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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, the authors derived a time-averaged "hydrostatic wave equation" from the Boussinesq equations that describes the propagation of inertia-gravity internal waves through quasi-geostrophic flow.
Abstract: We derive a time-averaged ‘hydrostatic wave equation’ from the hydrostatic Boussinesq equations that describes the propagation of inertia–gravity internal waves through quasi-geostrophic flow. The derivation uses a multiple-scale asymptotic method to isolate wave field evolution over intervals much longer than a wave period, assumes the wave field has a well-defined non-inertial frequency such as that of the mid-latitude semi-diurnal lunar tide, assumes that the wave field and quasi-geostrophic flow have comparable spatial scales and neglects nonlinear wave–wave dynamics. As a result the hydrostatic wave equation is a reduced model applicable to the propagation of large-scale internal tides through the inhomogeneous and moving ocean. A numerical comparison with the linearized and hydrostatic Boussinesq equations demonstrates the validity of the hydrostatic wave equation model and illustrates how the model fails when the quasi-geostrophic flow is too strong and the wave frequency is too close to inertial. The hydrostatic wave equation provides a first step toward a coupled model for energy transfer between oceanic internal tides and quasi-geostrophic eddies and currents.
16 citations
TL;DR: The Selcore corer as discussed by the authors uses a steel tank with built-in drive unit for sediment sampling and geophysical site characterization, which can operate in water depths from 300 to 3500 m.
16 citations
TL;DR: In this article, the stability problem on perturbations near the hydrostatic equilibrium for the 2D magnetic Benard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity is considered.
Abstract: In mathematics and physics, the problem of the stability of perturbations near the hydrostatic balance is very important. Due to the classical tools designed for the fully dissipated systems are no longer apply, stability and global regularity problems on partially dissipated magnetic Benard fluid equations can be extremely challenging. This paper considers the stability problem on perturbations near the hydrostatic equilibrium for the 2D magnetic Benard fluid equations. We establish the global $$H^1$$
-stability of the 2D magnetic Benard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity and affirm the global stability in the Sobolev space $$H^1$$
setting.
16 citations
TL;DR: In particular, the coefficient of the fourth zonal harmonic deduced from satellite motions is found to differ by a factor of two from the one computed on the equilibrium hypothesis as mentioned in this paper, revealing the extent to which the interior of our planet departs from hydrostatic equilibrium.
16 citations
TL;DR: The plunging of a large intruder sphere into a prefluidized granular bed with various constant velocities and various sphere diameters is investigated using a state-of-the-art hybrid discrete particle and immersed boundary method, in which both the gas-induced drag force and the contact force exerted on the intruder can be investigated separately.
Abstract: The plunging of a large intruder sphere into a prefluidized granular bed with various constant velocities and various sphere diameters is investigated using a state-of-the-art hybrid discrete particle and immersed boundary method, in which both the gas-induced drag force and the contact force exerted on the intruder can be investigated separately. We investigate low velocities, where velocity dependent effects first begin to appear. The results show a concave-to-convex dependence of the plunging force as a function of intruder depth. In the concave region the force fits to a power law with an exponent around 1.3, which is in good agreement with existing experimental observations. Our simulation results further show that the force exerted on the frontal hemisphere of the intruder is dominant. At larger intruder velocities, friction with the granular medium causes a velocity-dependent drag force. As long as the granular particles have not yet closed the gap behind the intruder, this drag force is independent of the actual intruder depth. In this regime, the drag force experienced by intruders of different diameter moving at different velocities all fall onto a single master curve if plotted against the Reynolds number, using a single value for the effective viscosity of the granular medium. This master curve corresponds well to the Schiller-Naumann correlation for the drag force between a sphere and a Newtonian fluid. After the gap behind the intruder has closed, the drag force increases not only with velocity but also with depth. We attribute this to the effect of increasing hydrostatic particle pressure in the granular medium, leading to an increase in effective viscosity.
16 citations