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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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TL;DR: In this paper, a three-dimensional mathematical model for free surface flow based on the Reynolds-averaged Navier-Stokes equations is developed in a sigma co-ordinate system.
Abstract: A three-dimensional mathematical model for free surface flow based on the Reynolds-averaged Navier-Stokes equations is developed in a sigma co-ordinate system. The time-splitting method is used to separate advection and diffusion terms from the pressure terms in the governing equations. The pressure variable is further separated into hydrostatic and hydrodynamic pressures so that the computer rounding errors can be largely avoided. The resulting hydrodynamic pressure equation is solved by a multigrid method, while the hydrostatic pressure equations are solved very efficiently by an Alternating Direction Implicit (ADI) scheme. The convection terms are discretized by the Roe's scheme of second-order accuracy. A staggered mesh is used. The model is tested against available analytical solutions and experimental data. Good agreement has been achieved.

12 citations

Journal ArticleDOI
TL;DR: In this paper, the sigma-coordinate pressure gradient force is calculated by computing the difference between two large terms of opposite signs, which results in a large truncation error.
Abstract: In connection with the employment of the sigma coordinates introduced by Phillips (1957), problems can arise regarding an accurate finite-difference computation of the pressure gradient force. Over steeply sloped terrain, the calculation of the sigma-coordinate pressure gradient force involves computing the difference between two large terms of opposite sign which results in large truncation error. To reduce the truncation error, several finite-difference methods have been designed and implemented. The present investigation has the objective to provide another method of computing the sigma-coordinate pressure gradient force. Phillips' method is applied for the elimination of a hydrostatic component to a flux formulation. The new technique is compared with four other methods for computing the pressure gradient force. The work is motivated by the desire to use an isentropic and sigma-coordinate hybrid model for experiments designed to study flow near mountainous terrain.

12 citations

Journal ArticleDOI
TL;DR: In this article, the effects of the aspect ratio, the Reynolds number and the jet strength on the flow pattern, pressure magnitudes, runner equilibrium position, stiffness and damping were analyzed.
Abstract: The flow in a hydrostatic pocket is numerically simulated using a dimensionless formulation of the Navier-Stokes equations. In essence, this paper continues the work of Braun et al. (1), (2) by extending it to the study of the effects of certain geometric (α and λ) and flow (R and F) parameters on stiffness and damping in the hydrostatic pocket. The numerical simulations evaluate parametrically the effects of the aspect ratio, the Reynolds number and the jet strength on the flow pattern, pressure magnitudes, runner equilibrium position, stiffness and damping. This synthesis analysis has direct pertinence to hydrostatic journal bearing parametric design, especially so for configurations when α << 1. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in San Diego, California, October 19–21, 1992

12 citations

Journal ArticleDOI
TL;DR: In this paper, the pressure field inside a porous bed induced by the passage of an Internal Solitary Wave (ISW) of depression is examined using high-accuracy numerical simulations.
Abstract: The pressure field inside a porous bed induced by the passage of an Internal Solitary Wave (ISW) of depression is examined using high-accuracy numerical simulations. Assuming a two-layer, continuously stratified water column, the velocity and density fields are obtained by solving the Dubreil-Jacotin-Long Equation. The total wave-induced pressure across the surface of the bed is computed by vertically integrating for the hydrostatic and nonhydrostatic contributions. The bed is assumed to be a continuum composed of either sand or silt, with a small amount of trapped gas. Results show variations in pore-water pressure penetrating deeper into more conductive materials and remaining for a prolonged period after the wave has passed. In order to quantify the potential for failure, the vertical pressure gradient is compared against the buoyant weight of the bed. The pressure gradient exceeds this weight for weakly conductive materials. Failure is further enhanced by a decrease in bed saturation, consistent with studies in surface-wave induced failure. In deeper water, the ISW-induced pressure is stronger, causing failure only for weakly conductive materials. The pressure associated with the free-surface displacement that accompanies ISWs is significant, when the depth of the water column is below 100m, but has little influence when it is above 100m, where the hydrostatic pressure due to the pycnocline displacement is much larger. Since the pore-pressure gradient reduces the specific weight of the bed, results show that particles are easier for the flow to suspend, suggesting that pressure contributes to the powerful resuspension events observed in the field.

12 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023282
2022708
202167
202089
201998
201893