Nonlinear axisymmetric Taylor–Couette flow in a dilute gas: multiroll transition and the role of compressibility

In this work, the asymmetric 2-roll modes (called the single-roll or ‘anomalous’ modes), that break the midplane \(Z_2\)-symmetry, are uncovered at \(\Gamma \leq O(1)\), where \(\Gamma = h/ \delta\) is the aspect ratio with \(h\) being the height of the cylinders and \(\delta\) being the gap width. The phase boundaries of both symmetric and asymmetric rolls and the coexisting regions of different number of rolls are identified in the \((\Gamma , Re )\)-plane, where \(Re\) is the inner Reynolds number. We were able to show that the ‘\(1 \leftrightarrow 2\)’-roll transition in small aspect ratio cylinders is subcritical in compressible TCF in contrast to the supercritical nature of bifurcation in its incompressible counterpart. This work was published in the Journal of Fluid Mechanics.