Hydrostatic equilibrium

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

Estimates for the Derivatives of the Velocity and Pressure in Shallow Water Flow and Approximate Shallow Water Equations

Abstract: Estimates are derived on the time and space derivatives of the velocity and pressure of a shallow fluid flow. These estimates depend upon the velocity and pressure being bounded and the free surface having a long wavelength compared to the depth of the fluid. The technique used is to derive $L_2 $-estimates on the derivatives of the velocity and pressure and then convert these to pointwise estimates. As a consequence of these results, the horizontal velocity is shown to be independent of the depth and the pressure hydrostatic to the first approximation. Higher order estimates lead to second order approximate equations which, under additional physically motivated assumptions, correspond to the Boussinesq and Korteweg–deVries equations.

Analytical model for non-thermal pressure in galaxy clusters - II. Comparison with cosmological hydrodynamics simulation

Abstract: Turbulent gas motion inside galaxy clusters provides a non-negligible non-thermal pressure support to the intracluster gas. If not corrected, it leads to a systematic bias in the estimation of cluster masses from X-ray and Sunyaev-Zel'dovich (SZ) observations assuming hydrostatic equilibrium, and affects interpretation of measurements of the SZ power spectrum and observations of cluster outskirts from ongoing and upcoming large cluster surveys. Recently, Shi & Komatsu developed an analytical model for predicting the radius, mass, and redshift dependence of the non-thermal pressure contributed by the kinetic random motions of intracluster gas sourced by the cluster mass growth. In this paper, we compare the predictions of this analytical model to a state-of-the-art cosmological hydrodynamics simulation. As different mass growth histories result in different non-thermal pressure, we perform the comparison on 65 simulated galaxy clusters on a cluster-by-cluster basis. We find an excellent agreement between the modelled and simulated non-thermal pressure profiles. Our results open up the possibility of using the analytical model to correct the systematic bias in the mass estimation of galaxy clusters. We also discuss tests of the physical picture underlying the evolution of intracluster non-thermal gas motions, as well as a way to further improve the analytical modeling, which may help achieve a unified understanding of non-thermal phenomena in galaxy clusters.

Calculation of optical depths from an integral of the Voigt function

Abstract: The optical depth along a vertical path in an atmosphere in hydrostatic equilibrium can be calculated from an integral of the Voigt function for the case where the absorption is due to spectral lines. Series expansions are presented that allow rapid evaluation of this integral over all values of the independent variables, frequency and pressure.

Effect of hydrostatic pressure on the viscosity of failure of polymeric materials

Abstract: A setup and method were developed for studying the effect of hydrostatic pressure on the characteristics of the crack resistance of polymeric materials. The viscosity of failure of material K-4I based on butyl rubber was determined in a wide range of rates of crack propagation and hydrostatic pressures. It was found that an increase in the hydrostatic pressure increases the resistance to crack propagation in a polymeric material. The pressure-time analogy method, where the dependences of the viscosity of failure on the rate of crack growth are parallelly shifted to the value of the pressure-time shift and a generalized curve is formed, can be used for taking the effect of the pressure into consideration.

The Toroidal Iron Atmosphere of a Protoneutron Star: Numerical Solution

Abstract: A numerical method presented by Imshennik et al. (2002) is used to solve the two dimensional axisymmetric hydrodynamic problem on the formation of a toroidal atmosphere during the collapse of an iron stellar core and outer stellar layers. An evolutionary model from Boyes et al. (1999) with a total mass of $25M_{\odot}$ is used as the initial data for the distribution of thermodynamic quantities in the outer shells of a high-mass star. We analyze in detail the results of three calculations in which the difference mesh and the location of the inner boundary of the computational region are varied. In the initial data, we roughly specify an angular velocity distribution that is actually justified by the final result - the formation of a hydrostatic equilibrium toroidal atmosphere with reasonable total mass, $M^{tot} = (0.117 \div 0.122)M_{\odot}$, and total angular momentum, $J^{tot} = (0.445 \div 0.472) x 10^{50} erg \cdot s$, for the two main calculations. We compare the numerical solution with our previous analytical solution in the form of toroidal atmospheres (Imshennik and Manukovskii 2000). This comparison indicates that they are identical if we take into account the more general and complex equation of state with a nonzero temperature and self-gravitation effects in the atmosphere. Our numerical calculations, first, prove the stability of toroidal atmospheres on characteristic hydrodynamic time scales and, second, show the possibility of sporadic fragmentation of these atmospheres even after a hydrodynamic equilibrium is established. The calculations were carried out under the assumption of equatorial symmetry of the problem and up to relatively long time scales $(\approx 10s)$.