A novel rapid methodology for generating bilayer base-flow solutions involving surface patterning

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Abstract
Two bilayer flow arrangements, involving either (i) shear- or (ii) gravity-driven fluids, are explored in the presence of a periodically repeating surface topography. Key simplifying assumptions are that the flow is considered two-dimensional and inertialess. The solutions are obtained utilising a novel first-integral representation of the Navier–Stokes equations, leading to a highly efficient methodology for generating the accompanying flow structure within the layers in tandem with the disturbance experienced by the internal interface separating them—for configuration (ii) this extends also to the upper layer’s free-surface shape. Representative examples of each flow type, with a change of key parameters, are provided with particular emphasis on (ii).
Funding Information
  • Hochschule Heilbronn

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