Hydrostatic equilibrium

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

A Nonhydrostatic Mesoscale Ocean Model. Part I: Well-Posedness and Scaling

Abstract: The incompressibility and hydrostatic approximations that are traditionally used in large-scale oceanography to make the hydrodynamic equations more amenable to numerical integration result in the primitive equations. These are ill-posed in domains with open boundaries and hence not well-suited to mesoscale or regional modeling. Instead of using the hydrostatic approximation, the authors permit a greater deviation from hydrostatic balance than what exists in the ocean to obtain a system of equations that is well-posed with the specification of pointwise boundary conditions at open or solid boundaries. These equations, formulated with a free-surface boundary, model the mesoscale flow field accurately in all three-dimensions, even the vertical. It is essential to retain the vertical component of the Coriolis acceleration in the model since it is nonhydrostatic.

Generalized Collapse Solutions with Nonzero Initial Velocities for Star Formation in Molecular Cloud Cores

Abstract: Motivated by recent observations that show that starless molecular cloud cores exhibit subsonic inward velocities, we revisit the collapse problem for polytropic gaseous spheres. In particular, we provide a generalized treatment of protostellar collapse in the spherical limit and find semianalytic (self-similar) solutions, corresponding numerical solutions, and purely analytic calculations of the mass infall rates (the three approaches are in good agreement). This study focuses on collapse solutions that exhibit nonzero inward velocities at large radii, as observed in molecular cloud cores, and extends previous work in four ways: (1) the initial conditions allow nonzero initial inward velocity, (2) the starting states can exceed the density of hydrostatic equilibrium so that the collapse itself can provide the observed inward motions, (3) we consider different equations of state, especially those that are softer than isothermal, and (4) we consider dynamic equations of state that are different from the effective equation of state that produces the initial density distribution. This work determines the infall rates over a wide range of parameter space, as characterized by four variables: the initial inward velocity v∞, the overdensity Λ of the initial state, the index Γ of the static equation of state, and the index γ of the dynamic equation of state. For the range of parameter space applicable to observed cores, the resulting infall rate is about a factor of 2 larger than that found in previous theoretical studies (those with hydrostatic initial conditions and v∞ = 0).