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 article, a new model of Enceladus internal structure based on the shape model by Tajeddine et al. and the gravity model by Iess et.al. is presented.
58 citations
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TL;DR: In this article, the equation of state for condensed matter in a strong magnetic field is constructed. But the regime for which statistical models and spherical Wigner-Seitz lattice cells are valid approximations is treated.
Abstract: The equation of state for condensed matter in a strong magnetic field is constructed. The regime for which statistical models and spherical Wigner-Seitz lattice cells are valid approximations is treated. The equation of state for a free nonrelativistic homogeneous electron gas in a uniform magnetic field is examined as a function of temperature, after which this treatment is refined by incorporating Coulomb interactions in a magnetic Thomas-Fermi model which allows for finite temperature. Gradient corrections to the zero-temperature equation of state are then evaluated by constructing a magnetic Thomas-Fermi-Dirac-Weizsaecker model, these corrections having a considerable effect on the zero-pressure density for matter in strong magnetic fields. Finally, the hydrostatic equilibrium equation for the surface structure of a neutron star is integrated using the presently computed equations of state. 52 refs.
58 citations
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TL;DR: In this paper, an upper mass limit is found, analogous to Buchdahl's theorem in 3+1 dimensions, and the possibility of collapse is discussed. And the case of uniform matter density is solved exactly and a new interior solution is presented.
Abstract: The hydrostatic equilibrium of a (2+1)-dimensional perfect fluid star in asymptotically anti-de Sitter space is discussed. The interior geometry matches the exterior 2+1 black-hole solution. An upper mass limit is found, analogous to Buchdahl's theorem in 3+1 dimensions, and the possibility of collapse is discussed. The case of a uniform matter density is solved exactly and a new interior solution is presented.
58 citations
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TL;DR: In this paper, a simple saturation argument in combination with linear theory is used to obtain the relevant dynamical scales for the dynamical situation of a gravity wave (GW) near breaking level, and the resulting equation hierarchy is consistent with that obtained from the pseudo-incompressible equations, both for non-hydrostatic and hydrostatic GWs.
Abstract: Multiple-scale asymptotics is used to analyse the Euler equations for the dynamical situation of a gravity wave (GW) near breaking level. A simple saturation argument in combination with linear theory is used to obtain the relevant dynamical scales. As a small expansion parameter, the ratio of the inverse of the vertical wavenumber and potential temperature and pressure scale heights is used, which we allow to be of the same order of magnitude here. It is shown that the resulting equation hierarchy is consistent with that obtained from the pseudo-incompressible equations, both for non-hydrostatic and hydrostatic GWs, while this is not the case for the anelastic equations unless the additional assumption of sufficiently weak stratification is adopted. To describe vertical propagation of wavepackets over several atmospheric-scale heights, Wentzel–Kramers–Brillouin (WKB) theory is used to show that the pseudo-incompressible flow divergence generates the same amplitude equation that also obtains from the full Euler equations. This gives a mathematical justification for the use of the pseudo-incompressible equations in the study of GW breaking in the atmosphere for arbitrary background stratification. The WKB theory interestingly even holds at wave amplitudes close to static instability. In the mean-flow equations, we obtain in addition to the classic wave-induced momentum-flux divergences a wave-induced correction of hydrostatic balance in the vertical momentum equation, which cannot be obtained from Boussinesq or anelastic dynamics.
58 citations
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TL;DR: In this article, a unified, idealised baroclinic instability test case is proposed for both deep and shallow-atmosphere models, which is suitable for models employing a pressure- or height-based vertical coordinate.
Abstract: Idealised studies of key dynamical features of the atmosphere provide insight into the behaviour of atmospheric models. A very important, well understood, aspect of midlatitude dynamics is baroclinic instability. This can be idealised by perturbing a vertically sheared basic state in geostrophic and hydrostatic balance. An unstable wave mode then results with exponential growth (due to linear dynamics) in time until, eventually, nonlinear effects dominate and the wave breaks.
A new, unified, idealised baroclinic instability test case is proposed. This improves on previous ones in three ways. First, it is suitable for both deep- and shallow-atmosphere models. Second, the constant surface pressure and zero surface geopotential of the basic state makes it particularly well-suited for models employing a pressure- or height-based vertical coordinate. Third, the wave triggering mechanism selectively perturbs the rotational component of the flow; this, together with a vertical tapering, significantly improves dynamic balance.
57 citations