Hierarchical similarity in the atmospheric boundary layer turbulence

The S-L (She and Leveque) scaling law, also named the hierarchical similarity theory, has been extensively tested for the turbulence made in the laboratory, but seldom been tested for the turbulence in the atmospheric boundary layer (ABL). In this paper, the S-L scaling law is applied to the turbulence in the ABL, observed under unstably stratified conditions and over different types of underlying surfaces. The results of analyses show that over this type of homogeneous and flat underlying surface, such as the underlying surface in HUBEX (Huaihe River Basin Energy and Water Cycle Experiment), vertical speed and temperature fields well satisfy the S-L scaling law. For the turbulence over the homogeneous but rather rough underlying surface of forest and under unstably stratified conditions in PFRD (Park Falls Ranger District of the Chequamegon National Forest, Wisconsin, USA), the analyses show that the vertical speed and temperature fields sometimes conform sometimes do not conform to the S-L scaling law. However, at a time, either both of the vertical speed and temperature fields conform to the S-L scaling law, or both of them do not. Horizontal speed fields in both of the field experiments do not satisfy the S-L scaling law. The new explanation of the above-mentioned phenomena is given.