Impulse response of turbulent flow in smooth and riblet-walled channels to a sudden velocity increase

Abstract

ABSTRACT This paper explores the use of a small-span direct numerical simulation for a transient, smooth-wall turbulent channel flow and then applies the small-span simulation to a transient channel flow with riblets. A flow configuration similar to that of S. He and M. Seddighi (J Fluid Mech. 2013;715:60–102) is used to study the impulse response of a half-height channel flow to an abrupt increase in bulk velocity (with a friction Reynolds number increasing from 180 to 418). A minimal domain span sufficient to include the near-wall quasi-streamwise vortices in the ‘healthy turbulence’ region is used. The turbulent flow undergoes reverse transition toward a quasi-laminar state, followed by a retransition phase to the new equilibrium state. On a smooth wall, detailed comparisons with a full-span case show that the small-span test case captures satisfactorily the essential dynamics during the entire transition process, although it yields a slight delay in recovery to the new equilibrium. This difference is attributed to a slower streak transient growth due to an underestimation of near-wall spanwise fluctuations. This underestimation is associated with the missing large attached eddies that are not contained in the small span of the simulation domain. These comparisons justify the use of small-span simulations for identifying the main flow physics in a non-equilibrium accelerating wall turbulence. The application to the riblet flow shows that riblets do not fundamentally affect the flow dynamics, but delay the retransition as a result of significantly milder streak meandering. The streak-stabilisation effect of riblets is still active in a strongly accelerating turbulence and tends to prolong the flow recovery.