The Monin-Obukhov length (L) is defined as:
$$L = - \frac{\rho C_p T_v u^3_*}{kgH}$$
where $\rho$=moist air density; $C_p$=air specific heat capacity; $T_v$=virtual temperature; $u^3_*$=wind friction velocity; $k$=0.41 (von Karman constant); $g$=gravity; and $H$=sensible heat. Note that there are lots of different formulations - this one is taken from this video on eddy covariance.
It is used when describing how turbulence is affected by bounancy, e.g. from rising thermals from the earth's surface. I would like to get some intuition for what the length actually physically represents. The wikipedia page states that:
A physical interpretation of L is given by the Monin–Obukhov similarity theory. During the day -L it is the height at which the buoyant production of turbulence kinetic energy (TKE) is equal to that produced by the shearing action of the wind (shear production of TKE).
However, that is still pretty opaque to me. To me, that sounds something like a parameter of a distribution that describes at what height wind shear starts to break up up-welling packets of air, but I really don't have any idea. Is there a good intuitive description of this quantity?