Hydrostatic equilibrium

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

Frequency spectra of wind velocity and temperature fluctuations observed with the MU radar-RASS

Abstract: MU radar-RASS observations were conducted on July 28–31, 1994 at Shigaraki, Japan (35°N, 136°E), to determine the detailed time variations of all three wind components and virtual temperature in the lower troposphere. We discuss their frequency spectra in comparison with a theoretical model of gravity waves. Assuming hydrostatic equilibrium, we also estimated the vertical wind velocity from the time derivative of temperature variations at each altitude. We found that the frequency spectra of the derived vertical wind were more consistent with a gravity wave model than those spectra calculated from direct measurements of the vertical wind.

The equilibrium of a rotating body of arbitrary density

Abstract: This paper extends Clairaut's theory of rotational equilibrium to third order terms in a small parameter and is meant to be a sequel to a 1962 publication by the author bearing on the same topic. It has been feasible to obtain the Clairaut equation, which governs the deformation of the equipotential surfaces within a rapidly rotating mass in hydrostatic equilibrium, as an ordinary differential equation. This has been achieved by eliminating the two integral terms which appeared in the original formulation. It is expected that the numerical integration of this newly obtained equation will contribute toward a more precise solution of certain geophysical problems — e.g., the determination of the geoid to an accuracy of ±1 m, and the correction to the travel-time of seismic waves; it should also assist in some planetary questions like the determination of the exterior shape for the rapidly rotating planets Jupiter and Saturn.

Accretion-driven turbulence in filaments - I. Non-gravitational accretion

Abstract: We study accretion-driven turbulence for different inflow velocities in star-forming filaments using the code RAMSES. Filaments are rarely isolated objects and their gravitational potential will lead to radially dominated accretion. In the non-gravitational case, accretion by itself can already provoke non-isotropic, radially dominated turbulent motions responsible for the complex structure and non-thermal line widths observed in filaments. We find that there is a direct linear relation between the absolute value of the total density-weighted velocity dispersion and the infall velocity. The turbulent velocity dispersion in the filaments is independent of sound speed or any net flow along the filament. We show that the density-weighted velocity dispersion acts as an additional pressure term, supporting the filament in hydrostatic equilibrium. Comparing to observations, we find that the projected non-thermal line width variation is generally subsonic independent of inflow velocity.

Polishing method using a hydrostatic fluid bearing support having fluctuating fluid flow

Abstract: A polishing system such as a chemical mechanical belt polisher includes a hydrostatic fluid bearing that supports polishing pads and incorporates one or more of the following novel aspects. One aspect uses compliant surfaces surrounding fluid inlets in an array of inlets to extend areas of elevated support pressure around the inlets. Another aspect modulates or reverses fluid flow in the bearing to reduce deviations in the time averaged support pressure and to induce vibrations in the polishing pads to improve polishing performance. Another aspect provides a hydrostatic bearing with a cavity having a lateral extent greater than that of an object being polished. The depth and bottom contour of cavity can be adjusted to provide nearly uniform support pressure across an area that is surrounded by a retaining ring support. Changing fluid pressure to the retaining ring support adjusts the fluid film thickness of the bearing. Yet another aspect of the invention provides a hydrostatic bearing with spiral or partial cardiod drain grooves. This bearing has a non-uniform support pressure profile but provides a uniform average pressure to a wafer that is rotated relative to the center of the bearing. Another aspect of the invention provides a hydrostatic bearing with constant fluid pressure at inlets but a support pressure profile that is adjustable by changing the relative heights of fluid inlets to alter local fluid film thicknesses in the hydrostatic bearing.

Linear stability analysis of an ice sheet interacting with the ocean

Abstract: A linear stability analysis of a two-dimensional flow of an isothermal ice sheet interacting with the ocean is considered. The set of boundary conditions determining motion of the grounding line is adopted to describe hydrostatic equilibrium of ice in water and a cubic dependence of the mass flow rate on ice thickness. The numerical analysis shows that the zero-growth (zero-eigenvalue) mode found for linear bed slopes and constant accumulation rates indeed determines neutral equilibrium and separates stable and unstable solutions. It is also argued that, provided some conditions of regularity of the solutions are satisfied, finding only one stable and one unstable solution would be enough to ascertain that the condition determining a zero eigenvalue also determines neutral equilibrium. This supports the intuitive understanding of ice-sheet stability: ice sheets are stable on bed slopes that ensure that the mass flow rate at the grounding line increases faster than the cumulative ice accumulation rate at the surface when the grounding line is perturbed; and ice sheets are unstable otherwise.