Hydrostatic equilibrium

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

An impact of hydrostatic extraction scheme on BMRC's global global spectral model

Abstract: There are two important features in geophysical fluid dynamics. One is that the atmospheric and oceanic equations of motion include the Coriolis force; another is that they describe a stratified fluid. The hydrostatic extraction scheme, or standard stratification approximation, posed by Zeng (1979), reflects the second aspect of geophysical fluid dynamics. There exist two major advantages in this scheme; accurate computation of the pressure gradient force can be obtained over steep mountain slopes, and the accumulation error in vertical finite differencing can be reduced, especially near the tropopause.

Basic properties of anisotropic stellar wind expansion in the fluid approach

Abstract: [1] Whereas in an isotropic temperature atmosphere both the hydrostatic equation and the momentum equation give the same conditions for hydrostatic equilibrium, in the anisotropic case the situation is ambiguous. It is found that for an anisotropic temperature the hydrostatic equilibrium conditions have to be deduced from the momentum equation. The condition for hydrostatic equilibrium is that both the parallel and the perpendicular temperatures, to the radial direction, decrease more rapidly than 1/r in the general case and that the perpendicular temperature decreases more rapidly than 1/r when the parallel temperature is constant. The momentum equation displays a transonic solution when at least one of the temperatures, parallel or perpendicular to the radial direction, decreases less rapidly than 1/r in the general case and when the perpendicular temperature decreases less rapidly than 1/r when the parallel temperature is constant. In an anisotropic atmosphere the parallel thermal velocity is the critical velocity. The properties of the transonic expansion in an isothermal and anisotropic atmosphere are studied. The initial velocity, the critical distance position, the terminal velocity, and the density profile are significantly different from the isotropic case. These properties are opposite with respect to the value of the anisotropy T⊥/T∥ > 1.0 and T⊥/T∥ 2.0. The extension of this study to multimoment anisotropic models can be useful for the interpretation of particle simulation of rarefied stellar atmosphere expansion.

Planet formation in a dusty disk: effects of collisional dust growth and dynamics

Abstract: Despite making a small contribution to total protoplanetary disk mass, dust affects the disk temperature by controlling the absorption of starlight. As grains grow from their initial ISM-like size distribution, settling depletes the disk’s upper layers of dust and decreases the optical depth, cooling the interior. In this dissertation, we will discuss the effects of collisional growth of dust grains and their dynamics on the thermal and optical profiles of the disk, the vertical distribution of dust grains, and the possibility that cooling induced by grain growth and settling could lead to gravitational instability in an otherwise marginally stable disk. We also discuss how the critical gap-opening mass of a growing planet changes with the growth, settling and inward radial drift of solids in the course of a disk's evolution. ☐ First, we present a new fast and numerically inexpensive Monte Carlo method with a weighting technique, which models collisional growth of dust, along with vertical settling, turbulent diffusion and radial drift. We present a comprehensive description of the structure of the massively parallel code we have developed. Next, as the first application of our dust model, we explore three disk models, the Minimum Mass Solar Nebula (MMSN), the Minimum-Mass Extra-solar Nebula (MMEN), and a “heavy” disk with higher surface density than the MMEN, and perform simulations for both constant and spatially variable profiles of the turbulence efficiency, $\alpha$. The variable α profile is computed from the ionization fraction determined by an ionization-recombination chemical network. We then calculate wavelength-dependent opacities for the evolving disks and perform radiative transfer to calculate the temperature profile. We find that the growth of large particles in the mid-plane can make a massive disk optically thick at millimeter wavelengths, making it difficult to determine the surface density of dust available for planet formation in the inner disk. Finally, we calculate the Toomre Q parameter, a measure of the disk's stability to gravitational perturbations, for each disk model after it reaches a steady state dust-size distribution, and show that for an initially massive disk, grain growth and settling can reduce the Toomre Q parameter, making the disk unstable under its self-gravity and possibly triggering spiral instabilities. ☐ In the second application, we apply our dust model to calculate the new hydrostatic equilibrium for vertical gas columns and show that the local gas scale heights become significantly less compared to the canonical value of $h(R)/R \sim 0.05$ for isothermal disk models, and can become as low as $0.005$ in a disk with weak turbulence. We also find that the gap opening criteria is not sensitive to the mass of the disk, but basically depends on the turbulence strength. We discuss this result in the context of the minimum mass for a planet to open a gap in a settled disk, and its possible implications for planet migration.

Experimental study on tsunami forces: estimation of tsunami force acting on structures related to run up distance, scale of building and pressure distribution

Abstract: The hydraulic experiments have been carried out for estimating tsunami wave force through water level, velocity, force and pressure measurements. Model of building was placed at several points with certain distance from shoreline. Wave force had been estimated by assuming as hydrostatic forces which only consider inundation depth while wave velocity data used as hydrodynamic forces assumption. Force estimation through integrating wave pressure had been conducted at almost all element on exposed area to ensure the effect of model’s breadth on magnitude of wave force (not only on the middle). However gap of time lag occurred certainly on each line of measurement points have been found. Therefore, precise estimation of wave force through wave pressure measurement seems very difficult. Present study data were compared to the past of available design guidelines for tsunami forces (Asakura et.al.2000) and some available data from past experiments (Yeom et.al.2007-2008) which had analyzed in order to check the validity of some tsunami wave force estimation methods. Some modification equations that refer to function of maximum inundation depth, maximum velocity and run up distance from shoreline are proposed for more considerable agreement of tsunami wave forces estimation

Theoretical analysis on fluid-structure coupling of hydrostatic mechanical seal

Abstract: Aiming at fluid-structure coupling for a kind of convergent gap hydrostatic mechanical seal,a theoretical analysis model is developed.Based on the FEM method,the pressure distribution in the seal gap is calculated by solving incompressible Reynolds equation,and by using the software ANSYS,the elastic deformation of seal components is got.The fluid-structure coupling is achieved by automatic iterative of the two steps.Results show that,under high pressure condition,the pressure distribution is influenced by the deformation of seal faces,and affects the deformation simultaneously.This model allows for the effect of contact and preload between seal components,and can accurately reflect the interaction between the fluid and seal components.The leakage fits well with the experimental results.The model has clear mechanical meaning and entails straightforward calculations to provide accurate analysis of fluid-structure coupling of hydrostatic seals under special conditions.