The dynamics of a columnar vortex in an imposed strain.

*(English)*Zbl 0582.76021Exact solutions of the time-dependent Euler equations are presented which correspond to uniform columnar vortices with elliptical cross sections undergoing rotation and deformation in a uniform three-dimensional straining flow. In this work, the recent solutions of S. Kida [J. Phys. Soc. Jpn. 50, 3517 (1981] are generalized to include the effect of a strain component along the axis of the vortex which results in its stretching. The time-dependent solutions should play a very useful role in modeling time-dependent vortex interactions in more complicated flow such as the mixing layer.

##### MSC:

76B47 | Vortex flows for incompressible inviscid fluids |

##### Keywords:

Exact solutions; time-dependent Euler equations; uniform columnar vortices with elliptical cross sections; uniform three-dimensional straining flow; stretching; time-dependent solutions; time-dependent vortex interactions; mixing layer
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##### References:

[1] | Saffman, Annu. Rev. Fluid Mech. 11 pp 95– (1979) |

[2] | D. Moore and P. Saffman,Aircraft Wake Turbulence, edited by J. Olsen, A. Goldberg, and N. Rogers (Plenum, New York, 1971), pp. 339–354. |

[3] | Kida, J. Phys. Soc. Jpn. 50 pp 10, 3517– (1981) |

[4] | J. Neu, J. Fluid Mech. (to be published). |

[5] | H. Lamb,Hydrodynamics, 6th ed. (Cambridge U.P., Cambridge, 1932), pp. 232–233. |

[6] | Moore, J. Fluid Mech. 69 pp 456– (1975) |

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