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Hydrostatic equilibrium
About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.
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TL;DR: Vyskocil et al. as discussed by the authors proposed a hydraulic pressure level using water at 4°C, which can more than double the speed of 1st-order spirit levelling and provide a measurement precision of better than 1 cm per vertical kilometer of traverse.
5 citations
TL;DR: In this paper, a simplified differential heating problem with a static temperature fluctuation imposed on a solid boundary was studied and a set of scaling relations for the stationary differential heating flow was derived.
Abstract: On the long nuclear time scale of stellar main-sequence evolution, even weak mixing processes can become relevant for redistributing chemical species in a star. We investigate a process of "differential heating," which occurs when a temperature fluctuation propagates by radiative diffusion from the boundary of a convection zone into the adjacent radiative zone. The resulting perturbation of the hydrostatic equilibrium causes a flow that extends some distance from the convection zone. We study a simplified differential-heating problem with a static temperature fluctuation imposed on a solid boundary. The astrophysically relevant limit of a high Reynolds number and a low P\'eclet number (high thermal diffusivity) turns out to be interestingly non-intuitive. We derive a set of scaling relations for the stationary differential heating flow. A numerical method adapted to a high dynamic range in flow amplitude needed to detect weak flows is presented. Our two-dimensional simulations show that the flow reaches a stationary state and confirm the analytic scaling relations. These imply that the flow speed drops abruptly to a negligible value at a finite height above the source of heating. We approximate the mixing rate due to the differential heating flow in a star by a height-dependent diffusion coefficient and show that this mixing extends about $4\%$ of the pressure scale height above the convective core of a $10\,M_\odot$ zero-age main sequence star.
5 citations
5 citations
TL;DR: Salmon's Hamiltonian approach is applied to formulate a balanced approximation to a hydrostatic one-layer isentropic model of the atmosphere as discussed by the authors, which describes an idealized atmosphere of which the dynamics is closely analogous to a one layer shallow-water model on the sphere.
Abstract: Salmon's Hamiltonian approach is applied to formulate a balanced approximation to a hydrostatic one-layer isentropic model of the atmosphere. The model, referred to as the parent model, describes an idealized atmosphere of which the dynamics is closely analogous to a one-layer shallow-water model on the sphere. The balance used as input in Salmon's approach is a simplified form of linear balance, in which the balanced velocity vb is given by vb = k×δf−1(M–M). Here k is a vertical unit vector, f is the Coriolis parameter, M is the Montgomery potential and M is the value of the Montgomery potential at the state of rest. This form of balance is used in preference to standard geostrophic balance, vb = k × f−1δM, which forces the meridional wind velocity to be zero at the equator. Salmon's Hamiltonian technique is applied to obtain an equation for the time rate of change of the balanced velocity that guarantees both the material conservation of potential vorticity as well as conservation of energy. New in this application of Salmon's approach is a nonlinear relation between Montgomery potential and surface pressure (characteristic for an isentropic ideal gas in hydrostatic equilibrium) in combination with spherical geometry and a variable Coriolis parameter. We discuss how the unbalanced velocity va can be calculated in a practical way and how the model can be stepped forward in time by advecting the balanced potential vorticity with the total velocity v = vb + va. The balanced model is tested against a ten-day integration of the parent model.
5 citations
TL;DR: In this paper, a modification of the diffusion matrix in the context of Roe-type schemes is proposed, which is able to resolve the incompressible limit, and does not violate the conditions of hydrostatic equilibrium when gravity is present.
Abstract: In order to perform simulations of low Mach number flow in presence of gravity the technique from [23] is found insufficient as it is unable to cope with the presence of a hydrostatic equilibrium. Instead, a new modification of the diffusion matrix in the context of Roe-type schemes is suggested. We show that without gravity it is able to resolve the incompressible limit, and does not violate the conditions of hydrostatic equilibrium when gravity is present. These properties are verified by performing a formal asymptotic analysis of the scheme. Furthermore, we study its von Neumann stability when subject to explicit time integration and demonstrate its abilities on numerical examples.
5 citations