Slip boundary effect on the critical Reynolds number of subcritical transition in channel flow

• Published in: Theoretical and applied mechanics letters Vol. 13; no. 2; p. 100431
• Main Authors: Xiao, Yue, Zhang, Linsen, Tao, Jianjun
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-03-2023; Elsevier
• Subjects: Channel flow; Localized wave packet; Slip length; Subcritical transition; Slip length; Localized wave packet; Channel flow; Subcritical transition
• ISSN: 2095-0349
• DOI: 10.1016/j.taml.2023.100431

•The effect of slip boundaries on the threshold Reynolds numbers of subcritical transitions in parallel shear flows is studied, to the best of our knowledge, for the first time numerically and theoretically.•It is shown for the two-dimensional channel flows that both the positive and the negative slip lengths postpone the formation of localized wave packet, the characteristic flow structure of the transition.•By applying a variable transformation, a power law found in simulations is explained theoretically, i.e. the relative increment of the critical Reynolds number due to the slip boundary is proportional to the square of the slip length.
In this letter, the effect of slip boundary on the origin of subcritical transition in two-dimensional channel flows is studied numerically and theoretically. It is shown that both the positive and the negative slip lengths will increase the critical Reynolds number of localized wave packet and hence postpone the transition. By applying a variable transformation and expanding the variables about a small slip length, it is illustrated that the slip boundary effect only exists in the second and higher order modulations of the no-slip solution, and hence explains the power law found in simulations, i.e. the relative increment of the critical Reynolds number due to the slip boundary is proportional to the square of the slip length.