Quasilinear Simulation of Annular Pipe Flows*

Fluid flowing in long pipes undergo a transition from laminar to turbulent as the speed of the flow increases. We seek to understand this transition by constructing a minimal reduced model for the flow. Our main tool is a the quasi-linear (QL) approximation, which has a long history beginning at least as early as the 1950s. The flow is Reynolds decomposed into the sum of a mean component and fluctuations.  The mean flow is chosen to be the average of the velocity and pressure over the azimuthal angle. We investigate whether the transition to turbulence can be captured by the QL approximation.