Influence of the precession angle on the flow inside a precessing cylinder

Precession driven flows are potential drivers for dynamo action in the Earth [1], the ancient moon, and some asteroids. As part of the DRESDYN project at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) a precession-driven dynamo experiment is presently under construction, which consists of a liquid sodium filled cylinder with a radius of 1 m and a height of 2 m respectively. The cylinder rotates with a frequency of up to 10 Hz and precess around the second axis with a frequency of up to 1 Hz [2].
To understand the hydrodynamics in a precessing cylinder a downscaled 1:6 water mockup was built with the same aspect ratio and rotation frequencies. The typical non-axisymmetric Kelvin mode that grows as the precession ratio rises is alone not suitable for dynamo action in the experiment. However, a secondary axisymmetric mode that emerges in a small region of the precession ratio was shown to be very promising for dynamo action in the sodium experiment [3].
The ability to predict dynamo behaviour for different precession ratios and precession angles requires a thorough understanding of the flow structure in the precessing cylindrical vessel. Consequently, we have performed series of precession measurements with Ultrasonic flow velocimetry (UDV) on the downscaled water experiment with various precession angles α at 60o, 75o, 90o [4]. In this paper, we present the effect of precession angle and rotation direction (i.e. prograde or retrograde) on the dominant flow modes, and quantify this behaviour in dependence of the rotation rate parameterized by the Reynolds number Re = ΩcR2/ν and the precession ratio Po = Ωp/Ωc, with ν the viscosity and Ωp = 2πfp the angular frequency of the precession. We have not taken into account the effect of the precession angle, which changes the definition of Reynolds number. The experimental results are supported by numerical simulations.