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.

Keywords:

Stationary wave , Falkner , Instability , Skan , Cooke boundary layer‎