title: Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence.
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.
authors.affiliation: University of Southampton, Southampton SO17 1BJ, United Kingdom.
authors.forename: Ati S
authors.initials: AS
authors.lastname: Sharma
authors.affiliation: California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Rashad
authors.initials: R
authors.lastname: Moarref
authors.affiliation: California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Beverley J
authors.initials: BJ
authors.lastname: McKeon
authors.affiliation: University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
authors.forename: Jae Sung
authors.initials: JS
authors.lastname: Park
authors.affiliation: University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
authors.forename: Michael D
authors.initials: MD
authors.lastname: Graham
authors.affiliation: University of Sheffield, Sheffield, S10 2TN, United Kingdom.
authors.forename: Ashley P
authors.initials: AP
authors.lastname: Willis