Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session M28: Flow Instability: Theory and Control
8:00 AM–10:10 AM,
Tuesday, November 20, 2018
Georgia World Congress Center
Room: B316
Chair: Lou Kondic, New Jersey Institute of Technology
Abstract ID: BAPS.2018.DFD.M28.3
Abstract: M28.00003 : A new novel fundamental formula for viscous parallel shear flows
8:26 AM–8:39 AM
Presenter:
Harry Lee
(University of Michigan - Ann Arbor)
Authors:
Harry Lee
(University of Michigan - Ann Arbor)
Shixiao Wang
(Auckland University)
A vorticity-based identity that is contrastingly different to the traditional energy-type identities, such as the renowned Reynolds-Orr equation, has been recently derived. The identity is shown to be more general than the one derived by Synge (1938). Based on this identity, we were able to provide a new set of physical interpretations to different phases of stability in classical 2D parallel shear flows. Specifically, we studied the mechanisms of stability and instability in planar Couette and Poiseuille flows- the two most important representatives of classical shear flow models.
As one direct implementation of the new identity, we demonstrated an example on vorticity boundary control for the planar Poiseuille flow, and it turned out that the flow becomes stable with the addition of a small amount of vorticity control. We foresee the prospect of the applicability of such control scheme in the field of CFD.
The study and application of the identity is only at a preliminary stage, but it has promising potential to be further exploited for unveiling the exact mechanism that governs the onset of turbulence in a wide range of shear flows- a grand task that has remained incomplete to generations of fluid dynamists for over 130 years.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2018.DFD.M28.3
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