  In systems governing two-dimensional turbulence, surface quasi-geostrophic
turbulence, (more generally $\alpha$-turbulence), two-layer quasi-geostrophic
turbulence, etc., there often exist two conservative quadratic quantities, one
``energy''-like and one ``enstrophy''-like. In a finite inertial range there
are in general two spectral fluxes, one associated with each conserved
quantity. We derive here an inequality comparing the relative magnitudes of the
``energy'' and ``enstrophy'' fluxes for finite or infinitesimal dissipations,
and for hyper or hypo viscosities. When this inequality is satisfied, as is the
case of 2D turbulence,where the energy flux contribution to the energy spectrum
is small, the subdominant part will be effectively hidden. In sQG turbulence,
it is shown that the opposite is true: the downscale energy flux becomes the
dominant contribution to the energy spectrum. A combination of these two
behaviors appears to be the case in 2-layer QG turbulence, depending on the
baroclinicity of the system.
