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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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TL;DR: In this article, a particle-in-cell model was developed to simulate flow over large areas, under the assumption that the fluid medium is an assembly of many small independent fluid particles, the momentum equation for a particle is derived for shallow-flow conditions.
Abstract: On the basis of traditional particle-in-cell methods, a particle model has been developed to simulate flow over large areas. Under the assumption that the fluid medium is an assembly of many small, independent fluid particles, the momentum equation for a particle is derived for shallow-flow conditions. In the formulation used, only two forces are involved. One is the hydrostatic force arising from the accumulation of different numbers of particles at different locations. The other is a friction force that varies inversely with flow depth and quadratically with particle velocity and bed roughness. The velocity and spatial positions of all particles are averaged at fixed grid points to obtain the overall flow behavior. The particle model is demonstrated through an application to a documented 1954 flood in the Jingjiang River flood diversion area in Hubei, China. The flood lasted 300 hours, with the total discharge volume being 4 billion cu m. Good agreement between computed and observed water levels was obtained. Convergence of the method is demonstrated by repeatedly doubling the number of particles employed in the computation until little change was found between simulations.

8 citations

Journal ArticleDOI
TL;DR: In this paper, a new earth elasto-gravitational deformation model was developed to take into account the heterogeneous structure of the mantle, and the authors used this model to calculate the theoretical perturbation induced by three types of spherical heterogeneities in the mantle on M2 body tides response.
Abstract: SUMMARY The body tides response (deformation and gravity) of the Earth is generally computed assuming radial symmetry in stratified earth models, at the hydrostatic equilibrium. We present in this paper numerical experiments with the aim to evaluate the impact of very large mantle heterogeneities of density on body tides. In a companion paper, we have developed a new earth elasto-gravitational deformation model able to take into account the heterogeneous structure of the mantle. We use this model to calculate the theoretical perturbation induced by three types of spherical heterogeneities in the mantle on M2 body tides response. The heterogeneities are: (1) our limit case, a heterogeneity of 1000 km of radius in the lower mantle; (2) a heterogeneity of 500 km of radius at the bottom of the lower mantle and (3) a heterogeneity of 285 km of radius in the upper mantle. The density variation has been set to −50 kg m −3 .F or each experiment, we first calculate the equilibrium state of the Earth when it contains a heterogeneity, including non-hydrostatic prestresses, dynamical topography and lateral variation of density. Then we compute the M2 tidal perturbation. We find that the surface tidal displacement perturbation is smaller than 1 mm, and that the gravity perturbation has a maximum amplitude of 525 nanoGal (nGal). Regarding to the present precision in position measurement, the displacement is too small to be detected. The gravity perturbation should be measurable with superconducting gravimeters, which have a nGal instrumental precision. In experiment 2, the maximum gravity perturbation is about 120 nGal, and in experiment 3, the maximum perturbation is about 33 nGal. Finally, we investigate the maximum theoretical impact of the Pacific and the African superplumes on the M2 body tide. The superplumes have been modelled as two spherical heterogeneities with a radius of 1000 km in the lower mantle. We find that these superplumes induce a maximum perturbation in gravity of about 370 nGal with a large part corresponding to a mean variation of gravity. We conclude that we can expect to have a gravity perturbation of body tide with an order of magnitude of about hundred of nGal induced by the biggest mantle heterogeneities of density. This perturbation in gravity should be measurable with superconducting gravimeters if all other contributions in the signal could be extracted with a sufficient precision.

8 citations

Journal ArticleDOI
TL;DR: In this article, the effects of the lowest-order fluid viscoelasticity, Coriolis force, fluid turbulence and inter-layer frictional coupling dynamics are concurrently considered in spatially-flat geometry.
Abstract: We analyze the gravitational instability of complex rotating astrofluids in the presence of dynamic role of dark matter in a homogeneous hydrostatic equilibrium framework The effects of the lowest-order fluid viscoelasticity, Coriolis force, fluid turbulence and inter-layer frictional coupling dynamics are concurrently considered in spatially-flat geometry The Coriolis rotation is relative to the center of the entire fluid mass distribution, contributed by both the gyratory bright (visible) and dark (invisible) sectors, conjugated via the mutual gravitational interaction The turbulence effects are included via the modified Larson equation of state We use a regular Fourier-based linear perturbation analysis over the rotating fluid field equations to obtain a unique form of quartic dispersion relation with variable coefficients We numerically carry out the dispersion analysis in two extreme limits: hydrodynamic (low-frequency) and kinetic (high-frequency) regimes It is demonstrated that, in the former regime, the gas as well as dark matter rotations have stabilizing effects on the Jeans instability of the bi-fluidic admixture In contrast, in the latter, the rotations play destabilizing roles on the instability An interesting feature noted here is that the magnitude of the group velocity of the fluctuations throughout increases with both the gas and dark matter rotation frequencies, and vice-versa We, finally, hope that the obtained results could be helpful in understanding the top-down kinetic mechanisms of bounded structure formation via gravitational collapse dynamics

8 citations

Journal ArticleDOI
TL;DR: In this paper, a linear stability analysis of the inviscid stratified Boussinesq equations is presented given a steady zonal flow with constant vertical shear in a tilted f plane.
Abstract: A linear stability analysis of the inviscid stratified Boussinesq equations is presented given a steady zonal flow with constant vertical shear in a tilted f plane. Full nonhydrostatic terms are included: 1) acceleration of vertical velocity and 2) Coriolis force terms arising from the meridional component of earth’s rotation vector. Calculations of growth rates, critical wavenumbers, and dominance regimes for baroclinic and symmetric instabilities are compared with results from the traditional nonhydrostatic equations, which include a strictly vertical rotation vector, as well as results from the hydrostatic equations. The authors find that for positive zonal z shear, tilted rotation enhances the dominance regime of symmetric instabilities at the expense of baroclinic instabilities and maintains symmetric instabilities at larger scales than previously indicated. Furthermore, in contrast to former studies, it is determined that hydrostatic growth rates for both instabilities are not maximal. Rath...

8 citations

Journal ArticleDOI
TL;DR: In this paper, the stability and dynamics of an isolated cloud of gas which is contained by external pressure, and which has imposed one-dimensional symmetry, uniform density and polytropic equation of state are investigated.
Abstract: We investigate the stability and dynamics of an isolated cloud of gas which is contained by external pressure, and which has imposed one-dimensional symmetry, uniform density and polytropic equation of state. The energies of the cloud in its three internally conserved modes are summed to form a potential function controlling radial motions, and the associated Lagrangian is obtained. Families of stable equilibrium states are then derived – where they exist – along with conditions for marginal instability. We show that this simple global model mimics closely the behaviour of clouds in detailed hydrostatic balance (DHB); and we use the global model to discuss the onset of gravitational instability in real clouds, and in particular, to evaluate the role of non-quasistatic compression

8 citations


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