  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.
