PIV OF A PRECESSING CYLINDER FLOW AT LARGE TILT ANGLES

Abstract

Planar particle image velocimetry measurements of the flow in a precessing cylinder are presented for nutation angles of up to 15◦. For a case of a moderate Reynolds number, we observe a rapid transition to a disordered state with a brief appearance of structures of high azimuthal wave numbers. Similarity to observations reported in previous experiments and numerical simulations at much lower tilt angle, but higher Poincare number suggests, a triadic resonance as the transition mechanism. Amplitudes of the forced mode and the mean streaming flow are extracted; their scaling with Reynolds number is found to agree reasonably well with weakly nonlinear theory. INTRODUCTION AND BACKGROUND Rotating flows are present in the atmosphere, in oceans and lakes, and also in astrophysical and many technical applications. A rotating system allows for inertial waves to exist owing to the restoring effect of the Coriolis force. One way to excite inertial waves is precession, the simultaneous rotation around two axes as sketched in Figure 1: a cylinder, tilted through an angle α and rotating at an angular frequency Ω1, is mounted on a turntable which rotates at Ω2. Precession is considered as a possible driver for the geo-dynamo, i.e., the creation of Earth’s magnetic field. Also, liquid fuel in spin-stabilised spacecraft may be subject to precessional forcing, destabilising the whole spacecraft (Manasseh, 1993). Some types of instability and transition of rotating flows may be associated with Kelvin modes, the linear, inviscid eigenmodes of solid-body rotation flow. These modes are not solutions of the full Navier-Stokes equations with no-slip boundary conditions. Yet in the weakly nonlinear regime they have proven to be useful diagnostics of experimental and numerical observations (Meunier et al., 2008; Blackburn et al., 2014). Each Kelvin mode is characterised by three integer indices (n, l,m) corresponding to axial, radial, and azimuthal directions, respectively, and is associated with a frequency. Velocity components of Kelvin modes all have radial profiles ui(r), vi(r), wi(r) consisting H R α Ω1 Ω2