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In an earlier paper, Oruba, Soward & Dormy (J.Fluid Mech., vol.818, 2017,pp.205-240) considered the primary quasi-steady geostrophic (QG) motion of aconstant density fluid of viscosity $\nu$ that occurs during linear spin-downin a cylindrical container of radius $L$ and height $H$, rotating rapidly(angular velocity $\Omega$) about its axis of symmetry subject to mixed rigidand stress-free boundary conditions for the case $L=H$. Direct NumericalSimulation (DNS) at large $L= 10 H$ and Ekman number $E=\nu/H^2\Omega=10^{-3}$by Oruba, Soward & Dormy (J.Fluid Mech., sub judice and referred to as Part I)reveals significant inertial wave activity on the spin-down time-scale. Theanalytic study in Part I, based on $E\ll 1$, builds on the results of Greenspan& Howard (J.Fluid Mech., vol.17, 1963, pp.385-404) for an infinite plane layer$L\to\infty$. At large but finite distance $r^\dag$ from the symmetry axis, themeridional (QG-)flow, that causes the QG-spin down, is blocked by the lateralboundary $r^\dag=L$, which provides the primary QG-trigger for the inertialwaves studied in Part I. For the laterally unbounded layer, Greenspan & Howardalso identified inertial waves of maximum frequency (MF), which are amanifestation of the transient Ekman layer. The blocking of the MF-waves by thelateral boundary provides a secondary MF-trigger for yet more inertial waves.Here we obtain analytic results for the wave activity caused by thecombined-trigger (QG+MF) that faithfully captures the character of thelaterally unbounded base flow including its transients. The results arecompared with the inertial wave part of the DNS (the so called "filtered DNS"or simply "FNS"), for which the agreement is excellent and accounts for minordiscrepancies evident in the Part I results for the QG-trigger.

The inertial wave activity during spin-down in a rapidly penny shaped cylinder. Part II The inertial wave of maximum frequency trigger