Growth mechanisms of perturbations in boundary layers over a compliant wall

The temporal modal and nonmodal growth of 3D perturbations in the boundary layer flow over an infinite compliant flat wall is considered. Using a wall-normal velocity/wall-normal vorticity formalism, the dynamic boundary condition at the compliant wall admits a linear dependence on the eigenvalue parameter, as compared to a quadratic one in the canonical formulation of the problem. As a consequence, the continuous spectrum is accurately obtained. This enables us to effectively filter the pseudospectra, which is a prerequisite to the transient growth analysis. An energy-budget analysis for the least-decaying hydroelastic and Tollmien--Schlichting modes in the parameter space reveals the primary routes of energy flow. Moreover, the maximum transient growth rate increases more slowly with the Reynolds number than for the solid wall case. Unlike the solid-wall case, viscosity plays a pivotal role in the transient growth. The initial and optimal perturbations are compared with the boundary layer flow over a solid wall; differences and similarities are discussed.