Mathematics – Logic
Scientific paper
Jul 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005qjrms.131.1863z&link_type=abstract
Quarterly Journal of the Royal Meteorological Society, vol. 131, Issue 609, p.1863-1892
Mathematics
Logic
26
Baroclinic Shear, Free-Flow Stability, Large-Eddy Simulation, Non-Local Turbulence, Non-Steady Regime
Scientific paper
The planetary boundary layer (PBL) resistance and heat-transfer laws express the surface fluxes of momentum and heat through the PBL governing parameters. Since the late sixties, the dimensionless coefficients (A, B and C) in these laws were considered as single-valued functions of internal stability parameters: = u*/|f|Ls in the steady state PBLs, or h/Ls in the evolving PBLs (u* is the friction velocity, f is the Coriolis parameter, Ls is the surface Monin-Obukhov length, and h is the PBL depth). Numerous studies revealed very wide spread of data in empirical plots of A, B and C versus μ or h/Ls. It is not surprising that the above laws, although included in all modern textbooks on boundary-layer meteorology, are not practically used. In the present paper the resistance and heat-transfer laws are revised, accounting for the free-flow stability, baroclinicity and the rise of a capping inversion. The coefficients A, B and C become functions not only of μ or h/Ls, but also of the external stability parameter μN = N/|f| (where N is the Brunt-Väisälä frequency in the free atmosphere above the PBL), the parameter of baroclinicity μΓ = Γ/N (or the free-flow Richardson number Ri = (N/Γ)2 = μΓ-2, where Γ is the geostrophic wind shear), and the ratio of the actual and equilibrium PBL depths h/hE. Moreover, the coefficient C is redefined to account for the effect of a capping inversion. It follows that A, B and C can be considered as single-valued functions of μ only in the steady-state, barotropic, nocturnal (that is short-lived) PBL. On the other hand, the advanced laws cover a wide range of the PBL regimes. They are validated through large-eddy simulations of different types of PBLs: truly neutral, conventionally neutral, nocturnal and long-lived. This new development explains why prior formulations performed so poorly, and promotes advanced resistance and heat-transfer laws as practical tools for use in environmental modelling applications.
Esau Igor N.
Zilitinkevich Sergej S.
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