Efficient representation of exact coherent states of the Navier–Stokes equations using resolvent analysis
A resolvent analysis of exact coherent states (ECS) of the Navier–Stokes equations (NSE) in a low Reynolds number channel is performed. The resolvent framework recasts the NSE into an input/output form in which the nonlinear term is treated as an internal forcing that drives the linear dynamics of the system. The framework has previously shown promise with regards to producing low-dimensional representations of ECS; here, we show that a componentwise analysis of the resolvent operator along with a Helmholtz decomposition of the nonlinear term reveals a simplified input/output form that clearly identifies and isolates the contributions of particular solenoidal forcing components to velocity/vorticity outputs. This new approach leads to an improved method for compact representations of ECS for both forcing and response fields, and establishes interesting connections to Orr–Sommerfeld/Squire modes in a nonlinear context.
© 2019 The Japan Society of Fluid Mechanics and IOP Publishing Ltd. Received 30 October 2017; Accepted 22 February 2018; Accepted Manuscript online 22 February 2018; Published 17 January 2019.