Topic
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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TL;DR: In this paper, a spherically symmetric, steady state model of galaxy clusters is presented, in which radiative cooling from the hot gas is balanced by heat transport through turbulent mixing.
Abstract: We present a spherically symmetric, steady state model of galaxy clusters in which radiative cooling from the hot gas is balanced by heat transport through turbulent mixing. We assume that the gas is in hydrostatic equilibrium and describe the turbulent heat diffusion by means of a mixing length prescription with a dimensionless parameter αmix. Models with αmix ~ 0.01-0.03 yield reasonably good fits to the observed density and temperature profiles of cooling core clusters. Making the strong simplification that αmix is time independent and that it is roughly the same in all clusters, the model reproduces remarkably well the observed scalings of X-ray luminosity, gas mass fraction, and entropy with temperature. The break in the scaling relations at kT ~ 1-2 keV is explained by the break in the cooling function at around this temperature, and the entropy floor observed in galaxy groups is reproduced naturally.
68 citations
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TL;DR: In this article, a three-dimensional, hydrodynamic model for free-surface flows without using the hydrostatic pressure assumption is presented, which includes two predictor-corrector steps.
Abstract: The hydrostatic pressure assumption has been widely used in studying water movements in rivers, lakes, estuaries, and oceans. While this assumption is valid in many cases and has been successfully used in numerous studies, there are many cases where this assumption is questionable. This paper presents a three-dimensional, hydrodynamic model for free-surface flows without using the hydrostatic pressure assumption. The model includes two predictor-corrector steps. In the first predictor-corrector step, the model uses hydrostatic pressure at the previous time step as an initial estimate of the total pressure field at the new time step. Based on the estimated pressure field, an intermediate velocity field is calculated, which is then corrected by adding the non-hydrostatic component of the pressure to the estimated pressure field. A Poisson equation for non-hydrostatic pressure is solved before the second intermediate velocity field is calculated. The final velocity field is found after the free surface at the new time step is computed by solving a free-surface correction equation
67 citations
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TL;DR: In this paper, a non-hydrostatic extension of free-surface primitive equation model with a general vertical coordinate and horizontal orthogonal curvilinear coordinates is presented for simulation of the free surface stratified flows.
Abstract: A three-dimensional non-hydrostatic numerical model for simulation of the free-surface stratified flows is presented. The model is a non-hydrostatic extension of free-surface primitive equation model with a general vertical coordinate and horizontal orthogonal curvilinear coordinates. The model equations are integrated with mode-splitting technique and decomposition of pressure and velocity fields on hydrostatic and non-hydrostatic components. The model was tested against laboratory experiments on the steep wave transformation over the longshore bar, solitary wave impact on the vertical wall, the collapse of the mixed region in the thin pycnocline, mixing in the lock-exchange flows and water exchange through the sea strait. The agreement is generally fair.
67 citations
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TL;DR: In this article, a system of equations is presented that unifies the nonhydrostatic anelastic system and the quasi-hydrogen compressible system for use in global cloud-resolving models.
Abstract: A system of equations is presented that unifies the nonhydrostatic anelastic system and the quasi-hydrostatic compressible system for use in global cloud-resolving models. By using a properly defined quasi-hydrostatic density in the continuity equation, the system is fully compressible for quasi-hydrostatic motion and anelastic for purely nonhydrostatic motion. In this way, the system can cover a wide range of horizontal scales from turbulence to planetary waves while filtering vertically propagating sound waves of all scales. The continuity equation is primarily diagnostic because the time derivative of density is calculated from the thermodynamic (and surface pressure tendency) equations as a correction to the anelastic continuity equation. No reference state is used and no approximations are made in the momentum and thermodynamic equations. An equation that governs the time change of total energy is also derived. Normal-mode analysis on an f plane without the quasigeostrophic approximation and...
66 citations
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TL;DR: In this paper, the authors used the shape and gravity field of Vesta determined from observations of the Dawn spacecraft to place constraints on the asteroid's interior structure by minimizing the power of the residual gravity anomaly.
66 citations