Linear perturbation analysis of flow over a flat plate with an elliptic leading edge

Linear perturbation analysis is used to investigate the impact of leading-edge geometry on disturbance amplification, and a flat plate is adopted to eliminate other geometric factors, e.g., thickness, camber, etc. The two-dimensional (2D) base flow is first examined across a range of Reynolds numbers (Re) and leading-edge aspect ratios (AR). The threshold for the formation of a laminar separation bubble (LSB) on the AR-Re plane is identified, with the critical AR increasing monotonically with Re. At Re=300, the optimal energy gain exhibits two competing branches: a three-dimensional (3D) steady branch at inflow frequency ω=0 and finite spanwise wavenumber β, and a 2D unsteady branch at β=0 and finite ω. For higher AR with attached base flow, the dominant response is the 3D steady branch, and its optimal perturbation structure and downstream evolution are consistent with the lift-up mechanism, while finite-frequency responses are weaker. For lower AR with an LSB, the dominant response is the 2D unsteady branch, which exhibits strong finite-frequency amplification over a broad frequency range and downstream wave-packet structures concentrated along the separated shear layer, consistent with Kelvin–Helmholtz instability. A transitional regime is identified near AR≈0.6, where the 3D steady and 2D unsteady branches attain comparable gains, and a 3D unsteady mode with mixed features is observed to be the most energetic one. As Re increases, the crossover between the 2D unsteady and 3D steady branches shifts to lower AR. These results demonstrate that the leading-edge geometry dominates the amplification of free-stream disturbance through its influence on leading-edge separation.