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The constraints imposed on tornado-like vortices by the top and bottom boundary conditions

Published online by Cambridge University Press:  28 March 2006

J. S. Turner
J. S. Turner
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
Present address: Department of Applied Mathematics and Theoretical Physics, Silver St., Cambridge.
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Abstract

A laboratory model of a tornado vortex has been produced, incorporating two features which are believed to be important to the understanding of the atmospheric phenomenon, but which have been largely ignored in previous studies. First, it has been shown that a vortex can be driven from above by a mechanism analogous to convection in a cloud, and that density differences within the funnel itself are not essential. Associated with this mechanism of formation is a circulation in the vertical, with an upflow in the centre surrounded by a compensating annular downflow. Secondly, the bottom boundary is seen to have a strong influence on the vortex, since the down and up flows are linked there by a rapid radial inflow in a thin boundary layer.

In the present paper an approximate theoretical description of such a vortex is proposed. The interior and boundary layer flows are first examined separately, and then a condition is sought which makes the two solutions consistent. The starting-point of the theory is the assumption of a form of stream function which describes a circulation in the vertical having the essential features of that observed. The result of the matching procedure is to fix both the form of the tangential velocity profile, and the relative magnitudes of the three components of velocity. These deductions are not critically dependent on the assumed form of the motion in the vertical, and are in good agreement with the first measurements in the laboratory vortices, though the quantitative experimental results are not emphasized here.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 25 , Issue 2 , June 1966 , pp. 377 - 400
Copyright
© 1966 Cambridge University Press

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