Precessional flows in cylinders: Resonance, instabilities, and mixing
Phys. Rev. Fluids 10, 114803 – Published 14 November, 2025
DOI: https://doi.org/10.1103/bllw-by4d
Abstract
Precessional flows arise in a precessing cylinder or in a rotating cylinder with a precessing tilted top. Alternatively, a similar flow can be observed in a partially filled rotating cylinder tilted with respect to the vertical, since the free surface undergoes precession in the cylinder's reference frame. Here, we unify the various models developed for these three configurations. The base flow consists of a superposition of inertial modes (Kelvin modes) with an azimuthal wave number . Each Kelvin mode reaches resonance when the cylinder height is a multiple of half its wavelength, leading to complex dynamics even under weak precessional forcing. In the inviscid linear model, the amplitude of the Kelvin mode diverges at resonance. However, its saturation can be accurately predicted by incorporating both viscous and nonlinear effects, in good agreement with experimental and numerical results. For strong precessional forcing, the resonant Kelvin mode becomes unstable due to a triadic instability involving two additional Kelvin modes whose azimuthal wave numbers differ by 1. This nonlinear interaction enables an analytical prediction of the growth rate and critical onset amplitude, with results that closely match experiments and simulations. Finally, we discuss the mixing efficiency of precessional flows based on numerical simulations using nondiffusive tracers and experiments using a diffusive dye.
