Abstract
Incompressible fluid flow with a linear relationship between the vorticity and the stream function past a circular cylinder is studied.
Vortical flows about profiles have been considered in several studies [1–15], but in all these studies with the exception of [15] a constant vorticity was assumed (in [15] an approximate solution is found of the problem of incompressible fluid flow about a Zhukovskii profile with parabolic distribution of the velocities in the approaching stream).
A freestream velocity profile similar to that considered below occurs, for example, in a planar jet (laminar or turbulent), in the wake behind a bluff body, in the boundary layer along an infinite plane [4,13], in turbulent jet flows with reverse fluid currents [16]. A similar situation also arises in the flow past an array of cylinders with large spacing which is located in the wake of another array.
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The author wishes to thank V. E. Davidson for posing the problem and for guidance in its solution.
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Yarmitskii, A.G. Incompressible fluid flow past a circular cylinder with linear relation between the vorticity and the stream function. Fluid Dyn 3, 12–16 (1968). https://doi.org/10.1007/BF01029529
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DOI: https://doi.org/10.1007/BF01029529