Hydrostatic equilibrium

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

Signature of helium rain and dilute cores in Jupiter's interior from empirical equations of state

Abstract: Measurements of Jupiter's gravity field by Juno have been acquired with unprecedented precision, but uncertainties in the planet’s hydrogen–helium equation of state (EOS) and the hydrogen–helium phase separation have meant that differences remain in the interior model predictions. We deduce an empirical EOS from Juno gravity field observations in terms of the hydrostatic equation and then investigate the structure and composition of Jupiter by comparison of the empirical EOS with Jupiter's adiabats obtained from the physical EOS. The deduced helium mass fraction suggests depletion of helium in the outermost atmosphere and helium concentration in the inner molecular hydrogen region, which is a signature of helium rain in Jupiter's interior. The deduced envelope metallicity (the heavy-element mass fraction) is as high in the innermost envelope as 11–13 times the solar value. Such a high metallicity provides sharp support to the dilute core model with the heavy elements dissolved in hydrogen and expanded outward. No matter how the core mass is varied, the empirical EOS derived from the two-layer interior model generally suggests higher densities in the innermost envelope than does the best-fit Jupiter's adiabat; this result is, again, a signature of dilute cores in Jupiter's interior. Moreover, no matter the core mass, the empirical EOS is found to exhibit an inflexion point in the deep interior, around 10 Mbar, which can be explained as the combined effect of helium concentration in the upper part and dilute cores in the lower part.

Hydrostatic and non-hydrostatic simulations of the East Greenland Spill Jet

Abstract: The cascade of dense waters off the East Greenland shelf during Summer 2003 is investigated with two very high-resolution (∼0.5 km) regional simulations. The first simulation is non-hydrostatic. The second simulation is hydrostatic and about 3.75 times less expensive. Both simulations are compared to a previous 2-km hydrostatic run (about 30 times less expensive as the 0.5 km non-hydrostatic case).

A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic Model

Abstract: As the sigma-p coordinate under hydrostatic approximation can be interpreted as the mass coordinate without the hydrostatic approximation, we propose a method that upgrades a hydrostatic model to a nonhydrostatic model with relatively less effort. The method adds to the primitive equations the extra terms omitted by the hydrostatic approximation and two prognostic equations for vertical speed w and nonhydrostatic part pressure p'. With properly formulated governing equations, at each time step, the dynamic part of the model is first integrated as that for the original hydrostatic model and then nonhydrostatic contributions are added as corrections to the hydrostatic solutions. In applying physical parameterizations after the dynamic part integration, all physics packages of the original hydrostatic model can be directly used in the nonhydrostatic model, since the upgraded nonhydrostatic model shares the same vertical coordinates with the original hydrostatic model. In this way, the majority codes of the nonhydrostatic model come from the original hydrostatic model. The extra codes are only needed for the calculation additional to the primitive equations. In order to handle sound waves, we use smaller time steps in the nonhydrostatic part dynamic time integration with a split-explicit scheme for horizontal momentum and temperature and a semi-implicit scheme for w and p'. Simulations of 2-dimensional mountain waves and density flows associated with a cold bubble have been used to test the method. The idealized case tests demonstrate that the proposed method realistically simulates the nonhydrostatic effects on different atmospheric circulations that are revealed in theoretical solutions and simulations from other nonhydrostatic models. This method can be used in upgrading any global or mesoscale models from a hydrostatic to nonhydrostatic model.

Density gradient columns: Dynamic modeling for linear profiles

Abstract: Rigorous mathematical modeling of the process dynamics associated with the construction and filling of density gradient columns is presented in this article. These models incorporate the hydrostatic driving forces for fluid flow, friction losses associated with this flow, and the unsteady‐state behavior of the liquid levels in the filling vessels and in the column itself. Four different filling arrangements are considered, corresponding to the density order of the two fluids in the filling vessels and two methods for introducing the fluid of varying density into the column. Time requirements for filling of the column and the resulting calibration curve for liquid density versus height in the gradient column are both obtained as a result of this modeling procedure. Further, extremely important operating guidelines for the final achievement of a linear density gradient in the column, which is normally the desired objective in most laboratory applications, are derived and presented. Conversely, the causes le...

Characteristic Analysis on Heavy Hydrostatic Bearing of DVT500 Vertical Lathe

Abstract: With increasing demands for product quality, and the performance of assembly equipment plays a decisive role for product quality, national experts and scholars conduct in-depth research on the performance of the assembly equipment. In this paper, a research simulation on hydrostatic bearing performance of heavy-duty vertical lathes DVT(digital vertical tool) 500 is carried out by using finite element software FLUENT to simulate the fluid pressure field and temperature field distribution of sector oil recess at different work platform rotational speed. The law of these field distributions is also obtained. The results show that: the rotational speed of the work platform has a greater impact on pressure field and temperature field of gap fluid flow. Numerical results can reflect the true hydrostatic bearing fluid movement, the actual simulation results provide a theoretical basis for optimization design of the Engineering hydrostatic bearing oil cavity.