## An equation for vortex motion including effects of buoyancy and sources with applications to tornadoesRobert C. Costen, United States. National Aeronautics and Space Administration, Langley Research Center A new equation is derived for the motion of vorticity in a general fluid, including the effects of viscosity, compressibility, nonhomogeneity, and nonconservative forces. The equation holds, in particular, for vortices which may not move with the fluid. A linearized form of this equation is applied to tornado cyclones and to the twin tornado of April 11, 1965, near Elkhart, Indiana. It is shown that the displacement of tornado cyclones to the right of the mean tropospheric winds may be accounted for by the upward efflux of fluid from the cyclone into the jet stream. Also, the retarded revolution rate of the twin tornado may be due in part to an attractive "buoyancy" force acting on the partially rarefied cores of the pair. |

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### Contents

SUMMARY | 1 |

DERIVATION OF GENERAL EQUATION FOR MOTION OF VORTICITY | 8 |

APPLICATIONS OF LINEARIZED EQUATION FOR VORTEX MOTION | 19 |

1 other sections not shown

### Common terms and phrases

APPENDIX April 11 arbitrary axial electric current azimuth angle boundary layer buoyancy buoyant attraction Cartesian coordinate system Cartesian coordinates center-to-center distance circulation convergent flow coordinate system Coriolis force Elkhart equation 15 equation 36 equation A24 equation for vortex estimated fluid flow fluid source force density free stream Fujita FUNNELS MOVED grad ground plane due Indiana inviscid fluid jet stream Lorentz force m/sec magnetic field Magnus force mean tropospheric winds mean values motion of vorticity partially rarefied rate of twin revolution rate scalar scalar field section entitled shown in figure single-valued function source fluid source strength source term spherical coordinate system Substituting equation surface of integration tilt angle tilted vortex tornado core tornado cyclone tornado of April tornado pair touchdown points tropopause twin tornado J-2 twin vortices twin-vortex model unit length unperturbed flow updraft vector vortex motion vortex pair vortex tube wind shear