A Theoretical Study of the Stratified Atmospheric Boundary Layer Through Perturbation Techniques

The structure of the stratified atmospheric boundary layer (ABL) over a flat uniform terrain is fairly well understood, but many known results remain mathematically unjustified. A number of factors contribute to this situation, the diversity of physical processes acting on the flow probably being the most important one. Much has been accomplished in the past in the fields of meteorology and fluid mechanics by the use of perturbation techniques. In this way, the atmospheric flow over small topographic features was addressed by (Towsend, 1972). The authors of (Knight, 1977) studied the turbulent flow over wavy surfaces and in (Jackson and Hunt, 1975) a two-layer structure for the ABL over a gentle hill was proposed. Another work (Sykes, 1980) used the asymptotic expansion method to study the influence of small terrain elevations on the main flow and on turbulence. The same idea was improved in (Hunt et al., in Quart. J. Roy. Meteor. Soc., 114:1435 1988), (Hunt et al., in Quart. J. Roy. Meteor. Soc., 114:859 1988) by introducing different upwind profiles in the analysis and considering a stably stratified atmosphere. In both articles a three layer structure was considered that shaped our understanding of the ABL up to present days. Further progress was made in (Walmsley, 1992) where matching techniques were used to propose a new ABL resistance law for neutrally-stratified flow and in (Baudauf and Fiedler, 2003) a parametrization of the effective roughness length over flat terrain in neutral atmosphere was obtained. The authors of (Pellegrini and Bodstein, 2005) introduced a modified logarithmic law for flows over gentle hills.