Exact Results on Scaling Exponents in the 2D Enstrophy Cascade

We establish rigorous inequalities for short-distance scaling exponents in 2D incompressible turbulence. Using only the condition of constant ultraviolet enstrophy flux, we show that 〈(Δₗω)ᵖ〉~^ζₚ must have ζ₂≤2/3 (Sulem-Frisch bound) and ζₚ≤0, for p≥3. If the minimum H\"older singularity of the vorticity is negative, hₘᵢₙ<0, then the bounds can be improved to ζₚ≤τp/3, where τₚ is the scaling exponent of a local enstrophy flux: 〈|Z_|ᵖ〉~^τₚ. However, if hₘᵢₙ0ex0ex=0ex0ex0, then ζₚ0ex0ex=0ex0ex0 for p≥2 and Kraichnan theory is exact.