The effect of compliant walls on secondary instabilities in boundary layer transition
The effect of compliant walls on the stage of transition where three-dimensional secondary instabilities (SIs) are excited is studied. A theory developed by Herbert (1983) to represent SIs for two-dimensional primary instabilities is extended to allow for oblique waves. The effects of the variations in primary amplitude, spanwise, wavenumber, and Reynolds number on the SIs are examined. As in the rigid-wall case, the subharmonic mode of SI dominates for low-amplitude disturbances over compliant walls. Both isotropic and nonisotropic compliant walls lead to reduced SI growth rates as compared to the rigid-wall results. Calculations show that, for high frequencies, the nonisotropic wall suppresses the amplification of the SIs, while for the isotropic wall SIs grow with an explosive rate similar to the rigid-wall results. For lower frequencies, both types of compliant wall suppress the amplification of SIs.