Calculations of laminar viscous flow over a moving wavy surface

The steady, laminar, incompressible flow over a periodic wavy surface with a prescribed surface-velocity distribution is found from the solution (via Newton's method) of the two-dimensional Navier–Stokes equations. Validation runs have shown excellent agreement with known analytical (Benjamin 1959) and analytico-numerical (Bordner 1978) solutions for small-amplitude wavy surfaces: For steeper waves, significant changes are observed in the computed surface-pressure distribution (and consequently in the nature of the momentum flux across the interface) when a surface orbital velocity distribution, of the type found in water waves, is included,