Turbulent plane Couette flow subject to strong system rotation

Abstract

System rotation is known to substantially affect the mean flow pattern as well as the turbulence structure in rotating channel flows. In a numerical study of plane Couette flow rotating slowly about an axis aligned with the mean vorticity, Bech & Andersson (1996a) found that the turbulence level was damped in the presence of anticyclonic system rotation, in spite of the occurrence of longitudinal counter-rotating roll cells. Moreover, the turbulence anisotropy was practically unaffected by the weak rotation, for which the rotation number Ro, defined as the ratio of twice the imposed angular vorticity Ω to the shear rate of the corresponding laminar flow, was ±0.01. The aim of the present paper is to explore the effects of stronger anticyclonic system rotation on directly simulated turbulent plane Couette flow. Turbulence statistics like energy, enstrophy and Taylor lengthscales, both componental and directional, were computed from the statistically steady flow fields and supplemented by structural information obtained by conditional sampling.

The designation of the imposed system rotation as ‘high’ was associated with a reversal of the conventional Reynolds stress anisotropy so that the velocity fluctuations perpendicular to the wall exceeded those in the streamwise direction. It was observed that the anisotropy reversal was accompanied by an appreciable region of the mean velocity profile with slope ∼2Ω, i.e. the absolute mean vorticity tended to zero. It is particularly noteworthy that these characteristic features were shared by two fundamentally different flow regimes. First, the two-dimensional roll cell pattern already observed at Ro=0.01 became more regular and energetic at Ro=0.10 and 0.20, whereas the turbulence level was reduced by about 50%. Then, when Ro was further increased to 0.50, a disordering of the predominant roll cell pattern set in during a transient period until the flow field settled at a new statistically steady state substantially less affected by the roll cells. This was accompanied by a substantial amplification of the streamwise turbulent vorticity and an anomalous variation of the mean turbulent kinetic energy which peaked in the middle of the channel rather than near the walls. While the predominant flow structures of the non-rotating flow were longitudinal streaks, system rotation generated streamwise vortices, either ordered secondary flow or quasi-streamwise vortices. Eventually, at Ro=1.0, the turbulent fluctuations were completely suppressed and the flow field relaminarized.