The global flow state in a precessing cylinder

TL;DR

This study investigates the flow dynamics in a precessing cylinder through simulations and experiments, revealing a transition from large-scale flow dominance to turbulence at a critical precession ratio, with implications for understanding geophysical and industrial flows.

Contribution

The paper introduces a combined numerical and experimental analysis of precession-driven flow, identifying the transition to turbulence and the scaling of the critical precession ratio with Reynolds number.

Findings

Flow energy is concentrated in a few large-scale modes.

A transition to turbulence occurs at a critical precession ratio.

The critical precession ratio scales as Re^(-1/5) at lower Re and saturates at higher Re.

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 (UDV). 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, ${\rm{Re}}$) 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 ${\rm{Re}}\approx 2\times 10^6$. We find that the critical precession ratio decreases with rotation, initially showing a particular scaling $\propto {\rm{Re}}^{-\frac{1}{5}}$ but developing an asymptotic behaviour for ${\rm{Re}}\gtrsim 10^5$ which might be explained by the onset of turbulence in boundary layers.