Spin-down in rotating Hagen–Poiseuille flow: a simple criterion to detect the onset of absolute instabilities

Abstract

We conduct experiments in a circular pipe with rotating Hagen–Poiseuille flow (RHPF) to which we apply spin-down or impulsive spin-down to rest, in order to analyse the threshold between convective and absolute instabilities through flow visualisations in the inlet region of the pipe. For a constant value of the Reynolds number, $Re$, the finite-amplitude wave packets generated by the arbitrary perturbation that results by reducing the swirl parameter, propagate upstream or downstream depending on the initial value of the swirl parameter, $L_{0}$. In fact, the main characteristic of the flow is that the velocity front of these wave packets changes from negative to positive when absolutely unstable modes are present in the initial state. The experimental results show that spin-down becomes a precise, reliable procedure to detect the onset of absolute instabilities. In addition, we give evidence of a gradual transition for Reynolds numbers ranging from 300 to 500 where a mode shift from $n=-1$ to $n=-2$ appears in the absolutely unstable region.

Nonlinear travelling waves in rotating Hagen–Poiseuille flow

“…In contrast, RHPF can display modes of absolute instability, as was shown by Fernandez-Feria and del Pino (2002). These modes of absolute instability were obtained experimentally in the recent study of Miranda-Barea et al (2016). They applied a spin-down to the pipe and could thus obtain the critical rotation rate for the switch from absolute instabilities to convective.…”

“…The axial flow through a rotating pipe has been studied over decades, both for its fundamental importance and for its wide application in turbomachinery and other fluid machines. Rotation changes the basic nature of the instability of the laminar Hagen-Poiseuille flow (Pedley 1968, 1969, Mackrodt 1976, Cotton and Salwen 1981, Fernandez-Feria and del Pino 2002, Rusak and Wang 2014, Miranda-Barea et al 2016 and the subsequent route towards turbulence. The final turbulent state too is rather different from that in the non-rotating pipe (Imao et al 1996).…”