Triadic instability of a non-resonant precessing fluid cylinder

TL;DR

This paper investigates the stability of a precessing fluid cylinder, revealing a triadic resonance mechanism involving Kelvin modes, which broadens understanding beyond previously studied resonant forcing cases.

Contribution

It introduces a comprehensive analysis of non-resonant precessional flow instability, deriving amplitude equations and instability thresholds for the first time.

Findings

Identifies triadic resonance as a key instability mechanism.

Derives explicit expressions for growth rates and thresholds.

Extends stability analysis to non-resonant precessional flows.

Abstract

Flows forced by a precessional motion can exhibit instabilities of crucial importance, whether they concern the fuel of a flying object or the liquid core of a telluric planet. So far, stability analyses of these flows have focused on the special case of a resonant forcing. Here, we address the instability of the flow inside a precessing cylinder in the general case. We first show that the base flow forced by the cylinder precession is a superposition of a vertical or horizontal shear flow and an infinite sum of forced modes. We then perform a linear stability analysis of this base flow by considering its triadic resonance with two free Kelvin modes. Finally, we derive the amplitude equations of the free Kelvin modes and obtain an expression of the instability threshold and growth rate.