Abstract
Uniform shear flow of an incompressible inviscid fluid past a two-dimensional smooth concave body is studied; a stream function for resulting flow is obtained. Results for the same flow past a circular cylinder or a circular arc or a kidney-shaped body are presented as special cases of the main result. Also, a stream function for resulting flow around the same body is presented for an oncoming flow which is the combination of a uniform stream and a uniform shear flow. Possible fields of applications of this study include water flows past river islands, the shapes of which deviate from circular or elliptical shape and have a concave region, or past circular arc-shaped river islands and air flows past concave or circular arc-shaped obstacles near the ground.
Highlights
Shear flow is a common type of flow that is encountered in many practical situations
We have examined two-dimensional incompressible inviscid uniform shear flow past a smooth concave cylinder
It is found that the stream function given in [1] for the resulting flow due to insertion of a circular cylinder in a uniform shear flow of an inviscid fluid is a special case of that of the resulting flow past the concave body presented in this paper
Summary
Shear flow is a common type of flow that is encountered in many practical situations. It is found that the stream function given in [1] (obtained by using Milne-Thomson’s second circle theorem [1]) for the resulting flow due to insertion of a circular cylinder in a uniform shear flow of an inviscid fluid is a special case of that of the resulting flow past the concave body presented in this paper. The stream function for each of shear flow past a circular arc or a kidney-shaped two-dimensional body has been calculated from the main result as special cases. As air flow near the ground is shear flow, the present study may have applications in scientific investigation of air flow past concave or circular arc-shaped obstacles near the ground
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