Gravity Driven Flow Past the Bottom with Small Waviness

We propose an introductory study of gravity driven Stokesian flow past the wavy bottom, based on Adler’s et al. papers. In examples the waviness is described by a sinus function and its amplitude is small, up to O(ε2). A correction to Hagen-Poiseuille’s type free-flow solution is found. A contribution of capillary surface tension is discussed.