Flow and transport modeling in the sea-breeze. Part I: A modified E - ∈ model with a non-equilibrium level 2.5 closure

In order to overcome shortcomings of the conventional E - ∈ model and to develop a more general model applicable to the variety of atmospheric conditions observed, for example, during a land-sea breeze cycle, a modified E - ∈ model is proposed. The model is a simplified form of an algebraic stress model including wall proximity effects of Gibson and Launder (1978). The proposed model is similar to the popular Mellor and Yamada (1982) level 2.5 model but does not employ a local equilibrium assumption in the algebraic equations for Reynolds stresses. The resulting model shows a wider realization region under unstable conditions than the Mellor and Yamada model. The modified model is compared herein to observations, higher order closure simulations and large eddy simulations under neutral, stable and convective conditions. Various dissipation rate equations were employed and compared to understand their performance with the modified model. The modified E - ∈ model reproduced the observed behavior well under all conditions except near the base of an elevated inversion layer under convective conditions. The ability of the model to describe flow dynamics under a wide range of atmospheric stabilities suggests that the model can be used to describe the complicated diurnal behavior of the land-sea breeze circulation.