THE STABILITY ANALYSIS OF TURBULENT MEAN FLOW OVER A COMPLIANT WALL

Abstract

This thesis is concerned with the stability of turbulent mean flow over rigid and compliant wall. A Turbulent Orr-Sommerfeld equation which includes the turbulent stress shear term is developed using a mixing length model. A companion matrix technique is used to linearize the eigenvalue problem for complex radian frequency, and all the eigenvalues can be determined without any initial estimate. An Iteration Method is employed to check some of the eigenvalues obtained which are of more importance. The results are compared with previous ·experimental results showing fair consistency. It is found that an upward shift of the basic velocity profile can stabilize the unstable modes found in turbulent boundary-layer flow over a slightly viscoelastic compliant wall, thereby implying that the shifted velocity profile is one of the Stable Velocity Profiles for turbulent flow over this kind of compliant wall which may also explain Gadel-Hak et. al's and T. Lee et. al's findings in their experiments.