The global flow state in a precessing cylinder

Abstract

We examine the fluid flow forced by precession of a rotating cylindrical container using numerical simulations and experimental flow measurements with ultrasonic Doppler velocimetry. The analysis is based on the decomposition of the flow field into contributions with distinct azimuthal symmetry or analytically known inertial modes and the corresponding calculation of their amplitudes. We show that the predominant fraction of the kinetic energy of the precession-driven fluid flow is contained only within a few large-scale modes. The most striking observation shown by simulations and experiments is the transition from a flow dominated by large-scale structures to a more turbulent behaviour with the small-scale fluctuations becoming increasingly important. At a fixed rotation frequency (parametrized by the Reynolds number, $Re$ ) this transition occurs when a critical precession ratio is exceeded and consists of a two-stage collapse of the directly driven flow going along with a massive modification of the azimuthal circulation (the zonal flow) and the appearance of an axisymmetric double-roll mode limited to a narrow range of precession ratios. A similar behaviour is found in experiments which make it possible to follow the transition up to Reynolds numbers of $Re\approx 2\times 10^6$ . We find that the critical precession ratio decreases with rotation, initially showing a particular scaling ${\propto }Re^{-({1}/{5})}$ but developing an asymptotic behaviour for $Re\gtrsim 10^5$ which might be explained by the onset of turbulence in boundary layers.