On the q(2)l equation by Mellor and Yamada (1982)

This short paper focuses on the problems caused by the equal contribution o f shear and buoyancy production in the length scale equation transporting t he product of turbulent kinetic energy q(2) and macro length scale l as sug gested by Mellor and Yamada. It is shown that this model has no steady-stat e solutions for homogeneous shear flows. The concept of the steady-state Ri chardson number is used for estimating the adequate contribution of the buo yancy production to the equation for q(2)l. In a simple wind entrainment ex periment, the failure of the q(2)l equation in the case of unlimited l is s hown. With the new estimate for the buoyancy production contribution to q(2 )l, physically sound results are obtained even for the unlimited case. In a pplications of the modified q(2)l equation to three oceanic test cases in t he northern North Sea and the northern Pacific, the results of the wind ent rainment experiment are confirmed.