On the dependence on the formulation of some nonparallel stability approaches applied to the Taylor flow

Abstract

In a study of the stability of the nonparallel Taylor flow in a channel with wall injection, see Taylor [Proc. R. Soc. London, Ser. A 234, 456 (1956)], Lee and Beddini [The 35th AIAA/ASME/ASEE Joint Propulsion Conference and Exhibit, AIAA-99-2508, 20–24 June 1999, Los Angeles, California, 1999] recently reported some discrepancies between their results and those of Casalis et al. [Phys. Fluids 10, 2558 (1998)], whereas they seem to agree perfectly with those of Varapaev and Yagodkin [Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 4, 91 (1969)]. In Casalis et al. [Phys. Fluids 10, 2558 (1998)], the difference with Varapaev and Yagodkin [Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 4, 91 (1969)] has not been clarified, so that it seems important to explain that the discrepancies do not come from a mistake but from a different choice of formulation. In addition, it will be shown that these discrepancies are related to the inconsistent nature of the stability approach which is used in the three papers.