Excitation and Linear Instability of Stationary Modes in Falkner-Skan-Cooke Boundary Layer

Past studies showed that a micron-sized surface roughness may cause the generation of a significant unstable, stationary wave in a crossflow boundary layer, and consequently promote or delay the laminar-turbulent transition. The crossflow boundary layer is usually driven by the favorable pressure gradient which is produced by accelerated inviscid velocity. Hence, for a fixed sweep angle, the magnitude of pressure gradient is the key parameter for the excitation and evolution of the stationary crossflow mode. In order to study the effect of pressure gradient on the excitation and subsequent linear development of stationary mode, a classical Falkner-Skan-Cooke boundary layer is introduced so that the magnitude of pressure gradient can be easily parameterized by an acceleration coefficient. Numerical simulation is performed to induce the stationary perturbation by chordwise-isolated, spanwise-periodic roughness at the lower branch of neutral curve. Then the excited waves develop into Rayleigh modes in the downstream region. The stationary modes with different spanwise wavenumbers in various favorable-pressure-gradient boundary layers are simulated and analysed to determine the effect of pressure gradient. an‎d the corresponding coupling coefficients are calculated to connect the initial amplitude and the eigenmode of linear stability theory for implementing the existing prediction method of laminar-turbulent transition.