The relation between Taylor-Dean flow and rotating curved channel flow

This study shows that a mathematical equivalence exists between rotating curved channel flow (RCCF) and Taylor-Dean (TD) flow. This equivalence relation explains the similarity of results for these two flow configurations that has been frequently remarked upon but not explained. In particular, it is shown that every RCCF flow corresponds to a TD flow. The equivalence is demonstrated by using TD flow to perform calculations of the stability of RCCF, while a stability criterion previously derived for RCCF is shown to be a restatement of Rayleigh’s well-known inviscid criterion on applying the equivalence relation.The identification of this relation between the two flow configurations allows for fresh perspectives and insights on flow phenomena and mechanisms, and the formation of the stability peak that has been observed in RCCF is discussed in relation to the narrowing and subsequent separation of the TD neutral stability surface that occurs as the Poiseuille flow component is increased. This narrowing and separation process further explains why TD and RCCF flows are dominated by non-axisymmetric modes at their stability peaks. One difference in the reported results for these two flow configurations, namely that RCCF can be restabilised for large enough rotation rates whereas such a phenomenon has not been observed in the TD studies, is further explained with reference to the different slices these flows make through the TD neutral surface.