Abstract
In the treatment of numerical models of symmetrical vortices, balanced radial and vertical velocity components may be obtained from a diagnostic equation first derived by Eliassen. However, when this equation is applied to vortices which resemble tropical cyclones, one finds hyperbolicity in regions where saturated ascent is accompanied by conditional static instability. Eliassen suggests that the equation can, nevertheless, be solved as a boundary-value problem through an iterative technique and predicts that the iterations will produce a solution in the form of a convergent geometric series. We have applied Eliassen's procedure to two vortices. For the first of these, we obtained the numerical values of the first three terms in the series. The results do not confirm Eliassen's suggestion concerning the behavior of the ratio of successive terms in the series. In the second case, 27 terms of the series were obtained. Here, convergence does appear to take place but not in the manner predicted by Eliassen's geometric formula.
