On the precession of a resonant cylinder

A fluid contained in a rotating cylinder has an inertial mode which is excited by forced precession of the container. Wood's (1965, 1966) early work specifically excluded resonance phenomena. Recently McEwan (1970) has discussed resonance phenomena for strong amplitude of excitation, corresponding to rapid precession in this work.In this paper the magnitude of the resonant response for small precession rate is precisely calculated by matching the Ekman layer suction to the precessional forces. The procedure is to find the resonant mode v₁, compute its boundary layers, $\tilde{{\bf v}}_1$, and the associated Ekman layer suction. The second-order problem has a solvability condition which is satisfied by matching the Ekman layer suction to the precession.