Patterns and dynamics in transitional plane Couette flow

Near transition, plane Couette flow takes the form of large-scale, oblique, and statistically steady alternating bands of turbulent and laminar flow. Properties of these flows are investigated using direct numerical simulation in a tilted computational domain. Four regimes—uniform, intermittent, periodic, and localized—are characterized. The Fourier spectrum along the direction of variation of the pattern is presented, and the component corresponding to the pattern wavenumber is investigated as an order parameter. The mean flow of a periodic pattern is characterized and shown to lead to a relation between the Reynolds number and the wavelength and angle of a pattern.