EXPERIMENTAL EVIDENCE OF NON-LINEAR RESONANCE EFFECTS BETWEEN RETROGRADE PRECESSION AND THE TILT-OVER MODE WITHIN A SPHEROID

Abstract

The Poincare flow (also known as the tilt-over mode) in a precessing cavity filled with water is investigated experimentally. Assuming that the flow is mainly a solid-body rotation, we have used three independent techniques to determine this rotation: introduction of light ceramic particles to materialize the fluid rotation axis, pressure measurements at the cavity wall, and ultrasonic Doppler anenometry. With the latter technique, we determine the angle between the solid body rotation vector and the cavity axis indirectly, through the secondary flow - oblique shear layers which are stationary in a frame rotating at the precession rate - that the differential rotation at the boundary induces within the fluid. Rapid changes in the direction of the axis of rotation of the fluid for critical values of the rate of precession and of the rate of rotation are demonstrated. In some cases, the inclination of the fluid rotation vector with respect to the cavity axis much exceeds the inclination of the prescribed precession vector. A torque approach, which can be generalized, shows that this effect is due to a non-linear resonance between the frequencies of the Poincare mode and of precession. As a result, we can determine the validity domain of current models of precession and nutations of planets enclosing a fluid core.