The authors thank Qin Xu and John Lewis of NSSL and Alan Shapiro, Brian Fiedler, Katharine Kanak, and John Snow of the University of Oklahoma for reading and making many useful suggestions in the earlier version of the paper. Particular thanks are extended to Kim Elmore of NSSL for providing editorial assistance in this version. The authors are grateful to Lynn Greenleaf of the University of Oklahoma for providing assistance in the computation of the Sullivan tangential velocity profile. The authors appreciate the efforts of the anonymous reviewers for reviewing and providing helpful comments, insights, and suggestions that led to an improved manuscript. The lead author would like to thank Ernest Agee of Purdue University for providing his figure (which appears herein as Fig. 2 for illustrative purposes). The author also is indebted to George Vatistas of Concordia University (Montreal, Quebec, Canada) for answering the author’s questions about the Vatistas and Sullivan models.
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A one-celled vortex structure consists of a jetlike vertical velocity everywhere being directed upward with a maximum at the vortex axis, whereas a two-celled vortex is characterized by downward motion along the axis in a circular region surrounded by an annular region of upward motion at outer radius, as described by Snow (1982, 1984), Davies-Jones (1986), Pauley and Snow (1988), Church and Snow (1993), and Davies-Jones et al. (2001).
When λ = 1 in (6) and (11), we formulated our old model several years ago before the lead author found out about the Vatistas et al. (1991) model online. Because our old model failed to produce a sharply peaked tangential velocity profile, we decided to adopt the Vatistas model, reformulated [starting with (6)] that led to (11); we further tested and verified our new model [(11)] by comparing satisfactorily radial profiles of parametric tangential velocity with those of the idealized Rankine, Burgers–Rott, and Sullivan vortex models, as will be shown in this study.
Sometimes called the Rankine-combined vortex by some investigators because the vortex’s inner and outer tangential velocity profiles are combined. The word “combined” is dropped for the sake of convenience.