Abstract
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.
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England, D.E., McNider, R.T. Stability functions based upon shear functions. Boundary-Layer Meteorol 74, 113–130 (1995). https://doi.org/10.1007/BF00715713
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DOI: https://doi.org/10.1007/BF00715713