Characteristics of a Secondary Instability in a Compressible Double Shear Layer

Characteristics of a secondary instability in a compressible double shear layer are investigated, using a two-staged linear stability analysis. By superimposing a small disturbance onto a basic flow, the temporal growth rate and eigenfunctions of the disturbance are investigated. Vortex evolution by flow instabilities is shown as follows: (i) Due to a flow instability, a disturbance is amplified and spanwise organized vortices are formed (Primary instability). (ii) As the spanwise vortices grow, a new instability appears and the vortices are distorted periodically (Secondary instability). It is shown that, in the secondary instability, there are two dominant modes of the disturbances, since there are upper and lower shear layers. It is shown that, in the secondary instability, the temporal growth rate of the disturbances has the maximum value, when the scale ratio between the secondary and primary instabilities is 0.7, and that the maximum value of the temporal growth rate is almost the same as that of the primary instability.