Surface wave dynamics of thin film flow over a rotating substrate

Abstract

Thin-film flow over a rotating substrate exhibits intricate surface waves, but their small scales and rapid dynamics make them challenging to analyze. In this study, we present direct three-dimensional observations of these waves, enabling precise quantification of their morphologies, including height, wavelength, and asymmetry. By combining experiments with scaling analysis, we classify global instability patterns under varying flow and rotational conditions. Beyond previously known patterns, we reveal two novel wave behaviors: the symmetric-to-asymmetric wave transition and the formation of capillary ripples. The symmetry transition is governed by the ratio of centrifugal to Coriolis forces (scaling as Ek/Ro, where Ek and Ro are the Ekman and Rossby numbers, respectively), with wave asymmetry inversely proportional to this ratio. High-amplitude asymmetric waves generate capillary ripples ahead of the main wave hump, driven by inertia and centrifugal effects [scaling as Re-r & varepsilon;(2)(RoEk)(-1), where Re is Reynolds number], while lower-amplitude waves do not. This study provides the first microscopic characterization of surface waves on a rotating substrate, firmly linking microscale dynamics to global instability patterns.