Decay of staggered roughness generated turbulence in a low Re number channel flow

Abstract Relaxation of the turbulent and fluctuating passive scalar fields generated by a specific staggered roughness distribution in the entrance region of an initially laminar channel flow is studied through direct numerical simulations. Large staggered roughness elements of height k = 0.27 H partly recover the entry zone, prior to a smooth channel (control channel) wherein both the turbulent flow and scalar fields decay, because the Karman (friction) number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>e</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>H</mml:mi> <mml:mover> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> <mml:mo stretchy="true">_</mml:mo> </mml:mover> <mml:mo>/</mml:mo> <mml:mi>ν</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>70</mml:mn> </mml:math> is significantly below the subcritical limit. Here u τ stands for the friction velocity, and H for the channel half width. Despite the low Reynolds numbers, the roughness elements are able to trigger the by-pass transition mechanism leading to massive clusters of quasi-streamwise vortices entering into the smooth channel. The characteristics of the turbulence decay at the centerline of the control channel collapse with those of a homogeneous isotropic turbulence. Despite the fact that the turbulent activity decreases and the flow approaches relaminarization, the Nusselt number averaged over large streamwise distances in the smooth channel remains close to a fully developed turbulent flow.