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 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.

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Cited by in corpus (6)

• On the correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations
• Energy transfer in turbulent channel flows and implications for resolvent modelling
• Interaction of forced Orr-Sommerfeld and Squire modes in a low-order representation of turbulent channel flow
• New equilibrium solution branches of plane Couette flow discovered using a project-then-search method
• Modal Analysis of Fluid Flows: An Overview
• Nonlinear forcing in the resolvent analysis of exact coherent states of the Navier-Stokes equations