Abstract：

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Although the linear mechanism is bypassed in transition from laminar state in channel flow, the role of the nonlinear secondary flows that bifurcate from the linear neutral stability points, and the higher-order flows that in turn bifurcate from these flows, remains an open question. We consider secondary and tertiary flows of this kind.

First, we present five classes of travelling-wave solutions in plane Poiseuille flow, which we found recently. They arise via a saddle-node bifurcation at moderate Reynolds numbers Two of the classes are obtained by homotopy continuation from the stationary and the travelling-wave mirror-symmetric solutions in plane Couette flow (Nagata & Deguchi, 2013), while the other three are obtained by reducing the rotation rate to zero for the solutions in rotating plane Poiseuille flow (Wall & Nagata, 2013, 2016). Of particular interest are vibrant flow structures observed in only near one wall in some of the classes.

For the second part of my talk, we re-examine and extend the problem previously considered by Ehrenstein & Koch (JFM, 1991). The main conclusions of this previous study, that an ' M(n;2m) ' solution branch could be continued down to Reynolds numbers at which transition is first observed with friction factor values corresponding to experimentally observed values, are significantly revised by the present study. It is demonstrated that the M(n;2m) solution does not exist, and that neither the Reynolds number nor friction factors of any of the tertiary flows corresponds to the first experimentally observed transition.

 

Introduction of the speaker

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Professor Nagata obtained his Ph.D. in Geophysics and Space Physics at University of California Los Angeles in 1982, and then continued his research in UK. He had been a lecturer since 1990 in The University of Birmingham. Later on he returned back to Japan and was a professor at Kyoto University. Since 2014 he is a professor at Tianjin University. Professor is a Fellow of Japan Society of Fluid Mechanics, and his research interests include shear flow instability and transition to turbulence.

 

 

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