Velocity profiles in strongly turbulent Taylor-Couette flow

Abstract

We derive the velocity profiles in strongly turbulent Taylor-Couette flow for the general case of independently rotating cylinders. The theory is based on the Navier-Stokes equations in the appropriate (cylinder) geometry. In particular, we derive the axial and the angular velocity profiles as functions of distance from the cylinder walls and find that both follow a logarithmic profile, with downwards-bending curvature corrections, which are more pronounced for the angular velocity profile as compared to the axial velocity profile, and which strongly increase with decreasing ratio $\eta$ between inner and outer cylinder radius. In contrast, the azimuthal velocity does not follow a log-law. We then compare the angular and azimuthal velocity profiles with the recently measured profiles in the ultimate state of (very) large Taylor numbers. Though the {\em qualitative} trends are the same -- down-bending for large wall distances and (properly shifted and non-dimensionalized) angular velocity profile ${\omega }^{+}(r)$ being closer to a log-law than (properly shifted and non-dimensionalized) azimuthal velocity profile $u_{\phi }^{+}(r)$ -- {\em quantitative} deviations are found for large wall distances. We attribute these differences to the Taylor rolls and the height dependence of the profiles, neither of which are considered in the theoretical approach.

References in corpus (5)

• Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection
• Optimal Taylor-Couette flow: direct numerical simulations
• Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow
• Heat transport by turbulent Rayleigh-Bénard convection for $\Pra\ \simeq 0.8$ and $4\times 10^{11} \alt \Ra\ \alt 2\times10^{14}$: Ultimate-state transition for aspect ratio $\Gamma =1.00$
• Logarithmic temperature profiles in the ultimate regime of thermal convection

Cited by in corpus (12)

• High Reynolds number Taylor-Couette turbulence
• Exploring the phase diagram of fully turbulent Taylor-Couette flow
• Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow
• Direct numerical simulation of Taylor-Couette flow with grooved walls: torque scaling and flow structure
• The near-wall region of highly turbulent Taylor-Couette flow
• Wall roughness induces asymptotic ultimate turbulence
• Disentangling the origins of torque enhancement through wall roughness in Taylor-Couette turbulence
• Anomalous Features in Internal Cylinder Flow Instabilities subject to Uncertain Rotational Effects
• Taylor-Couette turbulence at radius ratio $\eta =0.5$: scaling, flow structures and plumes
• Characterizing the turbulent drag properties of rough surfaces with a Taylor--Couette setup
• Controlling secondary flow in Taylor-Couette turbulence through spanwise-varying roughness
• Calculation of the mean velocity profile for strongly turbulent Taylor--Couette flow and arbitrary radius ratios