Cylinder instability in circulation flow bounded by external cylindrical wall

Abstract eng:
Within the framework of two-dimensional incompressible Euler equations, we study stability of the system composed of an inner free circular cylinder, the fluid with circular streamlines around the cylinder, and an exterior cylindrical wall. A dispersion relation is obtained for different mean flows realized between the cylinder and the wall: potential flow, flow with constant vorticity and flow with weakly decreasing/increasing vorticity. Exact solutions of the dispersion relation are provided and analyzed. It is shown that unlike the unbounded problem, the heavy cylinder in this case becomes unstable even in the potential flow. The sheared instability which is characteristic feature for the unbounded problem for the flow with decreasing vorticity, is realized in the bounded case not only for decreasing, but also for increasing vorticity. Amol’d theorem is used to perform the energy study of the stability loss in the system.

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