This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center...This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.展开更多
A preliminary attempt is made to address Stommel’s suggestion that the established offshore shear in the Gulf Stream’s surface velocity is large (up to 0.5 f, where f is the Coriolis parameter) and that this needs t...A preliminary attempt is made to address Stommel’s suggestion that the established offshore shear in the Gulf Stream’s surface velocity is large (up to 0.5 f, where f is the Coriolis parameter) and that this needs to be understood better. Using Bernoulli’s law in conjunction with the geostrophic relation leads to the prediction that the shear should equal f. If a certain sea level variation across the Stream is proposed within the warm Stream water, it is qualitatively possible to reduce the shear value below f, but more work in the future will confirm or refute this idea.展开更多
文摘This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.
文摘A preliminary attempt is made to address Stommel’s suggestion that the established offshore shear in the Gulf Stream’s surface velocity is large (up to 0.5 f, where f is the Coriolis parameter) and that this needs to be understood better. Using Bernoulli’s law in conjunction with the geostrophic relation leads to the prediction that the shear should equal f. If a certain sea level variation across the Stream is proposed within the warm Stream water, it is qualitatively possible to reduce the shear value below f, but more work in the future will confirm or refute this idea.
