Relationship between the Monin–Obukhov Stability Parameter and the Bulk Richardson Number at Sea under Unstable Conditions, Derived From a Turbulence-Closure Model

Abstract

Relationships between the Monin?Obukhov stability parameter and the bulk Richardson number are useful for explicit calculation of fluxes through the air?sea interface. The most straightforward method assumes simple proportionality and is supported well by experimental evidence in a recent work by Grachev and Fairall. On the other hand, the reference iterative method is regarded as more accurate. To recognize possible differences, calculated values of the proportionality factor as a function of wind speed and air?sea virtual potential temperature difference are shown. The calculation is based on commonly used sea roughness specifications and the Mellor?Yamada turbulence-closure model, which has been shown in previous studies to reproduce the three-sublayer structure of the atmospheric surface layer under convective conditions and to predict mean flow profiles that are consistent with empirical data. The results show that the proportionality factor varies with the wind speed and virtual potential temperature vertical differences and that this variability has a nonmonotonic character when wind speeds are smaller than 5 m s?1.