Phys. Rev. E 93, 021102(R) (2016) - Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence

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Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence

Ati S. Sharma, Rashad Moarref, Beverley J. McKeon, Jae Sung Park, Michael D. Graham, and Ashley P. Willis

Phys. Rev. E 93, 021102(R) – Published 19 February 2016

Abstract

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.

Received 6 March 2015
Revised 28 January 2016

DOI:https://doi.org/10.1103/PhysRevE.93.021102

©2016 American Physical Society

Physics Subject Headings (PhySH)

Navier-Stokes equation

Fluid Dynamics

Authors & Affiliations

Ati S. Sharma^*

University of Southampton, Southampton SO17 1BJ, United Kingdom

Rashad Moarref^† and Beverley J. McKeon^‡

California Institute of Technology, Pasadena, California 91125, USA

Jae Sung Park^§ and Michael D. Graham^∥

University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

Ashley P. Willis^¶

University of Sheffield, Sheffield, S10 2TN, United Kingdom

^*a.sharma@soton.ac.uk
^†rashad@caltech.edu
^‡mckeon@caltech.edu
^§park329@wisc.edu
^∥graham@engr.wisc.edu
^¶a.p.willis@sheffield.ac.uk

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Issue

Vol. 93, Iss. 2 — February 2016

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