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Excitation and Linear Instability of Stationary Modes in Falkner-Skan-Cooke Boundary Layer
Author(s): Luyu Shen, Changgen Lu
Keywords: Stationary wave, Instability, Falkner-Skan-Cooke boundary layer
Past studies showed that a micron-sized surface roughness can generate a significant steady instability 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 slip velocity. Hence, the magnitude of pressure gradient is the key parameter for the excitation and instability 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 similarity solution is employed to generate the base flow 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 mode 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.

Journal of Applied Fluid Mechanics

The Journal of Applied Fluid Mechanics (JAFM) is an international, peer-reviewed journal which covers a wide range of theoretical, numerical and experimental aspects in fluid mechanics. The emphasis is on the applications in different engineering fields rather than on pure mathematical or physical aspects in fluid mechanics. Although many high quality journals pertaining to different aspects of fluid mechanics presently exist, research in the field is rapidly escalating.