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Point vortices and point sources
| Content Provider | Scilit |
|---|---|
| Author | Nazarenko, Sergey |
| Copyright Year | 2014 |
| Description | Point vortex is a 2D flow generated by a singular vorticity distribution which is concentrated at a single point, such that the velocity circulation along a contour embracing this point has a finite value Γ. We have already met this solution in questions 6.2.7 and 6.2.8. In question 6.2.8 we obtained the point vortex solution as a limiting case of a Rankine vortex with vorticity Ω(x) which is constant inside a circle of radius a, Ω(x) = κ = const, and zero outside. Then, the limit a → 0 was taken while keeping the circulation constant, Γ = pia2κ = const. This means that the vorticity value inside the circle tends to infinity, κ ∼ 1/a2. In the limit, such a vorticity field will be represented by a Dirac delta function, Ω(x) = Γ δ(x). (7.1) This vortex generates the following velocity field, u = − Γ 2pi y x2 + y2 , v = Γ 2pi x x2 + y2 ; (7.2) see problem 6.2.7. Indeed, for this flow the circulation is zero for all contours which do not encircle the vortex, and equal to Γ for all contours encircling the vortex (please show that!). In question 6.2.7 you were also asked to find the stream function for the point vortex flow. Book Name: Fluid Dynamics via Examples and Solutions |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2011-0-08401-6&isbn=9780429112300&doi=10.1201/b17783-12&format=pdf |
| Ending Page | 194 |
| Page Count | 24 |
| Starting Page | 171 |
| DOI | 10.1201/b17783-12 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2014-12-01 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Fluid Dynamics Via Examples and Solutions Fluids and Plasmas Physics Function Flow Vortex Vorticity Contours Circle Encircling 2pi |
| Content Type | Text |
| Resource Type | Chapter |
