A Second-Order Closure Turbulence Model: New Heat Flux Equations and No Critical Richardson Number
Y. Cheng, V. M. Canuto, A. M. Howard, Andrew S. Ackerman, M. E. Kelley, Ann M. Fridlind, Gavin A. Schmidt, M. S. Yao, Anthony D. Del Genio, Gregory S. Elsaesser
Abstract
Abstract We formulate a new second-order closure turbulence model by employing a recent closure for the pressure–temperature correlation at the equation level. As a result, we obtain new heat flux equations that avoid the long-standing issue of a finite critical Richardson number. The new, structurally simpler model improves on the Mellor–Yamada and Galperin et al. models; a key feature includes enhanced mixing under stable conditions facilitating agreement with observational, experimental, and high-resolution numerical datasets. The model predicts a planetary boundary layer height deeper than predicted by models with low critical Richardson numbers, as demonstrated in single-column model runs of the GISS ModelE general circulation model.