A study on three-dimensional disturbances in a compressible shear layer

Early stages of transition to turbulence of compressible shear layers were investigated in the viewpoint of a linear stability analysis. The primary stage of the transition is by which instability of a laminar flow (primary instability), in which disturbances develop into spanwise vortices and form a secondary flow. The secondary stage of the transition is by which instability of the secondary flow (secondary instability), in which disturbances develop into streamwise vortices. In the present study, the primary and secondary instability problems were formulated as eigenvalue problems and solved numerically using spectral methods. At first, the primary instability problems were solved. From the eigenvectors of the primary instability, we obtain density, velocity, temperature and pressure fields of the secondary flow. Using these quantities, the instability of the secondary flow was calculated. For the secondary instability, it is shown that (1) growth rates of disturbances are larger than those in the primary instability, (2) growth rates of disturbances have a peak when the ratio of wavelength of the primary and secondary instability is approximately 0.8 and (3) growth rates of disturbances are less affected by flow compressibility than those in the primary instability.