physical properties measured at ambient conditions. These potentials were used to minimize the lattice enthalpy at high hydrostatic pressures. By comparing the enthalpies and lattice parameters of the three possible structures, it was possible to describe the complete phase transition sequence of the material. The model reliability is confirmed by a comparison with experimental results reported at ambient conditions, which are in good agreement with the model predictions.

Correcting Laboratory Retention Curves for Hydrostatic Fluid Distributions

Abstract: Many experimental methods for obtaining capillary pressure-volumetric fluid content relations in porous media are affected by the occurrence of hydrostatic pressures that create nonuniform fluid content distributions throughout the sample of interest. Such conditions exist, for example, in suction apparatuses and pressure cells, which are widely used in vadose zone hydrology, agronomy and environmental engineering, and for Hg intrusion porosimetry routinely applied in the petroleum industry. We show how to correct experimental data for nonuniform pressure and fluid content distributions, which leads to retention or pore-size distribution curves applicable to physical points. This is necessary to make the retention information consistent with the differential equations modeling fluid flow in porous media. The advantage of the proposed method is that it does not require an a priori assumption of any given model describing the retention relation. The proposed correction formula is validated both numerically and experimentally and is compared with an existing correction procedure. By deconvoluting retention relations from the averaging taking place in the sample, the correction method presented should enhance the description of porous media-immiscible fluids systems at low capillary pressure values.

From Stirring to Mixing of Momentum: Cascades from Balanced Flows to Dissipation in the Oceanic Interior

Abstract: : Under the influences of stable density stratification and Earth's rotation, large-scale flows in the ocean and atmosphere have a mainly balanced dynamic-sometimes called the slow manifold-in the sense that there are diagnostic hydrostatic and gradient-wind balances that constrain the fluid acceleration. The nonlinear balance equations are a successful approximate model for this regime, and we have identified mathematically explicit limits of their time integrability. We hypothesize that these limits are indicative, at least approximately, of the transition from the larger-scale regime of inverse energy cascades of anisotropic flows to the smaller-scale regimes of forward energy cascade to dissipation of more nearly isotropic flows and intermittently breaking inertia-gravity waves. In the oceans these regime transitions occur mostly in the scale range of 0.1-10 km-in between the mesoscale and fine-structure where Rossby (Ro), Froude (Fr), and Richardson (Ri) numbers are typically neither small nor large. In pursuit of testing this hypothesis we have revisited several classical problems, including gravitational, centrifugal/symmetric, elliptical, barotropic, and baroclinic instabilities. In all cases we find definite evidence, albeit still incompletely understood, of fluid-dynamical transitions in the neighborhood of loss of balanced integrability.

Numerical simulation of the vertical structure of discontinuous flows

Abstract: A numerical method to solve the Reynolds-averaged Navier–Stokes equations with the presence of discontinuities is outlined and discussed. The pressure is decomposed into the sum of a hydrostatic component and a hydrodynamic component. The numerical technique is based upon the classical staggered grids and semi-implicit finite difference methods applied for quasi- and non-hydrostatic flows. The advection terms in the momentum equations are approximated in order to conserve mass and momentum following the principles recently developed for the numerical simulation of shallow water flows with large gradients. Conservation of these properties is the most important aspect to represent near local discontinuities in the solution, following from sharp bottom gradients or hydraulic jumps. The model is applied to reproduce the flow over a step where a hydraulic jump forms downstream. The hydrostatic pressure assumption fails to represent this type of flow mainly because of the pressure deviation from the hydrostatic values downstream the step. Fairly accurate results are obtained from the numerical model compared with experimental data. Deviation from the data is found to be inherent to the standard k–e model implemented. Copyright © 2001 John Wiley & Sons, Ltd.

Reduction of Density and Pressure Gradient Errors in Ocean Simulations

Abstract: Existing ocean models often contain errors associated with the computation of the density and the associated pressure gradient. Boussinesq models approximate the pressure gradient force, ρ−1∇p, by ρ−10∇p, where ρ0 is a constant reference density. The error associated with this approximation can be as large as 5%. In addition, Cartesian and sigma-coordinate models usually compute density from an equation of state where its pressure dependence is replaced by a depth dependence through an approximate conversion of depth to pressure to avoid the solution of a nonlinear hydrostatic equation. The dynamic consequences of this approximation and the associated errors can be significant. Here it is shown that it is possible to derive an equivalent but “stiffer” equation of state by the use of modified density and pressure, ρ* and p*, obtained by eliminating the contribution of the pressure-dependent part of the adiabatic compressibility (about 90% of the total). By doing this, the errors associated with bo...

