Direct numerical simulations of turbulence in a film flowing over a rapidly spinning disc*

We consider the dynamics of a thin liquid film flowing over a rapidly spinning disc. This flow is accompanied by the formation of interfacial waves that originate near the flow inlet and travel towards the disc periphery. Several flow regimes have been identified as a result of previous experimental, modelling, and computational work; these include two-dimensional, transitional three-dimensional, and fully-three-dimensional waves. Reduced-order, weighted residual-type approaches,have been used to model theinterfacial dynamics with some success for moderate flow rates and disc rotational speeds for which the flow remains laminar throughoutthe film. Large eddy simulations have also been utilized to simulate turbulent film flows. In the present work, we use a direct numerical simulations (DNS) approach to examine the flow field within the film in the turbulent regime and its effect on the shapes of the interfacial waves. We start with a divergence-free, synthetic turbulent inflow and demonstrate the emergenceof sustained turbulence downstream of the inletand highlight how it imprints on the interface. An attempt is also made to abstract from the DNS results velocity closures with which to build reliable approximate models.