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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(4):406-424; doi:10.1093/qjmam/10.4.406
© 1957 by Oxford University Press
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NON-UNIFORM SHEAR FLOW PAST CYLINDERS

JAMES D. MURRAY

( Harvard University Massachusetts, U.S.A. )

A general method is described whereby an approximation of any desired degree of accuracy to the stream functions for two types of variable shear flows past finite cylinders can be obtained. The two shear distributions in the free stream can be approximated to the linear shear distribution and the shear present in an unretarded incompressible boundary layer respectively. In every case the stagnation streamline is displaced from the position opposite the line of symmetry of the cylinder, and general expressions are obtained for this displacement. The line of symmetry may be in the direction of or perpendicular to the direction of flow. The two particular examples cited are those of a general elliptic cylinder and cylinders of the form r = p(1+{gamma} cos {theta}), where ¦{gamma}¦ < 1, r and {theta} being the polar coordinates, and 2p the maximum width of the cylinder.


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