Stability functions based upon shear functions

The stability functions for momentum and heat under a Richardson number formulation are derived from the nondimensional shear functions under a Monin-Obukhov formulation. The Prandtl number is also derived as a function of the Richardson number. Previously, this has been done only in a limited sense. Because the Richardson number formulation is expressed in closed form, iterative techniques are no longer needed in numerical models that use Monin-Obukhov similarity theory. This time-saving approach is made possible by deriving expressions for the friction velocity and temperature in terms of the Richardson-number-dependent stability functions. In addition, the Richardson number approximation in the lowest layer is made to depend explicitly upon the surface roughness.