Analysis of turbulence in shear flows using the stabilization principle

Abstract

An analysis is made based upon the concept that the velocity fluctuations, and therefore, the Reynolds stresses, driven by the instability of the original flow grow until a new stable state is approached. The Reynolds stresses incorporated into the Orr-Sommerfeld equation are coupled with the main flow such that all the imaginary parts of the complex eigenvalues vanish, i.e., the original instability is eliminated. Using this stabilization principle, it is possible to find the Reynolds stresses as well as the mean velocity for plane Poiseuille flow with the Reynolds number slightly higher than the critical.