  In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors,
linear non-modal analysis is more useful than normal mode analysis in
predicting turbulent properties. However, the non-trivial time evolution of
non-modal structures makes quantitative understanding and prediction difficult.
We present a technique to overcome this difficulty by modeling the effect that
the advective nonlinearities have on spatial turbulent structures. The
nonlinearities are taken as a periodic randomizing force with time scale
consistent with critical balance arguments. We apply this technique to a model
of drift wave turbulence in the Large Plasma Device (LAPD) [W. Gekelman
\emph{et al.}, Rev. Sci. Inst. {\bf 62}, 2875 (1991)], where non-modal effects
dominate the turbulence. We compare the resulting growth rate spectra to that
obtained from a nonlinear simulation, showing good qualitative agreement,
especially in comparison to the eigenmode growth rate spectra.
