Empirical Scaling Law for Free Shear Layer Growth

Free shear layers exhibit large-scale coherent structures driven by Kelvin-Helmholtz instabilities that amplify downstream of the separation edge. Despite extensive research on both single- and two-stream configurations, a unified scaling law for their growth remains elusive. Previous studies offer conflicting arguments, while some indicate that shear layer (SL) growth rates depend on upstream boundary layer (BL) conditions but fail to establish a clear relationship, others assert the influence of downstream conditions. This point towards a complex interplay of turbulent flow scales possibly involving dominant forcing frequencies within the inner-region of the BL, small-scale turbulence within the shear layer core, and dynamics at the turbulent--non-turbulent interface of SL. While multiple mechanisms likely contribute to the observed variability, a combination of bulk flow parameters may serve as a practical surrogate to capture and explain growth behavior. In this study, we propose an empirical scaling law for the growth of free shear layers using 2D-PIV measurements within single-stream SLs over a range of Reynolds numbers. Time-averaged velocity fields and relevant flow parameters from both the SL and upstream BL are analyzed to identify and correlate key parameters governing SL development. The resulting scaling law is validated against both single- and two-stream SL datasets from the literature, showing strong agreement. Additionally, we demonstrate that this scaling framework extends to higher-order quantities, such as total turbulent kinetic energy (TKE), underlining the influence of upstream BL properties on SL growth. The findings offer a practical approach to predict SL growth and turbulence characteristics, relevant to numerous engineering systems involving free-shear and mixing flows.