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 p3. If the minimum Hölder 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 hmin=0, then ζp=0 for p2 and Kraichnan theory is exact. © 1995 The American Physical Society.