Hydrostatic equilibrium

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

Diffusion effects on the helium abundance of the solar transition region and corona

Abstract: The diffusion of helium in the solar transition region is studied by solving the mass and momentum conservation equations for a hydrogen-helium plasma given a representative temperature profile. Steady state solutions show that two distinct atmospheres may result. In cases where the thermal force on alpha-particles is balanced by the partial pressure gradient force, helium is the dominant coronal species. On the other hand, if it is the frictional force between protons and alpha-particles which balances the thermal force on alpha-particles then hydrogen is the major coronal component. In order to explore which of these solutions are attainable within reasonable time scales, the time-dependent equations are solved, starting from an initial state with a uniform helium abundance of 10 percent. The atmosphere as a whole is close to hydrostatic equilibrium, but due the thermal forces the individual elements are not. This force inbalance leads to a differential flow between species. It is found that this differential flow leads to a significant enhancement of the coronal helium abundance. Even for the relatively shallow temperature gradient used the helium abundance in the lower corona increases to 30 percent over a 24 hr period.

Normal Modes of a Global Nonhydrostatic Atmospheric Model

Abstract: Anticipating use of a very high resolution global atmospheric model for numerical weather prediction in the future without a traditional hydrostatic assumption, this article describes a unified method to obtain the normal modes of a nonhydrostatic, compressible, and baroclinic global atmospheric model. A system of linearized equations is set up with respect to an atmosphere at rest. An eigenvalue–eigenfunction problem is formulated, consisting of horizontal and vertical structure equations with suitable boundary conditions. The wave frequency and the separation parameter, referred to as “equivalent height,” appear in both the horizontal and vertical equations. Hence, these two equations must be solved as a coupled problem. Numerical results are presented for an isothermal atmosphere. Since the solutions of the horizontal structure equation can only be obtained numerically, the coupled problem is solved by an iteration method. In the primitive-equation (hydrostatic) models, there are two kinds of ...

A Highly Configurable Vortex Initialization Method for Tropical Cyclones

Abstract: A highly configurable vortex initialization methodology has been constructed in order to permit manipulation of the initial vortex structure in numerical models of tropical cyclones. By using distinct specifications of the flow in the boundary layer and free atmosphere, an array of parameters is available to modify the structure. A nonlinear similarity model that solves the steady-state, height-dependent equations for a neutrally stratified, axisymmetric vortex is solved for the boundary layer flow. Above the boundary layer, a steady-state, moist-neutral, hydrostatic and gradient wind balanced model is used to generate the angular momentum distribution in the free atmosphere. In addition, an unbalanced mass-conserving secondary circulation is generated through the assumption of conservation of mass and angular momentum above the boundary layer. Numerical simulations are conducted using a full-physics mesoscale model to explore the sensitivity of the vortex evolution to different prescriptions of t...

Schmidt–Kennicutt relations in SPH simulations of disc galaxies with effective thermal feedback from supernovae

Abstract: We study several versions of the Schmidt-Kennicutt (SK) relation obtained for isolated spiral galaxies in TreeSPH simulations run with the GADGET3 code including the novel MUlti-Phase Particle Integrator (MUPPI) algorithm for star formation and stellar feedback. This is based on a sub-resolution multi-phase treatment of gas particles, where star formation is explicitly related to molecular gas, and the fraction of gas in the molecular phase is computed from hydrodynamical pressure, following a phenomenological correlation. No chemical evolution is included in this version of the code. The standard SK relation between surface densities of cold (neutral+molecular) gas and star formation rate of simulated galaxies shows a steepening at low gas surface densities, starting from a knee whose position depends on disc gas fraction: for more gas-rich discs the steepening takes place at higher surface densities. Because gas fraction and metallicity are typically related, this environmental dependence mimics the predictions of models where the formation of H2 is modulated by metallicity. The cold gas surface density at which HI and molecular gas surface densities equate can range from 10 up to 34 M pc 2 . As expected, the SK relation obtained using molecular gas shows much smaller variations among simulations. We find that disc pressure is not well represented by the classical external pressure of a disc in vertical hydrostatic equilibrium. Instead is well fit by the expression Pt = cold cold= 6, where the three quantities on the right-hand side are cold gas surface density, vertical velocity dispersion and epicyclic frequency. When the “dynamical” SK relation, i.e. the relation that uses gas surface density divided by orbital time, is considered, we find that all of our simulations stay on the same relation. We interpret this as a manifestation of the equilibrium between energy injection and dissipation in stationary galaxy discs, when energetic feedback is effective and pressure is represented by the expression given above. These findings further support the idea that a realistic model of the structure of galaxy discs should take into account energy injection by SNe.