Statistical state dynamics-based study of the stability of the mean statistical state of wall-bounded turbulence

In wall turbulence, the time-mean flow is returned to after almost any disturbance, which indicates that it is a stable statistical feature underlying the disorder of turbulence. However, the stability of this statistical feature can not be determined directly from the stability of the time-mean flow itself. What is required is a statistical stability analysis method. We determine the statistical stability of the time-mean state by averaging the dynamics of the return to the time-mean state over the turbulent attractor using the linear inverse model method.