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Lloyd J. Shapiro
Huch E. Willoughby


Eliassen's (1951) diagnostic technique is used to calculate the secondary circulation induced by point sources of heat and momentum in balanced, hurricane-like vortices. Scale analysis reveals that such responses are independent of the horizontal scale of the vortex. Analytic solutions for the secondary circulation are readily obtained in idealized barotropic vortices, but numerical methods are required for more realistic barotropic and baroclinic vortices. For sources near the radius of maximum wind, the local, two-dimensional, streamfunction dipole response of Eliassen is modified by both the spatial variations of the vortex structure and the influences of boundary conditions.

The secondary flow advects mean-flow buoyancy and angular momentum and thus leads to a slow evolution of the vortex structure. In weak systems (maximum tangential wind <35 m s−1), the restraining influences of structure and boundaries lengthen the time scale of the vortex evolution. In stronger vortices, the horizontal scale of the response is smaller, the restraining influences are less important, and the evolution is faster. When the maximum wind exceeds 35 m s−1, recirculation of air within the vortex core tends to form an eye.

The most rapid temporal changes in tangential wind lie inside the eye, where the horizontal gradients of angular momentum are strongest. In most cases, the tangential wind increases most rapidly just inside the radius of maximum wind and decreases near the central axis of the vortex. This effect leads to contraction of the wind maximum as the vortex intensifies. The present results are compared with observations and other theoretical mutts.

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