Abstract
We investigate experimentally the instability of steady flow of fluid confined in weakly precessing spheroids. It is known that the conical-shear instability (CSI) proposed by Lin, Marti, and Noir [Phys. Fluids 27, 046601 (2015)] grows in a precessing sphere, and the elliptical and shearing instabilities [Kerswell, Geophys. Astrophys. Fluid Dyn. 72, 107 (1993)] can grow in precessing spheroids. Previous theories predict that when , where is the Reynolds number defined by the spin angular velocity and the equatorial radius of the spheroid and is its ellipticity, CSI dominates the other two instabilities even in a spheroid, and that, in particular, when the critical Poincaré number (i.e., the critical precession rate) is proportional to for . To experimentally verify these predictions, we measure a long time-series of fluid velocity to accurately estimate the power spectrum. Then, we determine as a function of and show the qualitative change of its scaling depending on . Our experimental results perfectly support the theoretical predictions, implying that CSI can grow in precessing spheroids.
- Received 5 December 2019
- Accepted 19 May 2020
DOI:https://doi.org/10.1103/PhysRevFluids.5.063901
©2020 American Physical Society