Lagrangian theory for 3D vortex sheets with axial or helical symmetry. (English) Zbl 0792.76009
Summary: Consider a three-dimensional vortex sheet in inviscid, incompressible flow which is irrotational away from the sheet. We derive an equation for the evolution of a vortex sheet in Lagrangian coordinates, i.e. an equation that is restricted to the sheet itself and is analogous to the Birkhoff-Rott equation for a two-dimensional (planar) sheet. This general equation is specialized to sheets with axial or helical symmetry, with or without swirl.
MSC:
| 76B47 | Vortex flows for incompressible inviscid fluids |
References:
| [1] | Abramowitz M., Handbook of Mathematical Functions (1965) |
| [2] | de Bernadinis, Studies of Vortex Dominated Flows |
| [3] | Caflisch R. E., Mathematical Aspects of Vortex Dynamics (1989) · Zbl 0674.76012 |
| [4] | DOI: 10.1017/S002211208900193X · doi:10.1017/S002211208900193X |
| [5] | Dahm W. J. A., J. Fluid Mech. |
| [6] | Gradsteyn I. S., Table of Integrals, Series and Products (1965) |
| [7] | DOI: 10.1017/S0022112090003573 · Zbl 0717.76126 · doi:10.1017/S0022112090003573 |
| [8] | Pugh, D. A. 1989. ”Development of vortex sheets in Boussinesq flows - formation of singularities”. London: Ph.D. thesis, Imperial College. |
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