Scaling of torque in turbulent Taylor-Couette flow with background rotation

We did an experimental study on Taylor-Couette flow in between two coaxial cylinders of length L = 220 mm and radii r i = 110 and r o = 120, respectively, the fluid-filled 'Taylor-Couette gap' or TC-gap being h = 10 mm, thus gap ratio η = r i /r o = 0.917, and gap aspect ratio L/h = 22). Both cylinders are rotating independently, with angular frequencies ω i,o , The torque T on the inner cylinder is measured through the axis driving the inner cylinder with a co-rotating torque meter. The system is characterised with parameters as given by Dubrulle et al. are inner and outer Reynolds number. With this choice, Re S is based on the laminar shear rate S; Re S = h 2 S/ν. The Rotation number Ro compares mean rotation to mean shear; its sign determines cyclonic (Ro > 0, stabilising) or anti-cyclonic (Ro < 0, destabilising) flow. Two other relevant values are Ro i = η − 1 −0.083 and Ro o = (1 − η)/η 0.091 for the inner and the outer cylinder rotating alone, respectively. We have estimated the wall shear stress at the inner wall by τ W,i = T /(2πr 2 i L), and from this the friction factor c F , i.e. non-dimensional wall shear stress, c F = τ //(Sh) 2 is obtained. We have done this for a range of Re S values far beyond those presented in Andereck's classical work [1]. Andereck investigated the occurrence of flow structures in laminar and low turbulent TC flows up to Re S = 4.10 3. Our results up to Re S = 5.10 4 are shown in Fig. 1. We observe that, for a given Ro, the friction factor c F decreases mono-tonically with increasing Re S. This torque-scaling is discussed in much detail in [4], with many references. In [6, 7], we summarise this briefly, and show that we retrieve in our sysstem up to Re S = 2.10 5 very similar torque scaling exponents for Ro = Ro i as in [5]. We further observe that for a given constant Re S the friction factor c F strongly depends on Ro: Friction increases monotonically when Ro decreases especially at lower Reynolds numbers, which clearly shows the role of rotation