Bifurcation and instability of annular Poiseuille flow in the presence of stable thermal stratification: Dependence on curvature parameter

Abstract

The bifurcation and instability of nonisothermal annular Poiseuille flow (NAPF) of air as well as water is studied. We have emphasized the impact of a gap between cylinders in terms of curvature parameter (C) for axisymmetric as well as nonaxisymmetric disturbances. The results from the linear stability analysis reveal that the first azimuthal mode acts as a least stable mode of the NAPF of air for relatively small values of C. In this situation, even though for some values of C, the NAPF has supercritical bifurcation, but the same flow may experience subcritical bifurcation under zero azimuthal mode. It has also been observed that for relatively larger values of the Reynolds number (Re) and lower values of C, the NAPF under axisymmetric disturbance always exhibits subcritical bifurcation. However, for small values of Re, the NAPF exhibits only supercritical bifurcation. The finite amplitude analysis predicts only supercritical bifurcation of NAPF of water. The influence of nonlinear interaction of different harmonics on the amplitude profile as well as kinetic energy spectrum is investigated. The amplitude profile possesses a jump in the vicinity of a point where the type of bifurcation is changed. In the subcritical regime, the induced shear production due to modification of the gradient production acts as a main destabilizing factor balanced by the gradient production of kinetic energy.