On an Improved Second‐Moment Closure Model for Langmuir Turbulence Conditions and Its Application

Recently, a k-omega second-moment closure (SMC) model including the Langmuir turbulence effects was proposed by Yu et al. (2018, ), however, the equations for determining the stability functions in it are very complicated. In this study, the equations of the stability functions are derived in more detail and a new explicit version is proposed. In the meantime, a new constant c(omega 4) = 0.15 is introduced into the turbulent frequency transport equation to manifest the role of the shear generating term caused by the Stokes drift. And then the performance of the new SMC model is investigated by one-dimensional Papa Ocean Station simulation and three-dimensional global climate model simulation. The results show that the use of the new SMC model produces significant changes in the results of the ocean surface boundary layer simulations at the Papa Ocean Station, especially for the summer and autumn sea surface temperature (SST) simulations, and for the mixed layer depth (MLD) and mixed layer temperature (MLT) in the mixed layer deepening process. In the three-dimensional simulation, the new SMC model resulted in a decrease of more than 34% in the annual root mean square error of SST in the northern extratropical region compared to the non-LT effects model. The simulated MLD for tropical regions in winter and summer has also improved by 61.9% and 53.6%, respectively. The effect of the new SMC model on the MLT is mainly found in the regions beyond the tropical in summer and the tropical and northern extratropical regions in winter.