An improvement on the theoretical model for the large-scale coherent structures in the outer region of a turbulent boundary layer

According to the experimental results, there exist large-scale coherent structures in the outer region of a turbulent boundary layer, which have been studied by many authors.As experimental results, Antonia (1990) showed the phase- aver aged streamlines and isovorticity lines of the large-scale coherent structures in a turbulent boundary layer for different Reynolds numbers. Based on the hydrodynamic stability theory, the 2-D theoretical model for the large-scale structures was proposed by Luo and Zhou, in which the eddy viscosity was defined as a complex function of the position in the normal direction. The theoretical results showed in ref. were in agreement with those in ref. However, there were two problems in the results. One is that in the experimental results, there were divergent focuses between two saddle points in the streamlines, but in the theoretical results, there were centers. The other is that the stretched parts of the isovorticity lines appear at the location of centers in the theoretical results, while in the experimental results they located somewhere between the focuses and saddle points. The reason is that the computations were based on a 2-D model.

An optimal theory for an expansion of flow quantities to capture the flow structures

An optimal theory on how database analysis to capture the flow structures has been developed in this paper, which include the POD method as its special case. By means of the remainder minimization method in the Sobolev space, for more general optimal conditions the new theory has the potential to overcome an inherent limitation of the POD method, i.e., it cannot be used to the situations in which the optimal condition is other than the inner product global one. As an example, using the new theory, the database of a two-dimensional flow over a backward-facing step is analyzed in detail, with velocity and vorticity bases.