The dynamics of spiral banding in a symmetric vortex with vertical shear

Spiral rain bands in tropical cyclones were revealed by Wexler (1947) through analysis of radar observations, and many investigators have directed their attention to them. The bands may now be easily observed through the use of radar (figure 1) and Tiros photographs. However, the mechanism responsible for this frequently observed phenomena is not as yet fully understood. As a possible mechanism for the formation of the spiral bands, Haurwitz (1947), Wexler (1947) and Kuettner (1959) have suggested elongation of convection cells in the tangential direction by vertical wind shear. Further studies are needed to establish this hypothesis, since there is as yet no clear evidence for the existence of Bernard cells in tropical cyclones. Tepper (1958) proposed a hypothesis of internal gravity waves. However, a necessary condition for the existence of gravity waves is an inversion layer which has not been observed in tropical cyclones, except in the eye. Thus, although the entire depth of the fluid may be subject to banded disturbances, the origin and energy source for these disturbances is restricted to those layers with marked vertical shear of the undisturbed flow, principally the Ekman layer. In the case of the atmosphere, moist air in the Ekman layer may be lifted by the periodic vertical motion field to its lifting condensation level becoming visible upon condensation in the form of spiral clouds and rain bands. The release of latent heat in the regions of maximum lifting should serve to increase the vertical motion in these bands and accentuate the upward propagation of the disturbances into the otherwise undisturbed layers above. Arons' observations and Stern's theoretical findings strongly suggest that the vertical shear in the Ekman layer is the dynamical mechanism for instability in the vertical motion field, which may manifest itself in the form of periodic motion in the radial direction. One might even suggest that without the presence of shear the banded structure might not arise. It was these findings and considerations that led the present author to re-examine Yamamoto's work and attempt to retain the vertical shear terms rather than consider only the case of zero shear as did Yamamoto.--Introduction