Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence
We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.
© 2016 American Physical Society. Received 6 March 2015; revised manuscript received 28 January 2016; published 19 February 2016. This work has been supported by the Air Force Office of Scientific Research (Flow Interactions and Control Program) under awards FA9550-11-1-0094, FA9550-15-1-0062 (J.S.P. and M.D.G.), and FA9550-12-1-0469 (R.M. and B.J.M.) and by the Air Force Office of Scientific Research (European Office of Aerospace Research and Development) under award FA9550-14-1-0042 (A.S.S.).
Submitted - 1503.01701v3.pdf
Supplemental Material - PRE_supplement_pipe_channel_solutions.tar.gz
Published - PhysRevE.93.021102.pdf