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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 paper, a theory of the coastal Kelvin wave is presented in which the pressure is assumed not to be hydrostatic, and it is shown that the non-hydrostatic Kelvin wave can be dispersive and that the e−1 decay distance from the coast decreases as the wave length becomes shorter.
Abstract: A theory of the coastal Kelvin wave is presented in which the pressure is assumed not to be hydrostatic. The results show that the non-hydrostatic Kelvin wave is dispersive and that the e−1 decay distance of the wave amplitude from the coast decreases as the wave length becomes shorter. Similar conclusions can be drawn on the equatorial Kelvin wave.
2 citations
TL;DR: In this paper, the shape and internal structure of the gas giant planet beta Pictoris b were derived by a hybrid inverse method, where the shape of the planet was described by an oblate spheroid whose eccentricity at the one-bar surface is 0.369 ± 0.28$ with the gravitational coefficient (J(2))(beta) = +15 375.972 x 10−6.
Abstract: A young extrasolar gas giant planet, beta Pictoris b, recently discovered in the beta Pictoris system, spins substantially faster than the giant gas planets Jupiter and Saturn. Based on the newly measured parameters - the rotation period of the planet, its mass and radius - together with an assumption that the gas planet beta Pictoris b is in hydrostatic equilibrium and made of a fully compressible barotropic gas with a polytropic index of unity, we are able to compute, via a hybrid inverse method, its non-spherical shape, internal density/pressure distribution and gravitational zonal coefficients up to degree 8. Since the mass M-beta for the planet beta Pictoris b is highly uncertain, various models with different values of M-beta are studied in this Letter, providing the upper and lower bounds for its shape parameter as well as its gravitational zonal coefficients. If M-beta is assumed to be 6M(J) with M-J being Jupiter's mass, we show that the shape of the planet beta Pictoris b is approximately described by an oblate spheroid whose eccentricity at the one-bar surface is $\mathcal {E}_{\beta }=0.369\,28$ with the gravitational coefficient (J(2))(beta) = +15 375.972 x 10(-6). It follows that our results open the possibility of constraining or inferring the mass M-beta of the planet beta Pictoris b if its shape can be measured or constrained. By assuming that the planet beta Pictoris b will shrink to the size of Jupiter in the process of cooling down and, hence, rotate much faster, we also calculate the future shape and internal structure of the planet beta Pictoris b.
2 citations
TL;DR: In this paper, the stability of the zonal axisymmetric quasi-geostrophic hydrostatic solution to the equations of atmospheric dynamics that is determined by the horizontal temperature gradient is studied.
Abstract: The stability of the zonal axisymmetric quasi-geostrophic hydrostatic solution to the equations of atmospheric dynamics that is determined by the horizontal temperature gradient is studied. Time-dependent regions of unstable solutions specified by the Rayleigh number describe ordinary convective (baroclinic) processes and the long-term weak growth of disturbances under the action of the centrifugal forces arising from the Earth’s rotation. Comparison with a centrifugal hydrodynamic instability is made. The spatiotemporal structure of the corresponding geophysical fields is described.
2 citations
TL;DR: In this article, it was shown that the primitive hydrostatic equations commonly used are not hyperbolic and no local boundary conditions can be chosen, but not all the characteristics involve the time variable.
Abstract: Discussion of the proper boundary conditions to use in limited area forecasting models requires knowledge of the properties of the governing equations. the theory of Oliger and Sundstrom states that the primitive hydrostatic equations commonly used are not hyperbolic and no local boundary conditions can be chosen. This paper shows their result to be incorrect, the equations are hyperbolic but not all the characteristics involve the time variable. Implications for the boundary conditions are discussed.
2 citations
TL;DR: In this article, the equations of gas dynamics are solved quasi-analytically by applying McVittie's method for spherical, cylindrical and plane configurations, and the hypothesis of linear wave flow is applied and it is assumed that the final state of collapsing clouds is a hydrostatic equilibrium state, determined by complete polytropes.
Abstract: The equations of gas dynamics are solved, quasi-analytically by applying McVittie's method for spherical, cylindrical and plane configurations. The hypothesis of linear wave flow is applied and it is assumed that the final state of collapsing clouds is a hydrostatic equilibrium state, determined by complete polytropes. Complete analytical solutions are found when the generalized (to the three symmetries) Emden equation admits of analytical solutions. Otherwise the solutions are left in terms of the numerical solutions of the Emden equation. Numerical solutions to the Emden equation in the plane case are found and tabulated. A strong dependence of amplification, of density, pressure and temperature of the gas, on the symmetry is found. In addition, it is conclude that the flow remains subsonic, during the collapse, except toward the boundaries of the collapsing clouds.
2 citations