AN ANALYTICAL STUDY OF THE DIFFERENTIAL FRICTIONAL EFFECT ON VORTEX MOVEMENT

GANDIKOTA V. RAO Meteorological Service of Canada, Toronto, Ontario

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Abstract

With a view to gaining insight into the role of differential friction in the movement of tropical cyclones, an analytical solution of the barotropic vorticity equation which included a frictionally induced vertical velocity term was obtained in the form of a Taylor's series in time. An axisymmetric vortex of maximum radius 1000 km having a peak tangential motion of 30 m sec–1 about 450 km from the center was studied. If the eastern (western) half of such a vortex lies over a rough surface with the other half over a relatively smooth surface, the familiar west-northwestward movement of the vortex due to β-effect is increased (decreased) by the differential friction. If only the underlying surface of the northern (southern) half of the vortex is rough, a 46-km, nearly westward (a 40-km northwestward) movement is produced by the β- and differential frictional effects over a 6-hr period. These movements, however, are nonlinear in time. The dependence of the vortex movement on the strength and size of the vortex circulation and on the frictional stress is described.

* A National Research Council of Canada Postdoctorate Fellow.

Abstract

With a view to gaining insight into the role of differential friction in the movement of tropical cyclones, an analytical solution of the barotropic vorticity equation which included a frictionally induced vertical velocity term was obtained in the form of a Taylor's series in time. An axisymmetric vortex of maximum radius 1000 km having a peak tangential motion of 30 m sec–1 about 450 km from the center was studied. If the eastern (western) half of such a vortex lies over a rough surface with the other half over a relatively smooth surface, the familiar west-northwestward movement of the vortex due to β-effect is increased (decreased) by the differential friction. If only the underlying surface of the northern (southern) half of the vortex is rough, a 46-km, nearly westward (a 40-km northwestward) movement is produced by the β- and differential frictional effects over a 6-hr period. These movements, however, are nonlinear in time. The dependence of the vortex movement on the strength and size of the vortex circulation and on the frictional stress is described.

* A National Research Council of Canada Postdoctorate Fellow.

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