Scaling of the mean transverse flow and Reynolds shear stress in turbulent plane jet

Abstract

Proper scaling for the mean transverse flow and Reynolds shear stress in a turbulent plane jet is determined using a scaling patch approach. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity equation, a proper scale for the mean transverse flow in a turbulent plane jet is found as Vref=−δdUctr/dx, where δ is the jet half width and dUctr/dx is the decay rate of the mean axial velocity at the jet centerline. By seeking an admissible scaling for the mean axial momentum equation, a proper scale for the kinematic Reynolds shear stress is found as Ruv,ref=Uctr Vref, which is a mix of the velocity scales in the axial and transverse directions. Approximation functions for the scaled mean transverse flow and Reynolds shear stress are developed and found to agree well with experimental and numerical data. Similarities and differences between the scales of the mean transverse flow and Reynolds shear stress in turbulent plane jets and zero-pressure-gradient turbulent boundary layer flows are clarified.