Large axisymmetric surface deformation and dewetting in the flow above a rotating disk in a cylindrical tank: Spin-up and permanent regimes

In this paper, we aim at characterizing the spin-up process and the permanent regime of a rotating flow with free surface. The motion is created by the quasi-impulsive rotation of a disk located at the bottom of a cylindrical tank partially filled with a Newtonian water-glycerol mixture at a fixed initial aspect ratio (height to radius) of 0.25. Two experimental setups with different radius sizes and two numerical codes with distinct formulations are used, allowing for numerous comparisons and cross validations. Time-dependent surface height profiles and azimuthal velocity profiles are accurately measured with a laser line sensor and Laser Doppler Velocimetry, respectively. These measurements are compared to numerical results showing an overall excellent agreement and whenever a discrepancy exists, explanations are given. The spin-up and permanent regime for two typical flow cases are detailed: (i) one for which the angular speed moderately deforms the free surface and (ii) one at higher angular speed for which the disk becomes partially dewetted. The shape of the free surface in the permanent regime for intermediate rotation speeds is also reported. The flow parameters are chosen in such a way that large deformations of the free surface are achieved, yet remaining under the threshold of appearance of rotating polygonal patterns. This enables us to characterize realistic base flows on which this instability may develop.