Mellor, G. L., 2001: One-dimensional, ocean surface layer modeling: A problem and a solution. Journal of Physical Oceanography, 31(3), 790-809.

Abstract:  The first part of this paper is generic: it demonstrates a problem associated with one-dimensional, ocean surface layer model comparisons with ocean observations.  Unlike three-dimensional simulations or the real ocean, kinetic energy can inexorably build up in one-dimensional simulations, which artificially enhances mixing.  Adding a sink term to the momentum equations counteracts this behavior.  The sink term is a surrogate for energy divergence available to three-dimensional models but not to one-dimensional models.

The remainder of the paper deals with the Mellor-Yamada boundary layer model.  There exists prior evidence that the model's summertime surface temperatures are too warm due to overly shallow mixed layer depths.  If one adds a sink term to approximate three-dimensional model behavior, the warming problem is exacerbated, creating added incentive to seek an appropriate model change.  Guided by laboratory data, a Richardson-number-dependent dissipation is introduced and this simple modification yields a favorable improvement in the comparison of model calculations with data even with the momentum sink term in place.