**Significance **

Precession is defined as the change in the orientation of the rotational axis of a rotating body. For most precession-driven flow, the sustained flow states and their dependence on the parameters (the spin and precession rates) are highly nontrivial, regardless of the motion of the container holding the fluid. This aspect has abundant practical applications. As such, numerous studies, some employing direct numerical simulations, have been conducted in a bid to comprehend flow in precessing containers. For instance, it is the phenomenon responsible for the geodynamo behavior of the planet earth.

Presently, studying this phenomenon has been quite difficult as it is challenging to establish a nonlinear theory applicable to the turbulence regime. Worse off, limited information has been obtained in laboratory experiments carried out using state-of-the-art techniques. The main challenge is that, it is quite difficult to measure three-dimensional flow fields in a precessing container.

Recently, Prof. Susumu Goto and Ken Komoda from Osaka University in Japan, presented a study where they conducted Direct Numerical Simulations (DNS), for a precessing body, using a finite difference method, instead of the spectral or finite element methods. The two researchers, in their study, adopted an appropriate grid generation algorithm so as to overcome the notorious problem associated with spherical coordinate. In general, their main objective was to conduct a series of DNS of turbulent flows in precessing spheroids with different values of the ellipticity. Their work is currently published in the research journal, *Physical Review Fluids*.

To begin with, the two researchers revisited studies by Poincaré, Busse and Malkus that show that a small ellipticity significantly affects the flow states in spheroids. The two scholars then conducted DNS of turbulence sustained in slowly precessing spheroids with the absolute value of the ellipticity η being between zero (i.e., a sphere) and 0.2. Lastly, by employing a flexible grid generation algorithm, they effectively simulated flows in an arbitrarily shaped container.

The numerical simulations revealed the three-dimensional turbulent flow structures in the following states. One, a high-energy state where the mean flow was approximated by a uniform-vorticity flow. The other was a low-energy state with twisted mean-flow streamlines, which lead to fully developed turbulence when the Reynolds number was high enough. The mean-flow structures in the low-energy state were seen to be common irrespective of the ellipticity; namely, the main component of the mean flow was a circulation about the axis perpendicular both to the spin and precession axes, but the torsion of the mean-flow streamlines was larger for smaller η.

In summary, the Goto-Komoda study presented DNS of turbulence in precessing spheroids. Remarkably, the simulated velocity fields were in good agreement with the experimental data. In particularly, the two scientists numerically realized bi-stable flow states for a given set of parameters and hysteresis loops connecting them. Altogether, following recent technological advancements and their work input, significant progress of the understanding of this fascinating flow system in a few years is expected. Furthermore, this work is expected to act as a stepping stone for future studies regarding the subject matter.

**Reference**

Ken Komoda,Susumu Goto. **Three-dimensional flow structures of turbulence in precessing spheroids. **Physical Review Fluids, volume 4, 014603 (2019)