Hydrostatic equilibrium

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

Figuring Out Gas & Galaxies in Enzo (FOGGIE). VI. The Circumgalactic Medium of L ∗ Galaxies Is Supported in an Emergent, Nonhydrostatic Equilibrium

Abstract: The circumgalactic medium (CGM) is often assumed to exist in or near hydrostatic equilibrium, with the regulation of accretion and the effects of feedback treated as perturbations to a stable balance between gravity and thermal pressure. We investigate global hydrostatic equilibrium in the CGM using four highly resolved L * galaxies from the Figuring Out Gas & Galaxies in Enzo (FOGGIE) project. The FOGGIE simulations were specifically targeted at fine spatial and mass resolution in the CGM (Δx ≲ 1 kpc h −1 and M ≃ 200M ⊙). We develop a new analysis framework that calculates the forces provided by thermal pressure gradients, turbulent pressure gradients, ram pressure gradients of large-scale radial bulk flows, centrifugal rotation, and gravity acting on the gas in the CGM. Thermal and turbulent pressure gradients vary strongly on scales of ≲5 kpc throughout the CGM. Thermal pressure gradients provide the main supporting force only beyond ∼0.25R 200, or ∼50 kpc at z = 0. Within ∼0.25R 200, turbulent pressure gradients and rotational support provide stronger forces than thermal pressure. More generally, we find that global equilibrium models are neither appropriate nor predictive for the small scales probed by absorption line observations of the CGM. Local conditions generally cannot be derived by assuming a global equilibrium, but an emergent global equilibrium balancing radially inward and outward forces is obtained when averaging over the nonequilibrium local conditions on large scales in space and time. Approximate hydrostatic equilibrium holds only at large distances from galaxies, even when averaging out small-scale variations.

The application of the method of characteristics for the simulation of nearly horizontal flow in two and three spatial dimensions

Abstract: SUMMARY Certain free surface flows exhibit in nature negligible vertical accelerations and as a result the pressure within the fluid remains hydrostatic. The method of characteristics is developed as a solution technique for the integration of the partial differential equations describing this kind of flow. The equations are integrated over the depth to provide a two-dimensional model which is then tested and validated by comparing its results with tide-induced flows occurring in a number of cases where either analytical or observational data are available for comparison. On the basis of the results of the 2D model, a finite difference 3D model is developed which provides the values of the unknown velocities u, u and w along the three axes x, y and z. This combined 2D-3D model is verified by applying it in cases of wind-induced flow inside closed or open basins for which the classical Ekman solution may be used as a testing means.

Finite-amplitude mountain waves in a compressible atmosphere including the effects of dissipation

Abstract: Adiabatic, two-dimensional, steady-state finite-amplitude, hydrostatic gravity waves produced by flow over a ridge are considered. Nonlinear self advection steepens the wave until the streamlines attain a vertical slope at a critical height zc. The height zc , where this occurs, depends on the ridge crest height and adiabatic expansion of the atmosphere. Dissipation is introduced in order to balance nonlinear self advection, and to maintain a marginal state above zc. The approach is to assume that the wave is inviscid except in a thin layer, small compared to a vertical wavelength, where dissipation cannot be neglected. The solutions in each region are matched to obtain a continuous solution for the streamline displacement δ. Solutions are presented for different values of the nondimensional dissipation parameter β. Eddy viscosity coefficients and the thickness of the dissipative layer are expressed as functions of β, and their magnitudes are compared to other theoretical evaluations and to value...

Study on Flowability of the Gap Oil Film of the Multi-oil Pad Hydrostatic Bearing with Variable Viscosity

Abstract: According to the large size multi-oil pad hydrostatic bearing, the mathematical model of three-dimensional flow of the gap oil film of the hydrostatic bearing is established in considering the influence of variable viscosity and centrifugal force condition. The finite element method and the finite volume method are used to simulate the flow field of the gap oil film of the large size hydrostatic bearing, and the flowing law of the gap oil film of the hydrostatic bearing is revealed. The results show that the interior of the gap oil exists turbulence when the inlet flowrate and the rotating velocity of the worktable are greater than a critical value. then The critical inlet flowrate and the worktable critical rotating velocity of the oil cavity from the laminar to the turbulence are found. The simulation matches well with the theoretical calculation value by comparative analysis of the simulation and the theoretical calculation value. That provides the theoretical basis for the characteristic research of the variable viscosity fluid and the theoretical calculation method for the large size hydrostatic bearing designing. method for the large size hydrostatic bearing designing.

On the propagation of gravity waves in a hydrostatic, compressible fluid with vertical wind shear

Abstract: The speed of propagation of the vertical modes of gravity waves is found in a non-rotating hydrostatic and compressible fluid with a vertical variation of mean temperature and wind. The analysis is based on a set of linearized equations, and it is assumed that the basic flow as well as the perturbations are hydrostatic. We are therefore concerned with one of the possible wave-type solutions to the primitive equations as they are being used in studies of the general circulation of the atmosphere and in other dynamical studies of the atmosphere. In the case of a constant static stability it is found that the speed of propagation of internal gravity waves is determined by the Richardson number. If the (positive) Richardson number is smaller than 1/4, the waves will move with a speed determined by the basic flow at the bottom of the fluid. For Richardson numbers larger than 1/4 several vertical modes moving with different speed will exist. The speed of propagation is evaluated as a function of the vertical wave number and the vertical windshear for given values of the static stability. The speed of the external gravity waves is evaluated numerically. It is found that the main difference is the existence of a mode which has a numerically large phase speed and which has a maximum amplitude of the vertical velocity at the boundary. The modes of the internal waves move with almost the same speed as before. The amplitudes of vertical velocity and geopotential are computed as functions of pressure for the internal and external gravity waves. The results of this study which apply to a hydrostatic and compressible atmosphere are compared in the last section with certain general results, obtained in earlier investigations, for a non-hydrostatic, incompressible fluid. A sufficient condition for stability has been found and an upper and lower limit on the magnitude of the complex root has been determined. DOI: 10.1111/j.2153-3490.1965.tb01423.x