Nonlinear forcing in the resolvent analysis of exact coherent states of the Navier-Stokes equations

The resolvent analysis of McKeon & Sharma (2010) recasts the Navier-Stokes equations into an input/output form in which the nonlinear term is treated as a forcing that acts upon the linear dynamics to yield a velocity response. The framework has shown promise with regards to producing low-dimensional representations of exact coherent states. Previous work has focused on a primitive variable output; here we show a velocity-vorticity formulation of the governing equations along with a Helmholtz decomposition of the nonlinear forcing term reveals a simplified input/output form in the resolvent analysis. This approach leads to an improved method for compact representations of exact coherent states for both forcing and response fields, with a significant reduction in degrees of freedom in comparison to the primitive variable approach.