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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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01 Mar 1982
18 citations
TL;DR: In this article, the authors present a generalization of the adiabatic pressure lapse ratio equation to include flow at small Mach numbers, analogous to the hydrostatic relationship between pressure, density, and height.
Abstract: This technical brief develops calculation methods for the pressure drop in very tall chimneys, as in solar chimney power plants. The methods allow for density and flow area change with height, for wall friction and internal bracing drag. It presents equations for the vertical pressure and density distributions in terms of Mach number One of these is a generalization of the adiabatic pressure lapse ratio equation to include flow at small Mach numbers. The other is analogous to the hydrostatic relationship between pressure, density, and height, but extends it to small Mach numbers. Its integration leads to an accurate value of the average density in the chimney.
18 citations
TL;DR: In this article, a two-dimensional non-hydrostatic ocean model and a hydrostatic version of the same model are used to simulate convective adjustment, without the use of an instantaneous adjustmentparameterization.
Abstract: A two-dimensional non-hydrostatic ocean model and a hydrostatic version of the same modelare used to simulate convective adjustment, without the use of an instantaneous adjustmentparameterization. The model geometry is a domain on the vertical plane of width 40 km anddepth 500 m. Model results for four cases are examined: hydrostatic and non-hydrostatic, at0.1 and 1 km spatial resolution. The convectively adjusted stable state obtained in all four casesare qualitatively similar; thus the hydrostatic approximation does not eliminate convectiveadjustment. The details of the simulated convective plumes depend on resolution and whetherthe hydrostatic approximation is made. The adjusted state has significant stratification whichcannot be captured by the conventional instantaneous adjustment or diffusion-based parameterizations.We also compare the results to the case when an instantaneous adjustmentparameterization is used. DOI: 10.1034/j.1600-0870.2002.00162.x
18 citations
TL;DR: In this paper, a semi-implicit finite difference and finite volume model is derived for arterial flow in one, two and three space dimensions, which is robust, efficient, locally and globally mass conservative, and applies to both hydrostatic and non-hydrostatic flows.
Abstract: SUMMARY
Blood flow in arterial systems can be described by the three-dimensional Navier–Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea of the method consists in a splitting of the pressure into a hydrostatic and a non-hydrostatic part, where first a small quasi-one-dimensional nonlinear system is solved for the hydrostatic pressure and only in a second step the fully three-dimensional non-hydrostatic pressure is computed from a three-dimensional nonlinear system as a correction to the hydrostatic one. The resulting algorithm is robust, efficient, locally and globally mass conservative, and applies to hydrostatic and non-hydrostatic flows in one, two and three space dimensions. These features are illustrated on nontrivial test cases for flows in tubes with circular or elliptical cross section where the exact analytical solution is known. Test cases of steady and pulsatile flows in uniformly curved rigid and elastic tubes are presented. Wherever possible, axial velocity development and secondary flows are shown and compared with previously published results. Copyright © 2014 John Wiley & Sons, Ltd.
18 citations
TL;DR: In this article, a polar stratospheric ice cloud (PSC type II) was observed by airborne lidar above Greenland on 14 January 2000, which was the unique observation of an ice cloud over Greenland during the SOLVE/THESEO 2000 campaign.
Abstract: A polar stratospheric ice cloud (PSC type II) was observed by airborne lidar above Greenland on 14 January 2000. Is was the unique observation of an ice cloud over Greenland during the SOLVE/THESEO 2000 campaign. Mesoscale simulations with the hydrostatic HRM model are presented which, in contrast to global analyses, are capable to produce a vertically propagating gravity wave that induces the low temperatures at the level of the PSC afforded for the ice formation. The simulated minimum temperature is ~8 K below the driving analyses and ~3 K below the frost point, exactly coinciding with the location of the observed ice cloud. Despite the high elevations of the Greenland orography the simulated gravity wave is not a mountain wave. Analyses of the horizontal wind divergence, of the background wind profiles, of backward gravity wave ray-tracing trajectories, of HRM experiments with reduced Greenland topography and of several instability diagnostics near the tropopause level provide consistent evidence that the wave is emitted by the geostrophic adjustment of a jet instability associated with an intense, rapidly evolving, anticyclonically curved jet stream. In order to evaluate the potential frequency of such non-orographic polar stratospheric cloud events, an approximate jet instability diagnostic is performed for the winter 1999/2000. It indicates that ice-PSCs are only occasionally generated by gravity waves emanating from an unstable jet.
18 citations