Abstract
A numerical method for reconstructing the velocity field of a viscous liquid flowing over unknown topography is presented. For a given fluid this procedure allows one to determine the velocity field as well as the topographic structure from the free-surface shape only. First, we confirm the results with previous computations in the thin-film limit and then generalize the numerical solution to arbitrary film thicknesses and focus on the velocity field. It is documented that even smoothly corrugated free-surface shapes require strongly undulated topographies to maintain the flow structure. Finally, we discuss details of the implementation in applications, solvability in general, and sensitivity of the solution.
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