Limiting behavior for an iterated viscosity

The behavior of an ordinary differential equation for the low wave number v elocity mode is analyzed. This equation was derived in [5] by an iterative process on the two-dimensional Navier-Stokes equations (NSE). It resembles the NSE in form, except that the kinematic viscosity is replaced by an iter ated viscosity which is a partial sum, dependent on the low-mode velocity. The convergence of this sum as the number of iterations is taken to be arbi trarily large is explored. This leads to a limiting dynamical system which displays several unusual mathematical features.