Decomposition of the Reynolds shear stress in a turbulent boundary layer modified by miniature vortex generators

Abstract

The investigation of the spanwise modulation of the Reynolds shear stress (RSS) distributions of a turbulent boundary layer modified by miniature vortex generators (MVGs) is performed, using an approach on a time-resolved velocity data set. The methodology is based on quadrant analysis of RSS to first identify the spatial and temporal information of the RSS events. We then apply the spanwise Fourier mode decomposition and triple velocity decomposition to obtain various statistics of the decomposed RSS events, including their conditional mean structures and actual mean skin friction contributions. In addition, the spanwise modification of the MVG on the RSS has been characterized by the fundamental and subharmonic modes of motions that scale with the spanwise separation distance (z) between MVG pairs. The interactions between the + z -scaled mode and subharmonic modes are further investigated using the scale-by-scale RSS transport equation [Kawata and Alfredsson, Phys. Rev. Lett. 120, 244501 (2018)]. Results show that the + z -scaled motion tends to strengthen due to the inverse cascade of its subharmonic modes of motions, allowing the + z -scaled motion to persist further downstream.