Hydrostatic equilibrium

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

Effect of Rotation in a Generalized Thermoelastic Medium with Hydrostatic Initial Stress Subjected to Ramp-Type Heating and Loading

Abstract: The present problem is concerned with the study of deformation of a rotating generalized thermoelastic medium with a hydrostatic initial stress. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The components of displacement, force stress, and temperature distribution are obtained in the Laplace and Fourier domains by applying integral transforms. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. These components are then obtained in the physical domain by applying a numerical inversion method. Some particular cases are also discussed in the context of the problem. The results are also presented graphically to show the effect of rotation and hydrostatic initial stress.

Balanced Flow States Resulting from Penetrative, Slantwise Convection

Abstract: Analytic solutions representing rectilinear flow in geostrophic and hydrostatic balance are constructed using the conformal mapping technique of Gill. Two types of mapping are used to characterize the state of a fluid after a parcel convects to a position of neutral buoyancy. The first mapping corresponds to the homogeneous intrusion in a rotating, stratified fluid studied by Gill. The second mapping describes an internal discontinuity of finite length, embedded in a fluid of uniform potential vorticity. In the idealized physical problem represented by these conformal transformations, an elliptical region of undisturbed fluid is considered to be “saturated” and in a state of unstable equilibrium. On perturbing the system, the saturated parcel convects to a new level distant from its initial position and is rendered homogeneous in absolute momentum and potential temperature by internal mixing. The resulting equilibrium configuration involves a two-dimensional fluid lens, which 1ocally distorts the...

Reduction of Density and Pressure Gradient Errors in Ocean Simulations

Abstract: Existing ocean models often contain errors associated with the computation of the density and the associated pressure gradient. Boussinesq models approximate the pressure gradient force, ρ−1∇p, by ρ−10∇p, where ρ0 is a constant reference density. The error associated with this approximation can be as large as 5%. In addition, Cartesian and sigma-coordinate models usually compute density from an equation of state where its pressure dependence is replaced by a depth dependence through an approximate conversion of depth to pressure to avoid the solution of a nonlinear hydrostatic equation. The dynamic consequences of this approximation and the associated errors can be significant. Here it is shown that it is possible to derive an equivalent but “stiffer” equation of state by the use of modified density and pressure, ρ* and p*, obtained by eliminating the contribution of the pressure-dependent part of the adiabatic compressibility (about 90% of the total). By doing this, the errors associated with bo...

Momentum Balance of the Wind-Driven and Meridional Overturning Circulation

Abstract: When a force is applied to the ocean, fluid parcels are accelerated both locally, by the applied force, and nonlocally, by the pressure gradient forces established to maintain continuity and satisfy the kinematic boundary condition. The net acceleration can be represented through a “rotational force” in the rotational component of the momentum equation. This approach elucidates the correspondence between momentum and vorticity descriptions of the large-scale ocean circulation: if two terms balance pointwise in the rotational momentum equation, then the equivalent two terms balance pointwise in the vorticity equation. The utility of the approach is illustrated for three classical problems: barotropic Rossby waves, wind-driven circulation in a homogeneous basin, and the meridional overturning circulation in an interhemispheric basin. In the hydrostatic limit, it is shown that the rotational forces further decompose into depth-integrated forces that drive the wind-driven gyres and overturning forces ...