Density Fluctuations and the Structure of a Nonuniform Hard Sphere Fluid

Abstract: We derive an exact equation for density changes induced by a general external field that corrects the hydrostatic approximation where the local value of the field is adsorbed into a modified chemical potential. Using linear response theory to relate density changes self-consistently in different regions of space, we arrive at an integral equation for a hard sphere fluid that is exact in the limit of a slowly varying field or at low density and reduces to the accurate Percus-Yevick equation for a hard core field. This and related equations give accurate results for a wide variety of fields.

Electronic Structures of MgB2 under Uniaxial and Hydrostatic Compression

Abstract: Electronic and lattice properties of MgB 2 under uniaxial and hydrostatic compression are calculated. Lattice properties are optimized automatically by using the first-principles molecular dynamics...

Spherically symmetric model atmospheres using approximate lambda operators - IV. Computational details of the thermal balance method

Abstract: The condition of a thermal balance of electrons is used in a linearization method of calculation of spherically symmetric NLTE model atmospheres in hydrostatic and radiative equilibrium Computational details of the method are presented and discussed The method is shown to be robust and powerful It is superior to the commonly used method based on the condition of radiative equilibrium

Hydrostatic and Geostrophic Adjustment in a Compressible Atmosphere: Initial Response and Final Equilibrium to an Instantaneous Localized Heating

Abstract: The initial and steady-state response of a compressible atmosphere to an instantaneous, localized heat source is investigated analytically. Potential vorticity conservation removes geostrophic and hydrostatic degeneracy and provides a direct method for obtaining the steady-state solution. The heat source produces a vertical potential vorticity dipole that induces a hydrostatically and geostrophically balanced cyclone–anticyclone structure in the final state. For a typical deep mesoscale heating, the net displacements required for the adjustment to the final steady state include a small, O(100 m) ascent of the core of the heated air with weak far-field descent and a large, O(10 km) outward/inward lateral displacement at the top/base of the heating. The heating initially generates available elastic and potential energy. The energy is then exchanged between kinetic, elastic, potential, and acoustic and gravity wave energy. In the final state, after the acoustic and gravity wave energy has dispersed,...

Material versus local incompressibility and its influence onglacial‐isostatic adjustment

Abstract: SUMMARY We present an analytical form of the layer propagator matrix for the response of a locally incompressible, layered, linear-viscoelastic sphere to an external load assuming that the initial density stratification ϱ0(r) within each layer is parametrized by Darwin's law. From this, we show that the relaxation of a sphere consisting of locally incompressible layers is governed by a discrete set of viscous modes. The explicit dependence of the layer propagator matrix on the Laplace transform variable allows us to determine the amplitudes of the viscous modes analytically. Employing Darwin's parametrization, we construct three simplified earth models with different initial density gradients that are used to compare the effects of the local incompressibility constraint, div (ϱ0u)=0, and the material incompressibility constraint, div u=0, on viscoelastic relaxation. We show that a locally incompressible earth model relaxes faster than a materially incompressible model. This is a consequence of the fact that the perturbations of the initial density are zero during viscoelastic relaxation of a locally incompressible medium, so that there are no internal buoyancy forces associated with the continuous radial density gradients, only the buoyancy forces generated by internal density discontinuities. On the other hand, slowly decaying internal buoyancy forces in a materially incompressible earth model cause it to reach the hydrostatic equilibrium after a considerably longer time than a locally incompressible model. It is important to note that the approximation of local incompressibility provides a solution for a compressible earth model that is superior to the conventional solutions for a compressible earth with homogeneous layers because it is based on an initial state that is consistent with the assumption of compressibility.

The cluster of galaxies Abell 970

Abstract: We present a dynamical analysis of the galaxy cluster Abell 970 based on a new set of radial velocities measured at ESO, Pic du Midi and Haute-Provence observatories. Our analysis indicates that this cluster has a substructure and is out of dynamical equilibrium. This conclusion is also supported by differences in the positions of the peaks of the surface density distribution and X-ray emission, as well as by the evidence of a large-scale velocity gradient in the cluster. We also found a discrepancy between the masses inferred with the virial theorem and those inferred with the X-ray emission, which is expected if the galaxies and the gas inside the cluster are not in hydrostatic equilibrium. Abell 970 has a modest cooling flow, as is expected if it is out of equilibrium. We propose that cooling flows may have an intermittent behaviour, with phases of massive cooling flows being followed by phases without significant cooling flows after the accretion of a galaxy group massive enough to disrupt the dynamical equilibrium in the centre of the clusters. A massive cooling flow will be established again, after a new equilibrium is achieved.

