Intuitive definition of the Monin-Obukhov length?
The way I understand it is the height above the surface at which buoyant (heat) production of turbulence first equals the mechanical (shear) production of turbulence.

A more useful definition is given by the American Meteorological Society:


  A parameter with dimension of length that gives a relation between parameters characterizing dynamic, thermal, and buoyant processes.
  
  At altitudes below this length scale, shear production of turbulence kinetic energy dominates over buoyant production of turbulence. It is defined by
  
  
  where k is von Kármán's constant, u* is the friction velocity (a measure of turbulent surface stress), g is gravitational acceleration, Tv is virtual temperature, and Qv0 is a kinematic virtual temperature flux at the surface. The parameter was first described by Obukhov in 1946, and therefore should not be called the Monin–Obukhov length, even though there is a Monin–Obukhov similarity theory that uses it. The Obukhov length, of order one to tens of meters, is the characteristic height scale of the dynamic sublayer. The Obukhov length is zero for neutral stratification, and positive (negative) for stable (unstable) stratifications. The dimensionless Obukhov length z/ L (where z is height above the surface) is used as a stability parameter, with z/L = 0 for statically neutral stability, and is positive (negative) in a typical range of 1 to 5 (-5 to -1) for stable (unstable) stratification.