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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, it was shown that a slow but continuous change of the Earth's curvature brought about by tidal friction must have led to continuous stress accumulation in the uppermost part of the lithosphere, where the temperature is below 400 °C and the rheological behaviour is likely to remain brittle over geological time scales.
38 citations
TL;DR: This paper presents well-balanced Runge–Kutta discontinuous Galerkin methods which can preserve the isothermal hydrostatic balance state exactly and maintain genuine high order accuracy for general solutions.
Abstract: Euler equations under gravitational field admit hydrostatic equilibrium state where the flux produced by the pressure is exactly balanced by the gravitational source term In this paper, we present well-balanced Runge---Kutta discontinuous Galerkin methods which can preserve the isothermal hydrostatic balance state exactly and maintain genuine high order accuracy for general solutions To obtain the well-balanced property, we first reformulate the source term, and then approximate it in a way which mimics the discontinuous Galerkin approximation of the flux term Extensive one- and two-dimensional simulations are performed to verify the properties of these schemes such as the exact preservation of the hydrostatic balance state, the ability to capture small perturbation of such state, and the genuine high order accuracy in smooth regions
37 citations
01 Dec 2006
TL;DR: In the case of Titan, the measured gravity coefficients of Titan imply that it is non-hydrostatic and thus the normal Darwin-Radau approach to determining internal structure cannot be applied.
Abstract: The obliquity of Titan is small, but certainly non-zero, and may be used to place constraints on Titan's internal structure. The measured gravity coefficients of Titan imply that it is non-hydrostatic and thus the normal Darwin–Radau approach to determining internal structure cannot be applied. However, if the obliquity is assumed to be tidally damped (that is, in a Cassini state) then combining the obliquity with the measured gravity coefficients allows Titan's moment of inertia to be determined without invoking hydrostatic equilibrium. For polar moment values in the range ( 0.3 C / M R 2 0.4 ), tidally-damped obliquity values of ( 0.115 ° | e | 0.177 ° ) result. If the inferred moment value exceeds 0.4, this strongly suggests the presence of a near-surface ice shell decoupled from the interior, probably by a subsurface ocean.
37 citations
TL;DR: In this paper, a non-hydrostatic numerical model suitable for simulating mesoscale meteorological phenomena is developed and described, which is the first to exploit the nonlinear equation system in σ (normalized pressure) coordinates.
Abstract: A nonhydrostatic numerical model suitable for simulating mesoscale meteorological phenomena is developed and described here. The model is the first to exploit the nonhydrostatic equation system in σ (normalized pressure) coordinates. In addition to the commonly recognized advantages of σ-coordinate models, this model is potentially advantageous in nesting with large-scale σ-coordinate models. The equation system does not support sound waves but it presents the internal gravity waves accurately. External gravity waves are the fastest wave modes in the system that limit the integration time step. However, since short nonhydrostatic external waves are much slower than the speed of shallow-water waves and because fast hydrostatic long waves imposes less severe restriction on the time step when they are resolved by many grid points, a large time step (compared to that determined by the speed of hydrostatic shallow-water waves) can be used when horizontal grid spacing is on the order of 1 km. The syste...
37 citations
TL;DR: In this article, the spin-down of a neutron star atmosphere due to hydrostatic expansion during a Type I X-ray burst was investigated and it was shown that the upper layers of the atmosphere spin down by an amount comparable to the observed values; however, there is no compelling reason to expect the observed spin frequency to be that of only the outermost layers.
Abstract: We present calculations of the spin-down of a neutron star atmosphere due to hydrostatic expansion during a Type I X-ray burst. We show that (i) Cumming and Bildsten overestimated the spin-down of rigidly-rotating atmospheres by a factor of two, and (ii) general relativity has a small (5-10%) effect on the angular momentum conservation law. We rescale our results to different neutron star masses, rotation rates and equations of state, and present some detailed rotational profiles. Comparing with recent observations of large frequency shifts in MXB 1658-298 and 4U 1916-053, we find that the spin-down expected if the atmosphere rotates rigidly is a factor of two to three less than the observed values. If differential rotation is allowed to persist, we find that the upper layers of the atmosphere spin down by an amount comparable to the observed values; however, there is no compelling reason to expect the observed spin frequency to be that of only the outermost layers. We conclude that hydrostatic expansion and angular momentum conservation alone cannot account for the largest frequency shifts observed during Type I bursts.
37 citations