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

TL;DR

This paper demonstrates that many exact invariant solutions of the Navier-Stokes equations for pipe and channel flows can be effectively represented using a low-dimensional basis derived from the resolvent model, linking invariant solutions and turbulence modeling.

Contribution

It shows that the resolvent model provides a compact basis to represent invariant solutions of the Navier-Stokes equations, bridging two approaches to turbulence analysis.

Findings

Invariant solutions are well represented by few resolvent modes.

The resolvent model links invariant solutions and turbulent statistics.

A new connection between invariant solutions and turbulence modeling is established.

Abstract

We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just few modes of the model of McKeon & Sharma J. Fl. Mech. 658, 356 (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.