Geometrical structure analysis of a zero-pressure-gradient turbulent boundary layer

Abstract

The present work focuses on the geometrical features of a zero-pressure-gradient turbulent boundary layer based on vectorline segment analysis. In a turbulent vector field, tracing from any non-singular point, along either the vector or the inverse direction, one will reach a local extremum of the vector magnitude. The vectorline between the two local extrema is defined as the vectorline segment corresponding to the given spatial point. Specifically the vectorline segment can be the streamline segment for the velocity vector case, or the vorticity line segment for the vorticity vector case. Such a quantitatively defined and space-filling vectorline segment structure reflects the natural vectorial topology. Because of inhomogeneity in the wall-normal direction, vectorline segments corresponding to the grid points at specified wall-normal distances are sampled for statistics. For streamline segments, the probability density function (p.d.f.) of the normalized segment length in different flow regions matches a model solution, and for vorticity line segments such a p.d.f. in the log-law region and beyond matches the same model solution, which indicates some universality of different flow regions and different vector field structures. Typically the joint p.d.f. of the characteristic parameters of streamline segments presents clear asymmetry, which is closely related to the skewness of the velocity derivative. Moreover, the orientation statistics of vectorline segments, characterized by the coordinate difference between the segment starting point and ending point, have been provided to quantify the flow anisotropy.