Subcritical transition of the Stokes layer induced by wall surface roughness

Wall defect is an important reason for the Stokes layer transition. The present study investigates the transition of the Stokes layer induced by wall surface roughness under subcritical Reynolds numbers, which is lower than the critical Reynolds number of the global neutral curve. A pseudo-spectral numerical method is utilized to simulate the interactive effects of different parameters related to surface roughness. Based on the cycle-average pulsation energy, a critical roughness height is defined for the flow transition. A characteristic curve, termed as the transition curve, is discovered to relate the most critical roughness height with the Reynolds number for a given wave number in the span-wise direction. This curve can provide a quantitative criterion to predict the transition of the Stokes layer caused by the surface roughness. The result demonstrates that the critical roughness height is lower for three-dimensional than for two-dimensional roughness. It is also shown that when the Reynolds number is close to the critical Reynolds number of the global neutral curve (R=600), even a roughness height in the order of one nanometre could significantly interact with the flow and causes the transition. Moreover, when the Reynolds number is around 300, the order of 1 roughness height could be sufficient for the transition. This offers a possible explanation as to why the transitions observed in most of the experimental findings usually occur when the Reynolds number is around 275.