  The strength of the nonlinearity is measured in decaying two-dimensional
turbulence, by comparing its value to that found in a Gaussian field. It is
shown how the nonlinearity drops following a two-step process. First a fast
relaxation is observed on a timescale comparable to the time of for-mation of
vortical structures, then at long times the nonlinearity relaxes further during
the phase when the eddies merge to form the final dynamic state of decay. Both
processes seem roughly independent of the value of the Reynolds number.
