In this comparative study, four different algebraic second-moment turbulence closure models are investigated in detail. These closure schemes differ in the number of terms considered for the closure of the pressure–strain correlations. These four turbulence closures result in the eddy-diffusivity principle such that the closure assumptions are contained in dimensionless so-called stability functions. Their performance in terms of Prandtl number, Monin–Obukhov similarity theory, and length scale ratios are first tested against data for simple flows. The turbulence closure is then completed by means of a k–ϵ two-equation model, but other models such as the two-equation model by Mellor and Yamada could also be used. The concept of the steady-state Richardson number for homogeneous shear layers is exploited for calibrating the sensitivity of the four models to shear and stable stratification. Idealized simulations of mixed layer entrainment into stably stratified flow due to surface stress and due to... Abstract In this comparative study, four different algebraic second-moment turbulence closure models are investigated in detail. These closure schemes differ in the number of terms considered for the closure of the pressure–strain correlations. These four turbulence closures result in the eddy-diffusivity principle such that the closure assumptions are contained in dimensionless so-called stability functions. Their performance in terms of Prandtl number, Monin–Obukhov similarity theory, and length scale ratios are first tested against data for simple flows. The turbulence closure is then completed by means of a k–ϵ two-equation model, but other models such as the two-equation model by Mellor and Yamada could also be used. The concept of the steady-state Richardson number for homogeneous shear layers is exploited for calibrating the sensitivity of the four models to shear and stable stratification. Idealized simulations of mixed layer entrainment into stably stratified flow due to surface stress and due to...

The purpose of this paper is to modify two-equation turbulence models such that they are capable of simulating dynamics in the wave-enhanced layer near the surface. A balance of diffusion of turbulent kinetic energy (TKE) and dissipation is assumed as the surface boundary condition for TKE following the suggestion of Craig and Banner. It is shown that this theory, originally developed under the assumption of a macro length scale linearly increasing down from the surface, fails for two-equation models such as the well-known k–ε model. Suggestions are made how to modify such models for overcoming this deficiency. The basic idea is to insert the analytic solution of a model problem suggested by Craig into the dissipation rate equation and solve for the turbulent Schmidt number of the dissipation rate equation, which may be formulated as a function of the production/dissipation ratio. With this modification, the linear behavior of the macro length scale is properly reproduced by the k–ε model. It is ... Abstract The purpose of this paper is to modify two-equation turbulence models such that they are capable of simulating dynamics in the wave-enhanced layer near the surface. A balance of diffusion of turbulent kinetic energy (TKE) and dissipation is assumed as the surface boundary condition for TKE following the suggestion of Craig and Banner. It is shown that this theory, originally developed under the assumption of a macro length scale linearly increasing down from the surface, fails for two-equation models such as the well-known k–ε model. Suggestions are made how to modify such models for overcoming this deficiency. The basic idea is to insert the analytic solution of a model problem suggested by Craig into the dissipation rate equation and solve for the turbulent Schmidt number of the dissipation rate equation, which may be formulated as a function of the production/dissipation ratio. With this modification, the linear behavior of the macro length scale is properly reproduced by the k–ε model. It is ...

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. 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.