Study of drag reduction using periodic spanwise grooves on incompressible viscous laminar flows

Engineered surface textures can manipulate boundary layers affecting fluid drag. We study periodic, infinitely long spanwise grooves on a laminar boundary layer over a plate for 1000 $R\phantom{\rule{0}{0ex}}{e}_{L}$ 25000. Below a certain width-to-depth aspect ratio (AR), a primary vortex inside each groove causes the freestream to ``slip over'', reducing skin friction. Increasing AR poses a tradeoff in drag reduction due to pressure drag from groove vertical walls. Overall, transverse grooves for laminar flow can reduce total drag up to 10% compared to a flat plate, despite increasing the wetted surface area.