The behavior of an ordinary differential equation for the low wave number velocitymode is analyzed. This equation was derived in [5]by an iterative process on the two-dimensional Navier-Stokes equations (NSE). Itresembles the NSE in form, exceptthat the kinematic viscosity is replaced by an iterated viscositywhich is a partial sum, dependent on the low-mode velocity. The convergence of this sum as the number of iterations is taken to be arbitrarily large is explored.This leads to a limiting dynamical system which displaysseveral unusual mathematical features.
