The motion of a uniform vortex in presence of a pointwise one is investigated. The fluid is assumed isochoric and inviscid and the flow planar. The shape of the uniform vortex is accounted for by means of the Schwarz function $\phibm$ of its boundary. A novel theoretical approach [$1$, $2$] based on the evolution equation: $(\partial_t + \Uv \partial_{\mbox{\fo$\xv$}}) \phibm = \oUv$ is adopted, $\Uv$ and $\oUv$ being the analytic continuations of the velocity and of its conjugate on the boundary. It leads to the integro-differential problem in the Schwarz function and in the point vortex position. The analytical solution of the above problem is faced by means of successive approximations. Results are compared with numerical simulations of the vortex motion.

### The interaction of a uniform vortex with a pointwise one

#### Abstract

The motion of a uniform vortex in presence of a pointwise one is investigated. The fluid is assumed isochoric and inviscid and the flow planar. The shape of the uniform vortex is accounted for by means of the Schwarz function $\phibm$ of its boundary. A novel theoretical approach [$1$, $2$] based on the evolution equation: $(\partial_t + \Uv \partial_{\mbox{\fo$\xv$}}) \phibm = \oUv$ is adopted, $\Uv$ and $\oUv$ being the analytic continuations of the velocity and of its conjugate on the boundary. It leads to the integro-differential problem in the Schwarz function and in the point vortex position. The analytical solution of the above problem is faced by means of successive approximations. Results are compared with numerical simulations of the vortex motion.
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2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/211145
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