The near-wall region of highly turbulent Taylor–Couette flow

Abstract

Direct numerical simulations of the Taylor–Couette (TC) problem, the flow between two coaxial and independently rotating cylinders, have been performed. The study focuses on TC flow with mild curvature (small gap) with a radius ratio of ${\it\eta}=r_{i}/r_{o}=0.909$, an aspect ratio of ${\it\Gamma}=L/d=2{\rm\pi}/3$, and a stationary outer cylinder. Three inner cylinder Reynolds numbers of $1\times 10^{5}$, $2\times 10^{5}$ and $3\times 10^{5}$ were simulated, corresponding to frictional Reynolds numbers between $Re_{{\it\tau}}\approx 1400$ and $Re_{{\it\tau}}\approx 4000$. An additional case with a large gap, ${\it\eta}=0.5$ and driving of $Re=2\times 10^{5}$ was also investigated. Small-gap TC was found to be dominated by spatially fixed large-scale structures, known as Taylor rolls (TRs). TRs are attached to the boundary layer, and are active, i.e. they transport angular velocity through Reynolds stresses. An additional simulation was also conducted with inner cylinder Reynolds number of $Re=1\times 10^{5}$ and fixed outer cylinder with an externally imposed axial flow of comparable strength to the wind of the TRs. The axial flow was found to convect the TRs without any weakening effect. For small-gap TC flow, evidence was found for the existence of logarithmic velocity fluctuations, and of an overlap layer, in which the velocity fluctuations collapse in outer units. Profiles consistent with a logarithmic dependence were also found for the angular velocity in large-gap TC flow, albeit in a very reduced range of scales. Finally, the behaviour of both small- and large-gap TC flow was compared to other canonical flows. Small-gap TC flow has similar behaviour in the near-wall region to other canonical flows, while large-gap TC flow displays very different behaviour.