Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.

Sustained gravity currents in a channel

Abstract: Gravitationally driven motion arising from a sustained constant source of dense fluid in a horizontal channel is investigated theoretically using shallow-layer models and direct numerical simulations of the Navier–Stokes equations, coupled to an advection–diffusion model of the density field The influxed dense fluid forms a flowing layer underneath the less dense fluid, which initially filled the channel, and in this study its speed of propagation is calculated; the outflux is at the end of the channel The motion, under the assumption of hydrostatic balance, is modelled using a two-layer shallow-water model to account for the flow of both the dense and the overlying less dense fluids When the relative density difference between the fluids is small (the Boussinesq regime), the governing shallow-layer equations are solved using analytical techniques It is demonstrated that a variety of flow-field patterns are feasible, including those with constant height along the length of the current and those where the height varies continuously and discontinuously The type of solution realised in any scenario is determined by the magnitude of the dimensionless flux issuing from the source and the source Froude number Two important phenomena may occur: the flow may be choked, whereby the excess velocity due to the density difference is bounded and the height of the current may not exceed a determined maximum value, and it is also possible for the dense fluid to completely displace all of the less dense fluid originally in the channel in an expanding region close to the source The onset and subsequent evolution of these types of motions are also calculated using analytical techniques The same range of phenomena occurs for non-Boussinesq flows; in this scenario, the solutions of the model are calculated numerically The results of direct numerical simulations of the Navier–Stokes equations are also reported for unsteady two-dimensional flows in which there is an inflow of dense fluid at one end of the channel and an outflow at the other end These simulations reveal the detailed mechanics of the motion and the bulk properties are compared with the predictions of the shallow-layer model to demonstrate good agreement between the two modelling strategies

Thickness of lithosphere deduced from gravity edge effects across the Mendocino Fault

Abstract: THE evolution of a lithospheric plate, as it migrates away from the accreting boundary (mid-ocean ridge crest), is mostly a result of vertical cooling by conduction. As density is a function of temperature and pressure, the density structure should be a function of the age of the plate and, in order to preserve isostatic equilibrium, the seafloor should subside as the plate cools1. Thus, the variation of heat flow, seafloor depth and the gravity field are different expressions of the same process, progressive cooling, occurring over the whole thickness of the plate. Sclater and Francheteau2 have verified these properties through an analysis of the variation of heat flow and depth with the age of the plate. Their model assumed that the plate remains a constant thickness and is floating in hydrostatic equilibrium over the asthenosphere. This led to an estimate of 75 km for the thickness of the plate.

Hydrostatic equilibrium in a magnetized, warped Galactic disc

Abstract: Hydrostatic equilibrium of the multiphase interstellar medium in the solar vicinity is reconsidered, with the regular and turbulent magnetic fields treated separately. The regular magnetic field strength required to support the gas is consistent with independent estimates provided energy equipartition is maintained between turbulence and random magnetic fields. Our results indicate that a midplane value of B0 = 4 � G for the regular magnetic field near the Sun leads to more attractive models than B0 = 2 � G. The vertical profiles of both the regular and random magnetic fields contain disc and halo components whose parameters we have determined. The layer at 1 < |z| < 4kpc can be overpressured and an outflow at a speed of about 50kms 1 may occur there, presumably associated with a Galactic fountain flow, if B0 ≃ 2 � G. We show that hydrostatic equilibrium in a warped disc must produce asymmetric density distributions in z, in rough agreement with H i observations in the outer Galaxy. This asymmetry may be a useful diagnostic of the details of the warping mechanism in the Milky Way and other galaxies. We find indications that gas and magnetic field pressures are different above and below the warped midplane in the outer Galaxy and quantify the difference in terms of turbulent velocity and/or magnetic field strength.

Numerical simulations of dense water cascading on a steep slope

Abstract: The sinking of dense shelf waters down the continental slope (or "cascading") contributes to oceanic water mass formation and carbon cycling. Cascading over steep bottom topography is studied here in numerical experiments using POLCOMS, a 3-D ocean circulation model using a terrain-following s-coordinate system. The model setup is based on a laboratory experiment of a continuous dense water flow from a central source on a conical slope in a rotating tank. The governing parameters of the experiments are the density difference between plume and ambient water, the flow rate, the speed of rotation and (in the model) diffusivity and viscosity. The descent of the dense flow as characterized by the length of the plume as a function of time is studied for a range of parameters. Very good agreement between the model and the laboratory results is shown in dimensional and nondimensional variables. It is confirmed that a hydrostatic model is capable of reproducing the essential physics of cascading on a very steep slope if the model correctly resolves velocity veering in the bottom boundary layer. Experiments changing the height of the bottom Ekman layer (by changing viscosity) and modifying the plume from a 2-layer system to a stratified regime (by enhancing diapycnal diffusion) confirm previous theories, demonstrate their limitations and offer new insights into the dynamics of cascading outside of the controlled laboratory conditions