Vortices by design in pipe flow by a mechanism of Langmuir circulation

Using DNS we study a mechanism for creating secondary flow by design in the form of longitudinal vortices in pipe flow. By furnishing the pipe wall with a pattern of crossing waves, vorticity already present in the wall boundary layer is rotated into the streamwise direction by a resonant kinematic mechanism known in oceanography as `CL1' (Craik & Leibovich's 1st mechanism), one of the drivers of Langmuir circulation. CL1 is strongest when the wall waves cross at an acute angle of $\varphi \sim 10^\circ$ to $20^\circ$ (a `contracted egg carton' pattern), vanishes in the vicinity of $45^\circ$ and is weak and oppositely directed for larger angles (`protracted egg carton'). The results are compared to a simple theory in the vein of Craik (1970).\\ \\ CL1 co-exists with a dynamic mechanism of secondary motion due to the asimuthally varying wall rougness caused by the pattern. For the `contracted' pattern the two effects oppose each other with CL1 prevailing, whereas the dynamic effect dominates at $45^\circ$ and above, causing a reversal of circulation. Flow reversal also results with increasing amplitude due to flow separation.\\ \\ We presently report only laminar simulations; the effect on turbulent pipe flow is a potentially important question for the future.