The quasilinear behavior of convective turbulence with sheared flows

In the present contribution, the quasilinear dynamics of convective turbulence is studied. In essence, and contrary to the "frozen gradient" assumption, the quasilinear approach takes into account the back-reaction of the convective flux on the mean gradient driving the instability. The dynamical regulation of convective transport by a sheared mean flows is also included. Close to the instability threshold it naturally gives rise to a transition from low to high confinement modes. Further away, regular relaxation oscillations are sustained. In this time-dependent state, each transient maximum of the convective flux activity triggers a ballistic transport event observed on the mean profile. The period of the oscillations is not controlled by the nonlinearity but by the dissipation on the mean flow. A "Dimits-shift" regime is thus identified in the limit of zero damping on the mean flow. This infinite period cycle corresponds to a single ballistic transport event triggered before the system settles into its diffusive state. Far away from the threshold, relaxation oscillations are still sustained in the presence of mean flow dissipation, but are superimposed on high-frequency fluctuations. This particular behavior makes the convective transport to follow exponential statistics when measured at a local probe. (C) 2003 American Institute of Physics.