Dual Nature of Heat Flux in Stable Atmospheric Surface Layer

Abstract:

The behavior of heat flux (H) with respect to the stability parameter (ζ) in stable surface layer (SSL) is analyzed with in the framework of Monin-Obukhov similarity (MOS) theory. The analytical expressions of H are obtained as functions of wind speed (U) and wind shear (dU/dz) using the linear similarity functions and accordingly two cases, (i) U = δ (constant) and (ii) dU/dz = δ are considered. The mathematical analysis shows that the magnitude of H increases with ζ till it attains a maximum value at ζ =ζ_c and then starts decreasing with increasing stability suggesting the dual characteristic of heat flux with stability parameter. The point of maximum heat flux is found to be dependent on the roughness length (z₀) as well as the height above the surface. An attempt has been made to analyze the sensitivity of this dual characteristic of H with ζ using the non-linear similarity functions. The analysis shows that the dual nature of H persists in the case of linear as well as non-linear similarity functions. However, the point of extremum appears to be dependent on the nature of the similarity functions. Turbulent data over a tropical site Ranchi (India) is analyzed to validate the observed nature of H with the theoretical nature as predicted by MOS. The analysis of observational data reveals the non-existence of any preferred stability state in SSL as speculated by Wang and Bras (2010, 2011) and supports the conclusions of Malhi 1995, Derbyshire 1999, van de Wiel et al. 2007, Basu et al. 2008, and van de Wiel et al. 2011. Thus, the non-uniqueness of MOS equations does not appear to be a mathematical artifact and it is consistent with the observations as far as the nature of heat flux with respect to stability parameter in SSL is concerned.