Modeling of plane Couette flow. I. Large scale flow around turbulent spots

Numerical simulations of a model of plane Couette flow focusing on its in-plane spatio-temporal properties are used to study the dynamics of turbulent spots. While the core of a spot is filled with small-scale velocity fluctuations, a large-scale flow extending far away and occupying the full gap between the driving plates is revealed upon filtering out small scales. It is characterized by streamwise inflow towards the spot and spanwise outflow from the spot, giving it a quadrupolar shape. A correction to the base flow is present within the spot in the form of a spanwise vortex with vorticity opposite in sign to that of the base flow. The Reynolds stresses are shown to be at the origin of this recirculation, whereas the quadrupolar shape of the in-plane flow results from the transport of this recirculation by the base flow that pumps it towards the spot in the streamwise direction and flushes it in the spanwise direction to insure mass conservation. These results shed light on earlier observations in plane Couette flow or other wall flows experiencing a direct transition to turbulence by spot nucleation. (c) 2007 American Institute of Physics.