Hydrostatic equilibrium

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

Analytical estimates of permeability and possible convective heat transfer in compact porous fluid–saturated rocks

Abstract: The possible occurrence of convection in fine-grained (low-porous <15%) fluid-saturated (argon, water) rocks under hydrostatic pressures of up to 100 MPa is studied. Calculations of the Rayleigh filtration number and the Darcy number are presented. It is shown that the convective motion of fluid does not occur in pore-saturating fluids within the considered range of pressure variation, pore sizes, and temperature differences.

Radially Symmetric Motions of Nonlinearly Viscoelastic Bodies Under Live Loads

Abstract: This paper treats radially symmetric motions of nonlinearly viscoelastic circular-cylindrical and spherical shells subjected to the live loads of centrifugal force and (time-dependent) hydrostatic pressures. The governing equations are exact versions of those for 3-dimensional continuum mechanics (so shell does not connote an approximate via some shell theory). These motions are governed by quasilinear third-order parabolic-hyperbolic equations having but one independent spatial variable. The principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations. The presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis. The interaction of geometrically exact formulations, the compatible use of general constitutive equations for material response, and the presence of live loads show how these factors play crucial roles in the behavior of solutions. In particular, for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior. The analysis (using classical methods) covers infinite-time blowup for cylindrical shells subject to centrifugal forces, infinite-time blowup for cylindrical shells subject to steady and time-dependent hydrostatic pressures, finite-time blowup for spherical shells subject to steady and time-dependent hydrostatic pressures, and the preclusion of total compression. This paper concludes with a sketch (using some modern methods) of the existence of regular solutions until the time of blowup.

Modelling and simulation of transient air-water two-phase flows in hydraulic pipes

Abstract: The present work is dedicated to the mathematical and numerical modelling of transient air-water flows in pipes which occur in piping systems of several industrial areas such as nuclear or hydroelectric power plants or sewage pipelines. It deals more specifically with the so-called mixed flows which involve stratified regimes driven by slow gravity waves, pressurized or dry regimes (pipe full of water or air) driven by fast acoustic waves and entrapped air pockets. An accurate modelling of these flows is necessary to guarantee the operability of the related hydraulic system. While most of available models in the literature focus on the water phase neglecting the air phase, a compressible two-layer model which accounts for air-water interactions is proposed herein. The derivation process relies on a depth averaging of the isentropic Euler set of equations for both phases where the hydrostatic constraint is applied on the water pressure gradient. The resulting system is hyperbolic and satisfies an entropy inequality in addition to other significant mathematical properties, including the uniqueness of jump conditions and the positivity of heights and densities for each layer. Regarding the discrete level, the simulation of mixed flows with the compressible two-layer model raises key challenges due to the discrepancy of wave speeds characterizing each regime combined with the fast underlying relaxation processes and with phase vanishing when the flow becomes pressurized or dry. Thus, an implicit-explicit fractional step method is derived. It relies on the fast pressure relaxation in addition to a mimetic approach with the shallow water equations for the slow dynamics of the water phase. In particular, a relaxation method provides stabilization terms activated according to the flow regime. Several test cases are performed and attest the ability of the compressible two-layer model to deal with mixed flows in pipes involving air pocket entrapment.

Surface-Wave Analysis in the Taipei Basin from Strong-Motion Data

Abstract: A new spectral moist convection model that employs both the least assumptionsin moist physics and a very accurate solution method is presented.The temperature and pressure in the model are diagnostically determinedfrom thermodynamics.There is no need to predict water vaporand condensate separately;rather,they are diagnostically separated fromthe predicted total airborne water.The model allows a modular separationof dynamics and thermodynamics;the link between dynamics and thermodynamicsis through the pressure gradient force.The modular separationallows the possibility of having a detailed,fine resolution,nonhydrostaticcloud model and a coarse resolution,hydrostatic model which can be runside by side with the identical moist thermodynamics.The height coordinateof the nonhydrostatic model can also extend into the hydrostatic regime.The only differences between the hydrostatic and nonhydrostaticmodels are spatial resolution and the way vertical motion is computed.Wehave performed numerical experiments in the nonhydrostatic model foracoustic adjustment and moist convection.The discontinuity in thermodynamicsdue to phase change is modified in the model by the”gradual saturation”technique.