[Seminar] "Subcritical transition in plane Poiseuille flow" by Prof. Masato Nagata

[Speaker]
Professor Masato Nagata, Department of Mechanics, Tianjin University, Tianjin, P. R. China

[Abstract]
Plane Poiseuille flow differs from other shear flows such as plane Couette flow or pipe flow, in that it loses instability to infinitesimal disturbances at a finite value of the Reynolds number, which is given by R = 5772. It is known that this linear instability mechanism is bypassed in practical conditions, but the role of Tollmien-Schlichting derived flows - that is the secondary flows that bifurcate from the linear neutral points, and the tertiary flows that in turn bifurcate from these secondary flows - in transition and turbulence in channel flow, and their relation to other known exact coherent states remains an open question. As a first step towards addressing this question we consider Tollmien-Schlichting derived flows, thus re-examining and extending the problem considered by Ehrenstein & Koch (1991). The main conclusions of this seminal study are significantly revised by the present study.
 We also obtain a three-dimensional secondary flow bifurcating directly from the basic state. The flow has two low-speed streaks in stream-wise velocity per span-wise wavelength accompanied by aligned vortical structures. Furthermore, the corresponding span-wise localised flow can be continued to smaller values of R.