Turbulent Couette flow up to

Abstract

Two simulations of turbulent Couette flows were performed at friction Reynolds numbers of 1000 and 2000 in a large box of dimensions $L_x=16{\rm \pi} h$ , $L_y=2h$ and $L_z=6{\rm \pi} h$ , where h is the semi-height of the channel. The study focuses on the differences in the intensity and scaling of turbulence at these two Reynolds numbers. The 2000 case showed a lack of a clear log layer with a higher value of the Von Kármán constant $\kappa$ than Poiseuille channels. The intensities were well-scaled in the buffer layer and below, with a second maximum of the streamwise intensity at approximately 350 wall units. Contrary to Poiseuille channels, the dissipation scales close to the wall in wall units. This fact can be attributed to the constant value of the derivative of the streamwise intensity in wall units. The intensities of the 2000 case showed remarkable differences compared with those at Reynolds number 1000 at the channel centre, likely due to the organization of large scales of the streamwise fluctuactions, $u$ . These large scales were thought to be considered ‘infinite’. However, for the 2000 case, while all the structures have a width of $\ell _z \approx 6/8{\rm \pi} h$ , their length varies from $\ell _x \approx 6{\rm \pi} h$ to $\ell _x \approx 16{\rm \pi} h$ , which clearly contradicts the trends obtained in the past. This is a new effect that has not been reported for turbulent Couette flow and points to the uncertainty and sensitivity that is observed for certain statistical quantities.