Point Vortex in a Viscous Incompressible Fluid
V. V. Pukhnachev1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: Navier-Stokes equations, no-slip condition, point vortex
Abstract
A plane steady problem of a point vortex in a domain filled by a viscous incompressible fluid and bounded by a solid wall is considered. The existence of the solution of Navier-Stokes equations, which describe such a flow, is proved in the case where the vortex circulation Γ and viscosity ν satisfy the condition | Γ | < 2πν. The velocity field of the resultant solution has an infinite Dirichlet integral. It is shown that this solution can be approximated by the solution of the problem of rotation of a disk of radius γ with an angular velocity ω under the condition 2πγ2ω → Γ as γ → 0 and ω → ∞.
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