We propose a family of two-dimensional incompressible fluid models ind
exed by a parameter alpha epsilon[0, infinity], and discuss the spectr
al scaling properties for homogeneous, isotropic turbulence in these m
odels. The family includes two physically realizable members. It is sh
own that the enstrophy cascade is spectrally local for alpha < 2, but
becomes dominated by nonlocal interactions for alpha > 2. Numerical si
mulations indicate that the spectral slopes are systematically steeper
than those predicted by the local scaling argument.