Session Ci - Vortex Dynamics.
ORAL session, Sunday, November 23
309, Moscone Center
The conically self-similar vortex of Long (1962) is reconsidered, with a view toward understanding what, if any, relationship exists between it and the recent similarity solutions of Mayer and Powell (1992), which are a rotational-flow analogue of the Falkner-Skan boundary layer flows. It is found that, when minor differences in the formulations are accounted for, the Long and Mayer/Powell (MP) flows in fact satisfy the same system of coupled ODEs, subject to different boundary conditions.
Long's equations thus can be seen as a special case of the MP equations corresponding to conical vortex growth, which can occur only if the outer axial velocity decelerates in a z^-1 fashion, implying a severe adverse pressure gradient. For pressure gradients this adverse MP were not able to find solutions of the similarity equations which satisfied a physicality criterion based on monotonicity of the total-pressure profile of the flow. It is shown that Long's solutions also violate this criterion in an extreme fashion, hence are nonphysical. However, the fact that the Long's flows fit into a more general similarity framework means that nonconical analogues of these flows should also exist. The generalized Long's flows which do satisfy the physicality criterion are described.