Turbulence driven by precession in spherical and slightly elongated spheroidal cavities

Phys. Fluids 26, 055107 (2014).

Susumu Goto, Arihiro Matsunaga, Masahiro Fujiwara, Michio Nishioka,Shigeo Kida, Masahiro Yamato, Shinya Tsuda.


Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan and

Department of Mechanical Engineering and Science, Kyoto University, Yoshida-Honmachi, Sakyo, Kyoto 606-8501, Japan and

Department of Mechanical Engineering, Okayama University 3-1-1, Tsushima-naka, Kita, Okayama 700-8530, Japan and

Department of Aerospace Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan and

Organization for Advanced Research and Education, Doshisha University, 1-3, Tatara-miyakodani, Kyotanabe 610-0394, Japan






Motivated by the fascinating fact that strong turbulence can be sustained in a weakly precessing container, we conducted a series of laboratory experiments on the flow in a precessing spherical cavity, and in a slightly elongated prolate spheroidal cavity with a minor-to-major axis ratio of 0.9. In order to determine the conditions required to sustain turbulence in these cavities,and to investigate the statistics of the sustained turbulence, we developed an experimental technique to conduct high-quality flow visualizations as well as measurements via particleimage velocimetry on a turntable and by using an intense laser. In general, flows in a precessing cavity are controlled by two non-dimensional parameters: the Reynolds number Re(or its reciprocal, the Ekman number) which is defined by the cavity size, spin angular velocity,and the kinematic viscosity of the confined fluid, and the Poincaré number Po, which is defined by the ratio of the magnitude of the precession angular velocity to that of the spin angularvelocity. However, our experiments show that the global flow statistics, such as the meanvelocity field and the spatial distribution of the intensity of the turbulence, are almost independent of Re, and they are determined predominantly by Po, whereas the instability of these global flow structures is governed by Re. It is also shown that the turbulence statistics are most likely similar in the two cavities due to the slight difference between their shapes. However, the condition to sustain the unsteady flows, and therefore the turbulence, differs drastically depending on the cavity shape. Interestingly, the asymmetric cavity, i.e., the spheroid, requires a much stronger precession than a sphere to sustain such unsteady flows. The most developed turbulence for a given Re is generated in these cavities when 0.04 ≲ Po ≲ 0.1. In such cases, the sustained turbulence is always accompanied by vigorous large-scale vortical structures, and shearing motions around these large-scale vortices create smaller-scale turbulent vortices. The spatial average of the Taylor-length based Reynolds number of the turbulence in the precessing sphere is about 0.15Re−−−√ for Po = 0.1.


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