Article Type:
Research Article

On the q2l Equation by Mellor and Yamada (1982)

Hans Burchard Institut für Meereskunde, Universität Hamburg, Hamburg, Germany

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Print Publication:
01 May 2001
DOI:
https://doi.org/10.1175/1520-0485(2001)031<1377:OTQLEB>2.0.CO;2
Page(s):
1377–1387
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Abstract

This short paper focuses on the problems caused by the equal contribution of shear and buoyancy production in the length scale equation transporting the product of turbulent kinetic energy q2 and macro length scale l as suggested by Mellor and Yamada. It is shown that this model has no steady-state solutions for homogeneous shear flows. The concept of the steady-state Richardson number is used for estimating the adequate contribution of the buoyancy production to the equation for q2l. In a simple wind entrainment experiment, the failure of the q2l equation in the case of unlimited l is shown. With the new estimate for the buoyancy production contribution to q2l, physically sound results are obtained even for the unlimited case. In applications of the modified q2l equation to three oceanic test cases in the northern North Sea and the northern Pacific, the results of the wind entrainment experiment are confirmed.

Corresponding author address: Dr. Hans Burchard, Institut für Meereskunde, Universität Hamburg, Troplowitzstraße 7, D-22529 Hamburg, Germany.

Email: hans@gotm.net

Abstract

This short paper focuses on the problems caused by the equal contribution of shear and buoyancy production in the length scale equation transporting the product of turbulent kinetic energy q2 and macro length scale l as suggested by Mellor and Yamada. It is shown that this model has no steady-state solutions for homogeneous shear flows. The concept of the steady-state Richardson number is used for estimating the adequate contribution of the buoyancy production to the equation for q2l. In a simple wind entrainment experiment, the failure of the q2l equation in the case of unlimited l is shown. With the new estimate for the buoyancy production contribution to q2l, physically sound results are obtained even for the unlimited case. In applications of the modified q2l equation to three oceanic test cases in the northern North Sea and the northern Pacific, the results of the wind entrainment experiment are confirmed.

Corresponding author address: Dr. Hans Burchard, Institut für Meereskunde, Universität Hamburg, Troplowitzstraße 7, D-22529 Hamburg, Germany.

Email: hans@gotm.net

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