Abstract
We study the spatiotemporal development of a thin viscous film flowing over a spinning disk. A coupled system of evolution equations for the film thickness and volumetric flow rates in the radial and azimuthal directions is derived using the Karman–Polhausen method, assuming a parabolic profile for the film velocity. In the limit of large Eckman number, this system reduces to equations previously used to study the falling film problem. Numerical solutions of the system are obtained starting from initially waveless profiles, which correspond to the Nusselt solution for the case of a spinning disk. Results from these simulations reveal the development of finite-amplitude waves, which, locally, approximate closely to the shape of quasisteady periodic traveling waves. These waves are found to be in good agreement with the predictions of the localized version of the model.
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