Conical shear-driven parametric instability of steady flow in precessing spheroids

Significance 

It is well known that in a container rotating at a constant angular velocity Ωs, the flow of a confined viscous fluid always tends to solid-body rotation irrespective of the initial conditions and of the container shape. Consequently, the sustainment of a nontrivial flow of confined fluid requires a time-dependent rotation of the container. One approach to achieve this is to change the sign or magnitude of Ωs of the angular velocity in time. Recent research has shown that the precession of a container realizes a surprising variety of flows of confined fluid. In particular, the fact that a weak precession sustains fully developed turbulence has been attracting the attention of researchers in many fields. The most important control parameter of the precession-driven flow is the Poincaré number (Po) which indicates the magnitude of the precession. On the other hand, the Reynolds number (Re) or the Ekman number, is the indicator of the spin rate. Nonetheless, it still remains a fundamental question how the flow state in a precessing container changes as Po increases for a fixed Re.

Previous studies showed that when Po is sufficiently small, the flow is steady in the precession frame, which rotates at Ωp with respect to the laboratory frame. Then, as Po increases, the steady flow becomes unstable to bifurcate to periodic flow and then to turbulence. It is therefore important to determine the first bifurcation point, namely the critical Poincaré number Po(c) as a function of Re and the container shape. To address this, Assistant professor Yasufumi Horimoto from the Tokyo University of Science, in collaboration with Atsushi Katayama and Professor Susumu Goto at the Osaka University, proposed to investigate experimentally the instability of steady flow of fluid confined in weakly precessing spheroids. Further, they focused on showing that conical-shear instability (CSI) can grow in spheroidal containers in addition to revealing the condition for the instability. Their work is currently published in the research journal, Physical Review Fluids.

Ideally, there are three possible instabilities of the steady flow driven by precession: namely, elliptical instability, shearing instability, and CSI. The instability of steady flow in the spheroids is more complicated than the case for a sphere because all three of the instabilities may occur. To address the issues raised, the team conducted long-time velocity measurements in two precessing spheroids whose ellipticities were O(0.1) and a sphere by using particle image velocimetry (PIV), which was validated by laser Doppler velocimetry.

From the experiments undertaken, the authors reported remarkable consistency with the theoretical predictions (Po(c) ∝ Re−4/5) reported in preceding literature, i.e. via numerical simulation and the flow visualization, which was evidence that CSI grows in the sphere. Furthermore, they showed that for the spheroids with the ellipticity η = O(0.1), CSI leads Po(c) ∝ Re−3/10 in the examined Re range.

In summary, well controlled laboratory experiments to investigate the instability of steady flow sustained in a slowly precessing sphere and spheroids were conducted and presented. It was seen to be interesting how the peaks of the spectra which stem from the nature of the PIV, enabled the researchers estimate the magnitude ω of the angular velocity of the circulation of the steady or weakly unsteady internal flow. Nonetheless, the estimations were in good agreement with the theory. In a statement to Advances in Engineering, the authors pointed out that their experimental results perfectly supported the theoretical predictions, implying that CSI can grow in precessing spheroids.

Conical shear-driven parametric instability of steady flow in precessing spheroids - Advances in Engineering

About the author

Dr. Yasufumi Horimoto, (Current position) Specially Appointed Assistant Professor of Laboratory for Flow Control, Faculty of Engineering, Hokkaido University

ORCID: 0000-0002-1792-1282

About the author

Dr. Susumu Goto, Professor of Fluid Mechanics, Graduate School of Mechanical Engineering, Osaka University

ORCID: 0000-0001-7013-7967

Reference

Yasufumi Horimoto, Atsushi Katayama, Susumu Goto. Conical shear-driven parametric instability of steady flow in precessing spheroids. Physical Review Fluids; volume 5, 063901.

Go To Physical Review Fluids

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