In this paper, the transition processes induced by three-dimensional wavy wall roughnesses with two different distribution topologies (staggered type-S and aligned type-A) are studied at Mach 5.92 by direct numerical simulations. For the first time, the effects of the two distribution topologies on transition are investigated. It is found that the type-S roughness can induce transition significantly earlier – about 34.5 % earlier than that of the type-A roughness under the conditions in this paper. Both the type-S and type-A roughnesses can induce counter-rotating pairs of streamwise vortices. A ‘staggered-enhancing’ mechanism for the vortices is discovered in the type-S roughness, which results in significantly stronger vortices than in the type-A case. The enhanced vortices in turn produce stronger shear layers, which is the key factor leading to the stronger transition-induced ability of the type-S roughness. Then, based on the spectral proper orthogonal decomposition, the linear and nonlinear instability characteristics of the two roughnesses are investigated. For type-S roughness, its downstream linear instability is dominated by the low-frequency shear layer instability near 50 kHz. Once the linear fluctuation amplitude saturates, the nonlinear breakdown is triggered from the shear layer. For type-A roughness, its downstream linear instability is co-dominated by two modes: the low-frequency shear layer instability near 23 kHz, and the high-frequency Mack’s second mode above 100 kHz. Both modes exhibit significantly lower growth rates than the dominant shear layer instability in the type-S case, ultimately delaying the transition onset compared to type-S roughness.
Yang et al. (Mon,) studied this question.