We discuss the small-scale energy spectrum E(k) of two-dimensional fully developed turbulence. As its scaling exponent is related to the fractal dimension of isovorticity lines, we suggest that it could be nonuniversal with a dependence on the particular class of initial conditions considered. This should explain the different values obtained in numerical experiments for decaying turbulence and for statistically stationary forced turbulence with particular kinds of forcing. Finally, the scaling E(k){~}k^-3 is related to the most random situation where the vorticity can be considered as a scalar passively advected by the velocity field.
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Benzi et al. (1990) studied this question.
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