Effect of streamwise domain size on the POD mode characteristics in an adverse pressure gradient turbulent boundary layer

Abstract

Proper orthogonal decomposition (POD) is used to study coherent structures on measurements of wall-bounded turbulent flows. In order to apply POD in the study of turbulent boundary layers, it is important to determine the appropriate size of the flow domain to be used in POD analysis. This study uses the 2C-2D PIV measurements of an adverse pressure gradient (APG) turbulent boundary layer (TBL) with beta ~ 0 - 3.74 and Re_delta2 ~ 1720 - 23430 where Re_delta2 is the momentum thickness based Reynolds number and beta is the Clauser's pressure gradient parameter. The measurements were obtained in the Laboratoire de Mecanique des Fluides de Lille (LMFL) High-Reynolds-Number (HRN) Boundary Layer Wind Tunnel, Lille, France. Spanning over 20 delta along the streamwise direction (where delta is the boundary layer thickness in the middle of the field of view), these are appropriate to be used in the study of the extent of the large-scale motions. POD analysis on the variable domain size along the streamwise direction (delta x) suggests that the POD mode shape changes with delta x. In this particular TBL, the shape of the first mode which represents the largest scales in the fluid flow, changes until delta x is equal to or greater than 8 delta. It is also observed the smaller scales of higher-order POD modes take longer delta x to converge in the mode shape. The streamwise integral-length-scale of 6.68 delta also confirms the size of the largest scales to be around 8 delta. Therefore, for this particular TBL, a minimum streamwise domain size of 8 delta is appropriate for the analysis of large-scale motions using POD.