1217 Comparison of linear disturbance in a two-dimensional turbulent jet with a linear stability theory

Abstract

It is recently revealed that there exists a linear disturbance in a two-dimensional turbulent jet. In this study, theoretical explanation for the linear disturbance was attempted based on disturbance equations, and velocity measurements using an x-type hot-wire anemometer and their comparison to a linear stability theory based on the parallel flow assumption were performed. An periodical-average was applied for the velocity data to extract a disturbance excited by a periodical initial disturbance, then it was confirmed linearity of the excited disturbance to the initial disturbance for low intensity of the initial disturbance. The growth rate of the excited disturbance is in qualitative agreement with the linear stability theory as well as the disturbance distribution. The disturbance equations for the periodic components of disturbances includes the second-order product terms of the random components, and the third-order and the fourth-order product terms appear in the high-order disturbance equations. The experimental data indicate that these terms are proportional to the initial disturbance amplitude until the initial disturbance is so strong that the excited disturbance is non-linear behavior, indicating that the disturbance equations are linear for an infinitesimal periodic component. This well explains existence of the linear disturbance in the turbulent flows.