  A general proof that more energy flows upscale than downscale in
two-dimensional (2D) turbulence and barotropic quasi-geostrophic (QG)
turbulence is given. A proof is also given that in Surface QG turbulence, the
reverse is true. Though some of these results are known in restricted cases,
the proofs given here are pedagogically simpler, require fewer assumptions and
apply to both forced and unforced cases.
