Dynamics and self-propulsion of a spherical body shedding coaxial vortex rings in an ideal fluid |
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Authors: | Phanindra Tallapragada Scott David Kelly |
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Institution: | 16212. Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, USA
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Abstract: | We describe a model for the dynamic interaction of a sphere with uniform density and a system of coaxial circular vortex rings in an ideal fluid of equal density. At regular intervals in time, a constraint is imposed that requires the velocity of the fluid relative to the sphere to have no component transverse to a particular circular contour on the sphere. In order to enforce this constraint, new vortex rings are introduced in a manner that conserves the total momentum in the system. This models the shedding of rings from a sharp physical ridge on the sphere coincident with the circular contour. If the position of the contour is fixed on the sphere, vortex shedding is a source of drag. If the position of the contour varies periodically, propulsive rings may be shed in a manner that mimics the locomotion of certain jellyfish. We present simulations representing both cases. |
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