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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, the basic governing equations for isotropic and homogeneous generalized thermoelastic half-space under hydrostatic initial stress are formulated in the context of the Green and Naghdi theory of types II and III.
147 citations
TL;DR: In this article, a theoretical study of the density field and the associated velocity field produced in an unlimited ocean by a prescribed density distribution at the surface is made, where all motions take place under geostrophic and hydrostatic balance, and that the density is simply advected by the motions occurring.
Abstract: A theoretical study is made of the density field and the associated velocity field produced in an unlimited ocean by a prescribed density distribution at the surface. It is assumed that all motions take place under geostrophic and hydrostatic balance, and that the density is simply advected by the motions occurring. The computation is carried out for a spherical earth. The theory gives a depth of penetration of the surface disturbances of the order of 1000 m, if one assumes a relative density variation of the order 10 −3 and a characteristic velocity below the boundary layer of the order 1 cm. sec −1 . The depth of penetration is proportional to the sine of the latitude. Assuming a stable ocean with a surface density increasing from the equator to the pole the theory gives a meridional distribution of density of the form observed in the real oceans. The associated zonal velocities are westerlies at high latitudes, easterlies near the equator. To permit a more precise check of the theory by laboratory experiments the corresponding solution is derived for a rotating “dishpan”. The solution is found to be of the same type as the one studied in the spherical case, but it is pointed out that fundamental differences between the spherical and parabolic cases are likely to occur in more general solutions than those studied here. DOI: 10.1111/j.2153-3490.1959.tb00036.x
146 citations
TL;DR: In this article, the equations of hydromagnetics appropriate for an incompressible inviscid fluid of finite electrical conductivity are considered in case the magnetic fields and the fluid motions have symmetry about an axis.
Abstract: The equations of hydromagnetics appropriate for an incompressible inviscid fluid of finite electrical conductivity are considered in case the magnetic fields and the fluid motions have symmetry about an axis By using a known theorem that a solenoidal vector field can be expressed as a superposition of a poloidal and a toroidal field, the equations are reduced to four equations for four governing scalars. In the limiting case of infinite electrical conductivity, a general relation is derived which includes, as special cases, the known theorems on force-free fields, isorotation, and conditions for hydrostatic equilibrium. Some integral relations which follow from the four equations are also derived.
145 citations
TL;DR: In this article, a set of time-dependent lateral boundary conditions is presented, which allow the changes outside the limited domain to influence the results while not contaminating the forecast with spurious boundary-reflected energy.
Abstract: Before high-resolution numerical models can be of use operationally, they must be restricted to a limited domain, thus necessitating lateral boundary conditions which allow the changes outside the limited domain to influence the results while not contaminating the forecast with spurious boundary-reflected energy. Such a set of time-dependent lateral boundary conditions are presented in this paper. This boundary condition set is investigated using the linear analytic and finite-difference advection equations, the non-linear finite-difference shallow-water equations, and the hydrostatic primitive equations. The results illustrate how the boundary condition transforms long- and medium-length interior advective and gravity waves into short waves which can then be removed by a low pass filter, thereby giving the appearance that the exiting wave simply passed through the boundary. The results also indicate that large-scale advective and gravity waves enter the forecast domain with little degradation. T...
145 citations
TL;DR: In this article, the authors study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones.
Abstract: We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical geopotential and shallow atmosphere approximations in addition to the hydrostatic approximation. As is well known, a consistent application of the shallow atmosphere approximation requires omission of those Coriolis terms that vary as the cosine of latitude and of certain other terms in the components of the momentum equation. An approximate model is here regarded as consistent if it formally preserves conservation principles for axial angular momentum, energy and potential vorticity, and (following R. Muller) if its momentum component equations have Lagrange's form. Within these criteria, four consistent approximate global models, including the HPEs themselves, are identified in a height-coordinate framework. The four models, each of which includes the spherical geopotential approximation, correspond to whether the shallow atmosphere and hydrostatic (or quasi-hydrostatic) approximations are individually made or not made. Restrictions on representing the spatial variation of apparent gravity occur. Solution methods and the situation in a pressure-coordinate framework are discussed. © Crown copyright 2005.
144 citations