Receptivity of stationary transient disturbances to surface roughness

Abstract

Recent experiments on transient disturbance growth in boundary layers indicate that disturbances generated by surface roughness undergo suboptimal growth. The implication is that the receptivity mechanism governing the distribution of disturbance energy among the continuous spectrum of damped Orr-Sommerfeld/Squire modes produces energy distributions that are significantly different from the theoretical optimum. Experiments presented here are intended to investigate how the amplitude and diameter of cylindrical roughness elements arranged in a spanwise array affect various features of transient growth. The objective is to infer how or to what extent the roughness features affect the continuous spectrum and to use this information as a foundation for future receptivity models. The results show that the energy of stationary disturbances varies as Rek2 and that the streamwise distance over which the disturbances grow increases slightly with increasing Rek. As the roughness diameter is varied, dramatic changes in the qualitative nature of the resulting transient growth occur. Both the variation of the growth length with Rek and the behavioral changes with roughness diameter indicate that the energy distribution among the continuous modes is a strong function of roughness features and that an accurate and sophisticated receptivity model will be necessary to accurately predict transient growth. © 2005 American Institute of Physics.