Study On The Transition To Turbulence In Slip Channel Flow

Why,when,and how fluid motion deviates from its ordered state and exhibits more complex turbulent behavior have been central problems in fluid dynamics.Considering the existence of super-hydrophobic surfaces in nature and the increasing application of such surfaces,it is of importance to study the influence of super-hydrophobic surfaces on the transition.In this case,instead of the usual no-slip boundary condition,slip boundary condition should be adopted.In this work,we mainly study the linear stability and transient growth of slip channel flow,so as to explore its potential impact on the transition from laminar to turbulent.Here,we study the stability of channel flow with streamwise and spanwise slip separately as two limiting cases of anisotropic slip and explore a broader range of slip length than previous studies did.Using the linear theory,we find that with a sufficiently large slip,both streamwise and spanwise slip trigger three-dimensional leading instabilities.Overall,the critical Reynolds number is only slightly increased by streamwise slip,whereas it can be greatly decreased by spanwise slip,indicating that the streamwise slip may slightly delay the transition of turbulent,while the spanwise slip has the opposite effects.However,in the presence of equal slip in both directions,the three-dimensional leading instabilities disappear and the flow is greatly stabilized.The results suggest that earlier instability can be triggered by introducing anisotropy in the velocity slip.In addition,we also analyze that Squire's theorem is not applicable to anisotropic slip.We adopt the adjoint method to analyze the non-modal stability of slip channel flow.It is found that streamwise slip suppresses the non-modal transient growth,whereas the spanwise slip enlarges the non-modal growth,although it does not affect the base flow.Interestingly,as the spanwise slip length increases,the optimal perturbations exhibit flow structures different from the well-known streamwise rolls.When equal slip length in streamwise and spanwise directions are present,we found that the non-modal transient growth is mainly affected by the streamwise slip,indicating that larger transient growth can be triggered by introducing anisotropy in the velocity slip and trigger earlier transition.