On the stability of medium gap corotating spiral Poiseuille flow

Abstract

New features of the linear stability of the spiral Poiseuille flow for a wide range of inner and outer independent rotation speeds of the cylinders and imposed axial pressure gradient are investigated. The analysis is focused on the corotating situation and for a particular radius ratio η=0.5. Unexpected changes in the angle of the bifurcated spiral regimes are found for moderate values of the axial speed as the outer rotation is increased. In particular, tricritical points are detected, where modes associated with azimuthal wave numbers of opposite signs coexist at criticality. The present study is extended to high values of the axial speed of the flow and, to the authors’ knowledge, the complete critical surface in the three-dimensional parameter space is obtained for the first time, providing new results on the behavior of the Tollmien-Schlichting instability. Increasing the rotation rate of the outer cylinder, the Tollmien-Schlichting instability is no longer dominant, resulting in a dramatic decrease in the critical axial Reynolds number. The sudden appearance of turning points in the critical curves recently obtained by other authors is also explained in terms of the geometry of the critical surface.