A study of the linear stability of asymmetric channel flows is presented. Three one-parameter families of basic velocity which possess, respectively, no, one, and two inflection points are treated. The competing effects of stabilizing asymmetry and destabilizing vorticity distributions are discussed. An inviscid wave speed theorem which extends a result of Stuart to flows with two inflection points is proved.

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2014 Une méthode générale a été développée pour déterminer le flux magnétohydrodynamique se développant à l'entrée d'un canal à plaques parallèles. Une forme fermée pour les solutions a été obtenue. Les résultats numériques sont présentés pour le développement de la distribution des vitesses, la chute de pression et la longueur de l'entrée magnétohydrodynamique pour différents nombres de Hartman. Pour de grandes valeurs du nombre de Hartman, l'effet de champ magnétique devient prédominant et la longueur d'entrée magnétohydrodynamique devient négligeable. D'autre part, la chute de pression est accrue par le champ magnétique. Les résultats sont en parfait accord avec ceux obtenus par une analyse numérique directe.Abstract. 2014 A general method has been developed for determining the developing magnetohydrodynamic flow in the entrance region of a parallel-plate channel. Closed form solutions are obtained. Numerical results are presented for the development of velocity distribution, pressure drop, and magnetohydrodynamic entrance length at different Hartmann numbers. At large Hartmann numbers, the magnetic field effect becomes dominant and the magnetohydrodynamic entrance length becomes negligible. Also, the pressure drop is enhanced by the magnetic field. Comparison of results with direct numerical analysis shows excellent agreement.

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The instability of hard and brittle mudstone wellbore in the Xujiahe Formation in the Western Sichuan Depression is widespread, which has led to accidents such as sticking and collapse. In this paper, the Xujiahe Formation in the Western Sichuan Depression is taken as the research object, and the method of indoor experiment and theoretical simulation is used to study the instability phenomenon of the wellbore. The following points of knowledge have been obtained: The clay minerals in the mudstones of the Xujiahe Formation in the Western Sichuan Depression are mainly illite and chlorite (content>90%), with a small amount of illite/montmorillonite mixed layer, and the pore throat radius is between 14.56nm-24.47nm, belonging to the mesoporous type; After the mudstone hydrates, its compressive strength, cohesion, elastic modulus, and tensile strength will continue to decrease with the increase of water, while the Poisson’s ratio will continue to rise; The relationship between the dry core and the wet core can be used to correct the acoustic velocity of the collapsed mudstone section; the nature of the wellbore instability is that the liquid pressure in the wellbore is less than the formation pressure, and the formation pressure exceeds the rock strength, which leads to instability. We use the borehole expansion rate to realize the evaluation of wellbore stability. The research results have guiding significance for the evaluation of the stability of the hard and brittle mudstone wellbore of the Xujiahe Formation in the Western Sichuan Depression, and provide technical support for the next step of drilling safety.