Abstract
Physical processes represented by the Monin–Obukhov bulk formula for momentum are investigated with field observations. We discuss important differences between turbulent mixing by the most energetic non-local, large, coherent turbulence eddies and local turbulent mixing as traditionally represented by K-theory (analog to molecular diffusion), especially in consideration of developing surface-layer stratification. The study indicates that the neutral state in a horizontally homogeneous surface layer described in the Monin–Obukhov bulk formula represents a special neutrality regardless of wind speed, for example, the surface layer with no surface heating/cooling. Under this situation, the Monin–Obukhov bulk formula agrees well with observations for heights to at least 30 m. As the surface layer is stratified, stably or unstably, the neutral state is achieved by mechanically generated turbulent mixing through the most energetic non-local coherent eddies. The observed neutral relationship between u_* (the square root of the momentum flux magnitude) and wind speed V at any height is different from that described by the Monin–Obukhov formula except within several metres of the surface. The deviation of the Monin–Obukhov neutral u_*-V linear relation from the observed one increases with height and contributes to the deteriorating performance of the bulk formula with increasing height, which cannot be compensated by stability functions. Based on these analyses, estimation of drag coefficients is discussed as well.
Highlights
The Monin–Obukhov similarity theory (MOST) was established more than 70 years ago (Monin and Obukhov 1954), and its historical impacts on the atmospheric boundary layer have been reviewed extensively (e.g., Foken 2006)
We investigate the physical process represented in the bulk formula only, recognizing that the contribution of Monin and Obukhov is not limited to momentum transfer
We investigate the physical processes that contribute to the observed turbulent momentum transfer and implicitly assumed in the Monin–Obukhov bulk formula
Summary
The Monin–Obukhov similarity theory (MOST) was established more than 70 years ago (Monin and Obukhov 1954), and its historical impacts on the atmospheric boundary layer have been reviewed extensively (e.g., Foken 2006). The stability function was expressed as a function of z/L (L is the Obukhov length) by Obukhov (1946), which was further investigated by Monin and Obukhov (1954) They assumed that u∗ is approximately invariant with height in the surface layer, that is, u∗(z) ≈ u∗0, and the atmospheric stratification does not deviate significantly from its neutral state. Under these conditions, the relationship between u∗ and V for z near the surface can be obtained by vertically integrating (2) as (Monin and Obukhov 1954). FLOSS-II is more complex than CASES-99, the most important difference between the two datasets relevant here is that CASES-99 has strong thermal diurnal variations during the one-month field campaign in October; FLOSS-II has a variety of thermal diurnal variations during a period of six months from November to April
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