Premium
A numerical study of boundary effects on concentrated vortices with application to tornadoes and waterspouts
Author(s) -
Bode L.,
Leslie L. M.,
Smith R. K.
Publication year - 1975
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49710142813
Subject(s) - tornado , vortex , mechanics , drag , physics , horseshoe vortex , vortex stretching , slip (aerodynamics) , geology , boundary value problem , classical mechanics , meteorology , vorticity , thermodynamics , quantum mechanics
This paper extends the numerical study of the structure and development of a concentrated vortex by Leslie (1971), in which a vortex is simulated by suddenly imposing an upwards body force along a section of the vertical axis of a contained rotating fluid, initially in a state of uniform rotation. Whereas the former paper was concerned primarily with demonstrating the prediction of Morton (1969) that a concentrated vortex may be generated only for a restricted range of the flow parameters, the present paper investigates the important role of boundaries on vortex behaviour. Particular interest is focused on the boundary which is normal to the vortex core and ‘behind’ the body force. On this boundary the surface stress is related to the surface velocity by a drag coefficient C D and experiments are performed in which C D is infinite, unity and zero corresponding with a no‐slip, a partially yielding and a free‐slip boundary respectively. These calculations are motivated by the desire to assess what differences, if any, between tornadoes (which develop over land) and waterspouts (which develop over the sea) can be attributed to the different surface constraint. We also study the effect on a vortex due to an abrupt change in surface condition as this is relevant to the behaviour of a tornado which happens to cross a water surface, or even one which traverses ground with varying roughness characteristics, and conversely to the behaviour of a waterspout which moves over land. It is shown that the strength of the meridional circulation associated with the vortex, and hence the strength of the upflow in the vortex itself, are increasing functions of the surface stress. On the other hand, the azimuthal kinetic energy, and in particular the strength of the vortex as measured by the maximum swirling velocity attained, decreases as the surface stress increases. Moreover, if the drag coefficient is suddenly increased, the meridional circulation increases, the azimuthal kinetic energy decreases and the vortex width (as measured by the radius of the maximum swirling velocity at a given height) increases. These effects are reversed if the drag coefficient is decreased and do not depend on the frictional effect of the container side wall. The role of the side wall itself is briefly explored. The results accord with the behaviour of laboratory vortices formed in air over surfaces of different roughness as studied by Dessens (1972). They also appear consistent with the observation reported by Golden (1971, p. 146) concerning the behaviour of a waterspout whose circulation decreased rapidly and visible funnel expanded during a traverse of about a kilometre over land and which subsequently reformed on moving back over water.