Designing a more nonlinearly stable laminar flow via boundary manipulation
Journal of Fluid Mechanics
Cambridge University Press
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Rabin, S., Caulfield, C., & Kerswell, R. (2013). Designing a more nonlinearly stable laminar flow via boundary manipulation. Journal of Fluid Mechanics, 738 (R1)https://doi.org/10.1017/jfm.2013.601
We show how a fully nonlinear variational method can be used to design a more nonlinearly stable laminar shear flow by quantifying the effect of manipulating the boundary conditions of the flow. Using the example of plane Couette flow, we demonstrate that by forcing the boundaries to undergo spanwise oscillations in a certain way, it is possible to increase the critical disturbance energy for the onset of turbulence by 41 %. If this is sufficient to ensure laminar flow (i.e. ambient noise does not exceed this increased threshold), nearly four times less energy is consumed than in the turbulent flow which exists in the absence of imposed spanwise oscillations.
nonlinear instability, transition to turbulence, variational methods
This work is supported by the Engineering and Physical Sciences Research Council [grant number EP/H050310/1].
External DOI: https://doi.org/10.1017/jfm.2013.601
This record's URL: https://www.repository.cam.ac.uk/handle/1810/245132