Evolution of waves in inertia-dominated thin liquid films flowing over a rapidly rotating disc

We study the complex wave regimes in thin film flows over rotating discs through direct numerical simulations (DNS) using a volume-of-fluid approach. Agreement is shown between the DNS results, and experimental data from the literature on global wave features over the disc and local measurements of the film height. With increasing inertial levels, the length of the smooth waveless zone decreases, wave intensity increases, and there is a transition from axisymmetric and spiral waves to three-dimensional waves. The evolution to complex three-dimensional waves begins with a destabilising periodic disturbance of the two-dimensional wavefront. This perturbed wavefront experiences differences in acceleration along the radial direction, amplifying the effect, ultimately leading to small wave humps that break away. A detailed analysis of the flow field within the liquid film shows how the local strain rate is influenced significantly by the presence of the primary wave and the smaller capillary ripples that precede. The parabolic, self-similar shape of velocity profiles within the film are also assessed.