Scaling patch analysis of planar turbulent mixing layers

Abstract

Proper scales for the mean flow and Reynolds shear stress in planar turbulent mixing layers are determined from a scaling patch analysis of the mean continuity and momentum equations. By seeking an admissible scaling of the mean continuity equation, a proper scale for the mean transverse flow is determined as Vref=(dδ/dx)Uref, where dδ/dx is the growth rate of the mixing layer width and Uref=Uh−Ul is the difference between the velocity of the high speed stream Uh and the velocity of the low speed stream Ul. By seeking an admissible scaling for the mean momentum equation, a proper scale for the kinematic Reynolds shear stress is determined as Ruv,ref=UavgVref=[12Audδdx]Uref2, where Au=def(Uh−Ul)/(Uh+Ul) is the normalized velocity difference that emerges naturally in the admissible scaling of the mean momentum equation. Self-similar equations for the scaled mean transverse flow V* and Reynolds shear stress Ruv*=Ruv/Ruv,ref are derived from the mean continuity and mean momentum equations. Approximate equations for V* and Ruv* are developed and found to agree well with experimental data.