Numerical simulation of banded turbulence in plane Couette flow

An analogy exists between Taylor-Couette and plane Couette flow. Both are driven by differential mo-tion of their boundaries in the azimuthal ( ) or streamwise ( ) direction, and contain another homoge-neous direction ( ), termed axial or spanwise, for the respective flows, whose extent is usually taken as infinite in theoretical analyses and large in experiments. Spiral turbulence, an intriguing state in which a region of turbulent flow spirals around a laminar region, was observed in Taylor-Couette flow by Andereck et al. [1] and Hegseth et al. [2]. By using an experimental apparatus with a very narrow gap ), Prigent et al. [3] were able to produce a spiral turbulent state containing several regular rep-etitions of the pattern and to measure the dependence of azimuthal and axial wavelength on Reynolds number. They also discovered that such a state exists in plane Couette flow as well, where it takes the form of oblique bands, oriented at an angle to the streamwise direction. We have carried out numerical simulations of plane Couette flow using Prism, a spectral element code written by Henderson [4]. An appealing feature of the banded turbulent flow is that the Reynolds numbers at which it occurs are relatively low. The major numerical challenge is the large size of the domain, necessitated by the fact that the streamwise and spanwise wavelengths of the turbulen