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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 Jan 1995
TL;DR: In this article, the authors present a global view of the Second Law of Gases and its implications on Heterogeneous Systems, including large-scale motions of the Earth and its environment.
Abstract: (Section Headings): A Global View. Thermodynamics of Gases. The Second Law and Its Implications. Heterogeneous Systems. Transformations of Moist Air. Hydrostatic Equilibrium. Hydrostatic Stability. Atmospheric Radiation. Aerosol and Clouds. Atmospheric Motion. Atmospheric Equations of Motion. Large-Scale Motion. The Planetary Boundary Layer. Atmospheric Waves. The General Circulation. Hydrodynamic Instability. The Middle Atmosphere. Appendices. Chapter Problems. Answers to Selected Problems. References. Subject Index. (Section Headings): A Global View. Thermodynamics of Gases. The Second Law and Its Implications. Heterogeneous Systems. Transformations of Moist Air. Hydrostatic Equilibrium. Hydrostatic Stability. Atmospheric Radiation. Aerosol and Clouds. Atmospheric Motion. Atmospheric Equations of Motion. Large-Scale Motion. The Planetary Boundary Layer. Atmospheric Waves. The General Circulation. Hydrodynamic Instability. The Middle Atmosphere. Appendices. Chapter Problems. Answers to Selected Problems. References. Subject Index.
383 citations
TL;DR: In this paper, a semi-implicit finite difference scheme for the numerical solution of a three-dimensional shallow water model is presented and discussed, in which pressure is assumed to be hydrostatic and the velocity gradient in the momentum equations and the velocities in the vertically integrated continuity equation are discretized with the θ-method, with θ being an implicitness parameter.
Abstract: The stability analysis, the accuracy and the efficiency of a semi-implicit finite difference scheme for the numerical solution of a three-dimensional shallow water model are presented and discussed. The governing equations are the three-dimensional Reynolds equations in which pressure is assumed to be hydrostatic. The pressure gradient in the momentum equations and the velocities in the vertically integrated continuity equation are discretized with the θ-method, with θ being an implicitness parameter. It is shown that the method is stable for 1 2 ≤ θ ≤ 1, unstable for θ 1 2 and highest accuracy and efficiency is achieved when θ = 1 2 . The resulting algorithm is mass conservative and naturally allows for the simulation of flooding and drying of tidal flats.
380 citations
TL;DR: In this paper, a numerical model for simulating the flow of stably stratified nonrotating air over finite-amplitude, two-dimensional mountain ranges is developed for accurate treatment of internal dissipation and formulation of an upper boundary region and lateral boundary conditions which allow upward and lateral propagation of wave energy out of the model.
Abstract: A numerical model is developed for simulating the flow of stably stratified nonrotating air over finite-amplitude, two-dimensional mountain ranges. Special attention is paid to accurate treatment of internal dissipation and to formulation of an upper boundary region and lateral boundary conditions which allow upward and lateral propagation of wave energy out of the model. The model is hydrostatic and uses potential temperature for the vertical coordinate. A local adjustment procedure is derived to parameterize low Richardson number instability. The model behavior is tested against analytic theory and then applied to a variety of idealized and real flow situations, leading to some new insights and new questions on the nature of large-amplitude mountain waves. The model proves to be effective in simulating the structure of two observed cases of strong mountain waves with very different characteristics.
369 citations
TL;DR: In this article, it was shown that the differencing scheme cited here, though conventional, is not hydrostatically inconsistent; the sigma coordinate, pressure gradient error decreases with the square of the vertical and horizontal grid size.
Abstract: Much has been written of the error in computing the horizontal pressure gradient associated with sigma coordinates in ocean or atmospheric numerical models. There also exists the concept of “hydrostatic inconsistency” whereby, for a given horizontal resolution, increasing the vertical resolution may not be numerically convergent. In this paper, it is shown that the differencing scheme cited here, though conventional, is not hydrostatically inconsistent; the sigma coordinate, pressure gradient error decreases with the square of the vertical and horizontal grid size. Furthermore, it is shown that the pressure gradient error is advectively eliminated after a long time integration. At the other extreme, it is shown that diagnostic calculations of the North Atlantic Ocean using rather coarse resolution, and where the temperature and salinity and the pressure gradient error are held constant, do not exhibit significant differences when compared to a calculation where horizontal pressure gradients are c...
367 citations
TL;DR: In this article, the authors show that the upper and lower crust and lithospheric mantle are totally coupled and that the total strength of the lithosphere is equal to the magnitude of tectonic driving forces.
359 citations