Hydrostatic equilibrium

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

Anisotropic compact stars in f(R) gravity

Abstract: We derive a new interior solution for stellar compact objects in $$f\mathcal {(R)}$$ gravity assuming a differential relation to constrain the Ricci curvature scalar. To this aim, we consider specific forms for the radial component of the metric and the first derivative of $$f\mathcal {(R)}$$ . After, the time component of the metric potential and the form of $$f({\mathcal {R}})$$ function are derived. From these results, it is possible to obtain the radial and tangential components of pressure and the density. The resulting interior solution represents a physically motivated anisotropic neutron star model. It is possible to match it with a boundary exterior solution. From this matching, the components of metric potentials can be rewritten in terms of a compactness parameter C which has to be $$C=2GM/Rc^2<<0.5$$ for physical consistency. Other physical conditions for real stellar objects are taken into account according to the solution. We show that the model accurately bypasses conditions like the finiteness of radial and tangential pressures, and energy density at the center of the star, the positivity of these components through the stellar structure, and the negativity of the gradients. These conditions are satisfied if the energy-conditions hold. Moreover, we study the stability of the model by showing that Tolman–Oppenheimer–Volkoff equation is at hydrostatic equilibrium. The solution is matched with observational data of millisecond pulsars with a withe dwarf companion and pulsars presenting thermonuclear bursts.

Gravity current down a steeply inclined slope in a rotating fluid

Abstract: The sinking of dense water down a steep continental slope is studied using laboratory experi- ments, theoretical analysis and numerical simulation. The experiments were made in a rotating tank contain- ing a solid cone mounted on the tank floor and originally filled with water of constant density. A bottom gravity current was produced by injecting more dense coloured water at the top of the cone. The dense water plume propagated from the source down the inclined cone wall and formed a bottom front separating the dense and light fluids. The location of the bottom front was measured as a function of time for various experimental parameters. In the majority of runs a stable axisymmetric flow was observed. In certain experiments, the bottom layer became unstable and was broken into a system of frontal waves which propagated down the slope. The fluid dynamics theory was developed for a strongly non-linear gravity current forming a near-bottom density front. The theory takes into account both bottom and interfacial friction as well as deviation of pressure from the hydrostatic formula in the case of noticeable vertical velocities. Analytical and numerical solutions were found for the initial (t 1 f ), intermediate (t 1 f ), and main t 1 f stages, where f is the Coriolis parameter. The model results show that during the initial stage non-linear inertial oscillations are developed. During the main stage, the gravity current is concentrated in the bottom layer which has a thickness of the order of the Ekman scale. The numerical solutions are close to the same analytical one. Stability analysis shows that the instability thresh- old depends mainly on the Froude number and does not depend on the Ekman number. The results of laboratory experiments confirm the similarity properties of the bottom front propagation and agree well with the theoretical predictions.

On the two-dimensional, hydrostatic flow of a stream of moist air over a mountain ridge

Abstract: The small perturbation of a steady, two-dimensional horizontal stream of a moist inviscid, Boussinesq fluid is treated analytically by use of an asymptotic method when a certain parameter ∊ is small and numerically by use of an iterative method for general values of ∊. This parameter is a measure of the difference between dry and wet adiabats in the model atmosphere, which is absolutely stable and which contains a moist layer near the ground. Vapour condenses (evaporates) where the vertical displacement of a fluid particle exceeds the ascent condensation level and the vertical motion is upward (downward). The condensation of vapour and release of latent heat are nonlinear phenomena which are treated, but otherwise the equations of motion and boundary conditions are linearized. We limit our attention to an airflow of uniform properties over a mountain ridge. The hydrostatic approximation is made. As a result, the horizontal wavelengths must be long compared to the vertical ones and lee waves are a...

Effects of the pressure perturbation field in numerical models of unidirectionally sheared thunderstorm convection - Two versus three dimensions

Abstract: The physical roles of 'buoyant' and 'dynamic' pressure components, and the distinction between buoyant and hydrostatic pressure perturbations, are aspects of the pressure perturbation field in strongly sheared convective storms studied by means of two- and three-dimensional anelastic numerical modeling experiments with common environmental profiles. The pressure analysis clarifies the differences between two- and three-dimensional storms. In the main updraft, strong midlevel thermal buoyancy is partly opposed by a downward-perturbed vertical pressure gradient force. This, however, occurs to a much greater extent in two dimensions than in three, contributing to smaller net upward accelerations. While the buoyant and hydrostatic fields are intimately related to the total buoyancy distribution, the buoyant pressure perturbation is smoother and of lower amplitude than its hydrostatic counterpart. For the model experiments, this distinction is far greater in three dimensions than in two, in association with the smaller scale of the active convection in three dimensions.