Simple analytical model for entire turbulent boundary layer over flat   plane: from viscous and mixing layers to turbulent logarithmic region
  We discuss a simple analytical model of the turbulent boundary layer (TBL) over flat plane. The model offers an analytical description of the profiles of mean velocity and turbulent activity in the entire boundary region, from the viscous sub-layer, through the buffer layer further into the log-law turbulent region. In contrast to various existing interpolation formulas the model allows one to generalize the description of simple TBL of a Newtonian fluid for more complicated flows of turbulent suspensions laden with heavy particles, bubbles, long-chain polymers, to include the gravity acceleration, etc. 
Victor S. L'vov, Anna Pomyalov, Vasil Tiberkevich