Continuous spectrum analysis of roughness-induced transient growth

Continuous spectrum amplitude distributions are calculated for transiently growing roughness-induced perturbations in it flat-plate boundary layer. A direct method is employed when the complete flow is known via direct numerical simulation. A new method using regularizing functionals is developed for calculating the distributions when only partial experimental data ire available. These amplitude distribution.;; provide a way of rigorously characterizing, the boundary layer receptivity to Surface roughness. Contrasting the present results to optimal theory results conclusively demonstrates that roughness-induced disturbances cannot be described by optimal disturbance calculations. The continuous spectrum analysis demonstrates the linearity of the perturbations by correctly reproducing the flow evolution over the measurement domain. Extracting the continuous spectrum amplitudes using the partial data technique reveals the underlying vortex behavior that creates transient growth. The method described is amenable to future work with realistic distributed roughness and complex surface geometries. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3264090]