Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness

Abstract

Highly turbulent Taylor–Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations with an immersed boundary method) to determine the effects of the spacing and spanwise width ss of the spanwise-varying roughness on the total drag and on the flow structures. We apply sandgrain roughness, in the form of alternating rough and smooth bands to the inner cylinder. Numerically, the Taylor number is O(109)O(109) and the roughness width is varied in the range 0.47⩽s~=s/d⩽1.230.47⩽s~=s/d⩽1.23 , where dd is the gap width. Experimentally, we explore Ta=O(1012)Ta=O(1012) and 0.61⩽s~⩽3.740.61⩽s~⩽3.74 . For both approaches the radius ratio is fixed at η=ri/ro=0.716𝜂=ri/ro=0.716 , with riri and roro the radius of the inner and outer cylinder respectively. We present how the global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacing s~s~ . Both numerically and experimentally, we find a maximum in the angular momentum transport as a function of s~s~ . This can be attributed to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, leading to correspondingly large-scale turbulent vortices.