Équilibre hydrostatique | EPFL Graph Search

En physique, on appelle équilibre hydrostatique l'état de repos atteint par un système lorsque la force d'attraction gravitationnelle subie par ce système est compensée par l'action des forces de pression d'un fluide (liquide, gaz ou plasma). Par exemple, les forces de pression empêchent la pesanteur de comprimer l'atmosphère terrestre en une coquille dense ; inversement, la pesanteur empêche la pression de diffuser l'atmosphère dans l'espace. L'équilibre hydrostatique est utilisé dans différents domaines tels que la statique des fluides, la météorologie, l'océanographie ou encore l'astrophysique. Expression de l'équilibre hydrostatique On considère un fluide quelconque (liquide ou gaz). Il s'établit un équilibre hydrostatique lorsque la variation de pression dans le fluide avec l'altitude est proportionnelle à l'accélération de la pesanteur et à la masse volumique du système en équilibre. L'équilibre hydrostatique s'exprime par : \frac{\mathrm{d}p}

The distribution of dark matter and gas spanning 6 Mpc around the post-merger galaxy cluster MS0451-03

David Richard Harvey, Mathilde Jauzac, Baptiste Philippe Klein, Jean-Paul Richard Kneib, Richard Massey

Using the largestmosaic of Hubble Space Telescope images around a galaxy cluster, we map the distribution of darkmatter throughout an similar to 6 x 6 Mpc(2) area centred on the clusterMS 0451-03 (z = 0.54, M-200 = 1.65 x 10(15) M-circle dot). Our joint strong- and weak-lensing analysis shows three possible filaments extending from the cluster, encompassing six group-scale substructures. The dark matter distribution in the cluster core is elongated, consists of two distinct components, and is characterized by a concentration parameter of c(200) = 3.79 +/- 0.36. By contrast, XMM-Newton observations show the gas distribution to be more spherical, with excess entropy near the core, and a lower concentration of c(200) = 2.35(-0.70)(+0.89) (assuming hydrostatic equilibrium). Such a configuration is predicted in simulations of major mergers 2-7 Gyr after the first core passage, when the two dark matter haloes approach second turnaround, and before their gas has relaxed. This post-merger scenario finds further support in optical spectroscopy of the cluster's member galaxies, which shows that star formation was abruptly quenched 5Gyr ago. MS0451-03 will be an ideal target for future studies of the growth of structure along filaments, star formation processes after a major merger, and the late-stage evolution of cluster collisions.

OXFORD UNIV PRESS2020

Watertable fluctuation-induced variability in the water retention curve: Sand column experiments

David Andrew Barry, Zhaoyang Luo

The soil water retention curve (WRC), describing the relation between the soil water content and its corresponding capillary pressure, relies not only on whether drying or wetting occurs but also on the pore scale water flow velocity. Here, we investigated the effects of the watertable fluctuations on the WRC through 28 laboratory experiments covering a wide range of fluctuation amplitudes and periods. Results show that both the response of the capillary pressure and soil water content lag behind the watertable fluctuation, and the vertical capillary pressure distribution in the unsaturated zone is non-hydrostatic, especially for the fluctuations with shorter period. As a consequence of watertable fluctuation, the measured WRC deviates from that under static conditions, depending on both the fluctuation amplitude and period. Moreover, the air-entry pressure under dynamic conditions is considerably larger than that under static conditions, and it first increases and then decreases as the fluctuation period decreases. The effects of the watertable fluctuations on the dynamic capillary coefficient was further examined. It is found that the relation between the dynamic capillary coefficient and saturation is nonunique even for the drying and wetting of a given sand and watertable fluctuation, suggesting a hysteretic dynamic capillary coefficient, and the dynamic capillary coefficient is rate-dependent, decreasing with an increase of fluctuation rate.

2020

From coating flow patterns to porous body wake dynamics via multiscale models

Pier Giuseppe Ledda

Multiscale phenomena are involved in countless problems in fluid mechanics. Coating flows are known to exhibit a broad variety of patterns, such as wine tears in a glass and dripping of fresh paint applied on a wall. Coating flows are typically modeled under the assumption that the thickness of the fluid layer is much smaller than the characteristic length of the free-surface deformations, i.e. there is a separation of scales between the microscopic variations of the velocity and pressure field along the thin layer and the macroscopic modulations of the free-surface. A different multiscale phenomenon of undeniable interest in the fluid dynamics community is the flow around and through porous objects. Dandelion seeds are transported by the wind thanks to a hairy structure, called pappus, known to present larger values of the aerodynamic drag and a more stable wake compared to an impervious disk in the same flow conditions.This thesis investigates the pattern formation of several coating flows and the wake dynamics past diverse permeable bodies via multiscale models. We initially consider the flow of a thin viscous film underneath an inclined planar substrate. We show the emergence of free-surface structures modulated along the direction transversal to the main flow, called rivulets. These rivulets result from a pure equilibrium between hydrostatic gravity and surface tension effects, and may destabilize with the formation of traveling drops. We determine via a linear stability analysis the critical values of the inclination angle and film thickness beyond which rivulets destabilize. We numerically study the linear and non-linear response with respect to a harmonic forcing in the inlet flow rate, determining the diverse lenses' patterns emerging on a steady rivulet. The dripping problem is deepened by considering a single drop deposited on a very thin film. Very slight inclinations with respect to the horizontal, of the order of degrees, lead to the formation of a rivulet in the wake of a shrinking drop. Subsequently, we investigate the role of these instabilities in karst draperies formation, by coupling the hydrodynamic model with the deposition of calcium carbonate on the substrate. We implement an algorithm which retrieves the asymptotic properties of the two-dimensional linear impulse response from numerical simulations. The analysis shows the predominance of streamwise structures, reminiscent of draperies, growing on the substrate. The role of modifications of the substrate is then investigated in the cases of dewetting of very thin polymer films, in the context of production of optical metasurfaces, and in the case of three-dimensional spreading of a mass of fluid. The last part of the thesis is devoted to the modifications of wake flows instabilities past bluff bodies when composed of a permeable microstructure, with a focus on the case of a porous sphere and a cylindrical circular membrane. We develop an inverse procedure to optimize and retrieve the microstructure based on flow objectives. The analysis is concluded by studying the path instability of a freely-falling permeable disk. A complex series of bifurcations occurs but, as the ratio between voids and solid structure increases, all wake and path instabilities are damped.

EPFL2022

From coating flow patterns to porous body wake dynamics via multiscale models

Pier Giuseppe Ledda

EPFL2022