Does multifractal theory of turbulence have logarithms in the scaling   relations?
  The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating known exact relations such as the four-fifths law. Using the theory of large deviations applied to the random multiplicative model of turbulence and calculating subdominant terms, we explain here why such corrections cannot be present. 
Uriel Frisch, Marco Martins Afonso, Andrea Mazzino, Victor Yakhot