Comments on "A generic length-scale equation for geophysical turbulence models" by L. Umlauf and H. Burchard

Umlauf and Burchard (2003) present a generic length scale equation for use in two- equation models of turbulence. However, it is of limited utility in the sense that it is valid for only negative values of n, one of the exponents in the prognostic quantity . This deficiency can be traced to the traditional form for the diffusion term used in their generic length scale equation. We show that the use of the so-called “polymorphism” approach, which results in fractional values for n, is unnecessary. A simple modification of the diffusion term is sufficient to insure a more universal generic length scale equation that is valid for all values of m and n, including positive values of n. We also show that their best-performing generic equation with m = 1 and n = -0.67 is equivalent to the traditional equation for the dissipation rate, but with an additional diffusion term.