text: In the buffer layer, between 5 wall units and 30 wall units, neither law holds, such that:
  :For 
  with the largest variation from either law occurring approximately where the two equations intersect, at .  That is, before 11 wall units the linear approximation is more accurate and after 11 wall units the logarithmic approximation should be used, though neither are relatively accurate at 11 wall units.
  The mean streamwise velocity profile  is improved for  with an eddy viscosity formulation based on a near-wall turbulent kinetic energy  function and the van Driest mixing length equation. Comparisons with DNS data of fully developed turbulent channel flows for  showed good agreement.