Hydrostatic equilibrium

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

The Dynamical Influence of Orography on the Large-Scale Motion of the Atmosphere.

Abstract: In an attempt to understand the dynamical influence of the earth's orography upon the large-scale motion of the atmosphere, the system of “shallow water” equations on the rotating earth is integrated numerically. The model consists of an incompressible, homogeneous, hydrostatic and inviscid fluid. The “beta-plane” approximation is used to simplify the model. The fluid is confined in a channel bounded on the north and south by two parallel “walls” extending in the cast-west direction. Periodicity is the boundary condition applied at the east and west boundaries to simulate the cyclic continuity of the zone with longitude. A circular obstacle of parabolic shape is placed at the bottom in the middle of the channel. The steady-state solutions in the absence of the obstacle are used as the initial conditions of the problem. Five different cases are investigated in detail. All computations were performed for an interval of 20 days (some cases were run longer) with a time step of 6 minutes. The followin...

Water table waves in an unconfined aquifer: Experiments and modeling

Abstract: [1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Nonhydrostatic Model for Surf Zone Simulation

Abstract: A previously developed model for nonhydrostatic free surface flow is adapted to simulate breaking waves in the surf zone. The model solves the Reynolds-averaged Navier-Stokes equations in a fraction step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver. This approach is particularly well suited for simulating discontinuous flow associated with breaking waves because the model prediction converges to the classical solution for a turbulent bore, which closely resembles breaking waves in the surf zone. The hydrostatic solution is then corrected by including the nonhydrostatic pressure. The model uses a sigma coordinate discretization in the vertical direction, which has been previously demonstrated to yield significant truncation errors with highly skewed grids over large bottom slopes. This potential problem is investigated in the context of highly skewed (but transient) grids that occur with steep br...

The steady-state flow pattern past gravitating bodies

Abstract: Gravitating bodies significantly alter the flow pattern (density and velocity) of the gas that attempts to stream past. Still, small protoplanets in the Mars–super-Earth range can only bind limited amounts of nebular gas; until the so-called critical core mass has been reached (�1–10 Earth masses) this gas is in near hydrostatic equilibrium with the nebula. Here we aim for a general description of the flow pattern surrounding these low-mass, embedded planets. Using various simplifying assumptions (subsonic, 2D, inviscid flow, etc), we reduce the problem to a partial differential equation that we solve numerically as well as approximate analytically. It is found that the boundary between the atmosphere and the nebula gas strongly depends on the value of the disc headwind (deviation from Keplerian rotation). With increasing headwind the atmosphere decreases in size and also becomes more asymmetrical. Using the derived flow pattern for the gas, trajectories of small solid particles, which experience both gas drag and gravitational forces, are integrated numerically. Accretion rates for small particles (dust) are found to be low, as they closely follow the streamlines, which curl away from the planet. However, pebble-size particles achieve large accretion rates, in agreement with previous numerical and analytical works.