Hydrostatic equilibrium

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

Combining magneto-hydrostatic constraints with Stokes profiles inversions. II. Application to Hinode/SP observations

Abstract: Context. Inversion techniques applied to the radiative transfer equation for polarized light are capable of inferring the physical parameters in the solar atmosphere (temperature T , magnetic field B , and line-of-sight velocity v los ) from observations of the Stokes vector (i.e., spectropolarimetric observations) in spectral lines. Inferences are usually performed in the (x , y , τ c ) domain, where τ c refers to the optical-depth scale. Generally, their determination in the (x , y , z ) volume is not possible due to the lack of a reliable estimation of the gas pressure, particularly in regions of the solar surface harboring strong magnetic fields.Aims. We aim to develop a new inversion code capable of reliably inferring the physical parameters in the (x , y , z ) domain.Methods. We combine, in a self-consistent way, an inverse solver for the radiative transfer equation (Firtez-DZ) with a solver for the magneto-hydrostatic equilibrium, which derives realistic values of the gas pressure by taking the magnetic pressure and tension into account.Results. We test the correct behavior of the newly developed code with spectropolarimetric observations of two sunspots recorded with the spectropolarimeter (SP) instrument on board the Hinode spacecraft, and we show how the physical parameters are inferred in the (x , y , z ) domain, with the Wilson depression of the sunspots arising as a natural consequence of the force balance. In particular, our approach significantly improves upon previous determinations that were based on semiempirical models.Conclusions. Our results open the door for the possibility of calculating reliable electric currents in three dimensions, j (x , y , z ), in the solar photosphere. Further consistency checks would include a comparison with other methods that have recently been proposed and which achieve similar goals.

Some large‐scale features of the vertical distribution of atmospheric ozone associated with the thermal structure of the atmosphere

Abstract: Ten-case running means of the vertical distributions of hydrostatic stability and of the vertical fractional gradient of the partial pressure of ozone computed from ozone and temperature soundings arranged according to tropopause height are presented for four stations located in different latitudes. It is shown that the characteristic large-scale features of the vertical distributions of the vertical ozone gradient correspond closely to similar characteristic large-scale features of the thermal structure of the atmosphere depicted by the vertical distributions of the hydrostatic stability. The layer structure of the ozone gradient and of the hydrostatic stability both show characteristic features that vary significantly with latitude and with the height of the tropopause.

On Hydrostatic Free Surface Problems

Abstract: We consider the hydrostatic Euler equations in a strip bounded by two free surfaces. We show that the initial value problem is well-posed only if the horizontal velocity is uniform in every cross section of the strip.

A numerical magnetohydrodynamic scheme using the hydrostatic approximation

Abstract: In gravitationally stratified fluids, length scales are normally much greater in the horizontal direction than in the vertical one. When modelling these fluids it can be advantageous to use the hydrostatic approximation, which filters out vertically propagating sound waves and thus allows a greater timestep. We briefly review this approximation, which is commonplace in atmospheric physics, and compare it to other approximations used in astrophysics such as Boussinesq and anelastic, finding that it should be the best approximation to use in context such as radiative stellar zones, compact objects, stellar or planetary atmospheres and other contexts. We describe a finite-difference numerical scheme which uses this approximation, which includes magnetic fields.

Evaluation of a Hydrostatic, Height-Coordinate Formulation of the Primitive Equations for Atmospheric Modeling

Abstract: The hydrostatic form of the primitive equations described by Ooyama is evaluated by comparing nonhydrostatic and hydrostatic integrations of a dry axisymmetric model with a specified entropy (heat) source. In this formulation, pressure is a diagnostic variable, so that the hydrostatic approximation can be included simply by replacing the vertical momentum equation with a diagnostic vertical velocity equation. his diagnostic equation is a one-dimensional (height) second-order elliptic equation that can be solved using a direct method. Results show that hydrostatic solutions are very sensitive to the accuracy of the method used to solve the diagnostic vertical velocity equation. However, this sensitivity can be eliminated by adding an extra term to the diagnostic equation that ensures that the solution does not drift away from hydrostatic balance due to numerical approximation. When the extra term is added, this formulation of the primitive equations allows for the design of a numerical model in he...