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Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.


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Journal ArticleDOI
TL;DR: In this article, the authors used the hydrostatic equations of a porous medium to solve for the ICM density for a given temperature as a function of the filling factor of dilute bubbles.
Abstract: The presence of dilute hot cavities in the intracluster medium (ICM) at the cores of clusters of galaxies changes the relation between gas temperature and its X-ray emission properties. Using the hydrostatic equations of a porous medium, we solve for the ICM density for a given temperature as a function of the filling factor of dilute bubbles. We find that at a given temperature, the core X-ray luminosity increases with the filling factor. If the frequency of active galactic nuclei (AGN) in clusters were higher in the past, then the filling factor could correspondingly be significant, with implications for the cluster scaling relations at high redshifts. This is especially important for the core properties, including the temperature-luminosity (Lx-T) relation and estimates of the core gas mass. The results imply an epoch-dependent sensitivity of the Lx-T relation in the core to the porosity of the ICM. Detection of such an effect would give new insights into AGN feedback.

2 citations

Book ChapterDOI
01 Jan 1975
TL;DR: The behavior of turbulence can be greatly affected by fluctuating body forces if the latter are correlated with the velocity fluctuations as discussed by the authors, and the most common example is the large effect of gravity on flows with density fluctuations.
Abstract: The behavior of turbulence can be greatly affected by fluctuating body forces if the latter are correlated with the velocity fluctuations. The most common example is the large effect of gravity on flows with density fluctuations. If the density fluctuations arise because there is a mean density gradient in the same direction as the mean velocity gradient (as in a boundary layer on a heated or cooled horizontal surface) or if the flow is actually driven by the mean density differences (as in buoyant plumes in still air) then the density and velocity fluctuations are highly correlated and buoyancy can have a large effect. If the density increases upward (heavy fluid on top of light fluid) the flow is “unstable” and the density-velocity correlation can convert potential energy into turbulent kinetic energy. Conversely if the density decreases upward at a faster rate than is expected for fluid in hydrostatic equilibrium, existing turbulent energy can be converted into potential energy (because turbulent mixing tends to reduce the density gradient and thus raise the center of gravity of the fluid). We shall see below that a convenient parameter for correlating the effects of a density difference difference Δϱ across a fluid layer of thickness h with a typical velocity U is $$ \frac{{\Delta \varrho gh}}{{\varrho {U^2}}} $$ which is the ratio of the hydrostatic pressure difference across the layer to (twice) a typical dynamic pressure.

2 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that low-frequency acoustic gravity waves propagating parallel to the earth's surface satisfy the Korteweg-De Vries equation or the Kadomtsev-Petviashvili equation and have a discrete spectrum of group velocities.
Abstract: It is shown that low-frequency acoustic gravity waves propagating parallel to the earth's surface satisfy the Korteweg-De Vries equation or the Kadomtsev-Petviashvili equation and have a discrete spectrum of group velocities. The atmosphere is considered to be incompressible, homogeneous in composition and isothermal and the gravitational acceleration depends upon the height. The hydrostatic approximation is used and adapted in such a way that dispersion is not neglected. The nonlinear wave equations are obtained using the reductive perturbation technique. Finally, changes for a compressible atmosphere are discussed.

2 citations

Book ChapterDOI
01 Jan 2011
TL;DR: In this article, the basics of hyperbolic systems are described as needed to solve the initial boundary value problem for hydrostatic atmospheric modeling, and the relevance of the open boundary problem for the numerical problem of static and adaptive mesh refinement is discussed.
Abstract: This lecture describes the basics of hyperbolic systems as needed to solve the initial boundary value problem for hydrostatic atmospheric modeling. We examine the nature of waves in the hydrostatic primitive equations and how the modal decomposition can be used to effect a complete solution in the interior of an open domain. The relevance of the open boundary problem for the numerical problem of static and adaptive mesh refinement is discussed.

2 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered a stratified laminar flow of several fluids in a channels with an arbitrarily shaped cross section and proved the property of reciprocity between the applied forces Fj and the flows of different components Qi.
Abstract: A stratified laminar flow of several fluids in a channels with an arbitrarily shaped cross section is considered It is assumed that the hydrostatic problem of finding free boundaries between different fluids is solved and domains of motion of individual fluids are known Under the assumption that the medium motion arises under the action of an applied pressure gradient and volume gravity forces (or forces of inertia), the property of reciprocity between the applied forces Fj and the flows of different components Qi, which is manifested as symmetry of the matrix of the flow rate coefficients Lij (Qi = LijFj), is proved in the general form General symmetric solutions of the problem for a plane channel and a circular tube are presented Formulas for the coefficient of increasing of the fluid flow rate owing to the presence of a near-wall layer of the gas are derived It is shown that the flow rate of water in a partly filled channel may exceed the flow rate in a completely filled channel by more than an order of magnitude

2 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023282
2022708
202167
202089
201998
201893