  An exact Craik-Criminale (CC) solution to the incompressible Navier-Stokes
(NS) equations describes the instability of an elliptical columnar flow
interacting with a single Kelvin wave. These CC solutions are extended to allow
multi-harmonic Kelvin waves to interact with any exact ``base'' solution of the
NS equations. The interaction is evaluated along an arbitrarily chosen flowline
of the base solution, so exact nonlinear instability in this context is locally
convective, rather than absolute. Furthermore, an iterative method called
``WKB-bootstrapping'' is introduced which successively adds Kelvin waves with
incommensurate phases to the extended CC solutions. This is illustrated by
constructing an extended CC solution consisting of several Kelvin waves with
incommensurate phases interacting with an elliptical columnar flow.