Salmon's Hamiltonian approach to balanced flow applied to a one‐layer isentropic model of the atmosphere

Abstract: Salmon's Hamiltonian approach is applied to formulate a balanced approximation to a hydrostatic one-layer isentropic model of the atmosphere. The model, referred to as the parent model, describes an idealized atmosphere of which the dynamics is closely analogous to a one-layer shallow-water model on the sphere. The balance used as input in Salmon's approach is a simplified form of linear balance, in which the balanced velocity vb is given by vb = k×δf−1(M–M). Here k is a vertical unit vector, f is the Coriolis parameter, M is the Montgomery potential and M is the value of the Montgomery potential at the state of rest. This form of balance is used in preference to standard geostrophic balance, vb = k × f−1δM, which forces the meridional wind velocity to be zero at the equator. Salmon's Hamiltonian technique is applied to obtain an equation for the time rate of change of the balanced velocity that guarantees both the material conservation of potential vorticity as well as conservation of energy. New in this application of Salmon's approach is a nonlinear relation between Montgomery potential and surface pressure (characteristic for an isentropic ideal gas in hydrostatic equilibrium) in combination with spherical geometry and a variable Coriolis parameter. We discuss how the unbalanced velocity va can be calculated in a practical way and how the model can be stepped forward in time by advecting the balanced potential vorticity with the total velocity v = vb + va. The balanced model is tested against a ten-day integration of the parent model.

Three-dimensional aspects of nonlinear stratified flow over topography near the hydrostatic limit

Abstract: Steady, finite-amplitude internal-wave disturbances, induced by nearly hydrostatic stratified flow over locally confined topography that is more elongated in the spanwise than the streamwise direction, are discussed. The nonlinear three-dimensional equations of motion are handled via a matched-asymptotics procedure: in an inner' region close to the topography, the flow is nonlinear but weakly three-dimensional, while far upstream and downstream the outer' flow is governed, to leading order, by the fully three-dimensional linear hydrostatic equations, subject to matching conditions from the inner flow. Based on this approach, non-resonant flow of general (stable) stratification over finite-amplitude topography in a channel of finite depth is analysed first. Three-dimensional effects are found to inhibit wave breaking in the nonlinear flow over the topography, and the downstream disturbance comprises multiple small-amplitude oblique wavetrains, forming supercritical wakes, akin to the supercritical free-surface wake induced by linear hydrostatic flow of a homogeneous fluid. Downstream wakes of a similar nature are also present when the flow is uniformly stratified and resonant (i.e. the flow speed is close to the long-wave speed of one of the modes in the channel), but, in this instance, they are induced by nonlinear interactions precipitated by three-dimensional effects in the inner flow and are significantly stronger than their linear counterparts. Finally, owing to this nonlinear-interaction mechanism, vertically unbounded uniformly stratified hydrostatic flow over finite-amplitude topography also features downstream wakes, in contrast to the corresponding linear disturbance that is entirely locally confined.

Double mechanical effects of flow through fracture network in rock mass on fracture walls

Abstract: Flow through fissures in rock mass applies simultaneously the normal hydrostatic seepage pressure and the tangent hauling pressure (the dynamic seepage pressure) on fissure walls. The cubic law of single fissure flow, the seepage theory and the basic equation of fluid mechanics are utilized to deduce the equations for the hydrostatic seepage pressure and the hauling pressure under three cases of single fissure without fillings, single fissure with fillings and water-filling flow. A computation example is also given to analyze quantitatively the double mechanical effects of flow through fracture network in rock mass. It can be shown that both the hydrostatic seepage pressure and the hauling pressure make the stress components in rock mass bigger, and especially the hauling pressure makes the shear stress component obviously much bigger.

Off-Axis Cluster Mergers: Effects of a Strongly Peaked Dark Matter Profile

Abstract: (Abridged) We present a parameter study of offset mergers between clusters of galaxies. Using the Eulerian hydrodynamics/N-body code COSMOS, we simulate mergers between nonisothermal, hydrostatic clusters with a steep central dark matter density profile and a beta-model gas profile. We constrain global properties of the model clusters using observed cluster statistical relationships. We consider impact parameters between zero and five times the scale radius and mass ratios of 1:1 and 1:3. The morphological changes, relative velocities, and temperature jumps we observe agree with previous studies using the King profile for the dark matter. We observe a larger jump in X-ray luminosity (~4-10x) than in previous work, and we argue that this increase is most likely a lower limit due to our spatial resolution. We emphasize that luminosity and temperature jumps due to mergers may have an important bearing on constraints on Omega derived from the observation of hot clusters at high redshift. Shocks are relatively weak in the cluster cores; hence they do not significantly increase the entropy there. Instead, shocks create entropy in the outer regions, and this high-entropy gas is mixed with the core gas during later stages of the merger. Ram pressure initiates mixing by displacing the core gas from its potential center, causing it to become convectively unstable. The resulting convective plumes produce large-scale turbulent motions with eddy sizes up to several 100 kpc. This turbulence is pumped by dark matter-driven oscillations in the gravitational potential. Even after nearly a Hubble time these motions persist as subsonic turbulence in the cluster cores, providing 5-10% of the support against gravity.