Transition & Turbulence in Wall Flows

It's stil not widely recognized that the Linearized Navier-Stokes (LNS) equations contain a lot of information about transition and turbulence dynamics. This appears to be especially true in the case of wall-bounded shear flows, for which satisfactory transition scenarios and turbulence models have been elusive. In the past 15 yrs a new analysis of the LNS equations has emerged, with substantially different consequences than classical hydrodynamic stability analysis based on normal modes. A recent summary of this approach appears in the book Stability and Transition in Shear Flows by Schmid & Henningson.

One way to carry out this analysis is from an “input-output” point of view. This means introducing inputs (e.g. body force fields) and considering various velocity and vorticity fields as outputs. As such, we have studied the spatio-temporal frequency and impulse responses of the LNS. This reveals an amazing richness of behavior of the LNS equations; something which is not at all obvious from normal mode analysis. Coherent flow structures and transition mechanisms that are sometimes blamed on “nonlinear mechanisms” show up in these linear models. This should not be as surprising as it sounds. It is another example of how the widely spread, and vague terminology of “nonlinear mechanisms” and “nonlinear phenomena” leads to confusion (see “Myths, Misconceptions ….” in the talks page).

Each of the pictures below represent commonly observed phenomena of transition or turbulence that can related to either the frequency or impulse response of the LNS.

(this page is still under construction)

Coherent structures from spatio-temporal frequency response	TS waves vs. streamwise vortices & streaks in supercritical channel flows
Impulse excitation of channel flow	Impulse excitation movie
Component-wise input-output analysis