Surface-roughness restricts families of exact coherent structures in wall-bounded flows

Sabarish Vadarevu, Ati Sharma, Bharathram Ganapathisubramani

Published 2016-12-22Version 1

Recent progress indicates that highly symmetric recurring solutions of the Navier-Stokes equations such as equilibria and periodic orbits provide a skeleton for turbulence dynamics in state-space. Many of these solutions have been found for smooth-walled plane Couette, channel, and pipe flows. Rough-walled flows are of great practical significance, yet no recurring solutions are known for these flows. We present a numerical homotopy method to continue solutions from smooth-walled flows to corresponding rough-walled flows, illustrated here for grooved Couette flow at a Reynolds number of 400. Loss of spanwise homogeneity reduces continuous families of solutions, identical up to translational shifts, in smooth Couette flow to multiple discrete families in grooved Couette flow. The discrete families are ones that can preserve the discrete symmetries of Couette flow. Continuation of these solutions suggests that the exact coherent structures of smooth-walled flows also dominate rough-walled flows. Reduction of continuous families to discrete families implies that turbulence statistics in grooved Couette flow, and rough-walled flows by extension, must retain the spatial variation of exact solutions. These results raise important questions concerning the role of symmetries in understanding rough-walled turbulence.