A low-dimensional model for turbulent shear flows

We analyse a low-dimensional model for turbulent shear flows. The model is based on Fourier modes and describes sinusoidal shear flow, in which the fluid between two free-slip walls experiences a sinusoidal body force. The model contains a total of nine modes, including modes describing the basic mean velocity profile and its modification, downstream vortices, streaks, and instabilities of streaks, with other modes being a consequence of the nonlinear interactions. The transition to turbulence for the model is subcritical and intermittent, and the distributions of turbulent lifetimes are exponential, in agreement with observations in many shear flows.