Numerical Study On Instability And Evolution Of Subharmonic Low-speed Streaks In Turbulent Channel Flow

Coherent structure is the main structure in near-wall turbulence,the evolution of such a structure has an important effect on the generation of the turbulent skin-friction drag and on the procession of heat and mass transfer.As the key element of coherent structure observed in near wall turbulence,the instability of the unstable low-speed streaks is an intrinsic reason for turbulence sustaining.In this paper,from the perspective of the near-wall turbulent coherent structure,two subharmonic low-speed streaks are constructed in a small size of the channel,and the evolution of the low-speed streaks in the small channel is systematic studied by using direct numerical simulation（DNS）.（1）Evolutions of subharmonic sinuous low-speed streaks are investigated by changing the value of the Reynolds number and the initial perturbation amplitudes,the results show that:an unique ’X’-like streamwise vortical structure can be induced by the subharmonic sinuous low-speed streaks,due to the stretching motion and the mutual induction between streamwise vortices.Such an ’X’-like streamwise vortical structure can not only improving the oscillation amplitude of the streaks but also give rise to the lift-up of the streaks,which in turn enhance the streamwise vorticity by increasing the stretching term of streamwise vorticity（+（?）u/（?）x）.Therefore,the positive feedback between low-speed streaks and the streamwise vortices happens and thus contribute to the self-sustaining of the turbulence.In addition,both the Reynolds number and the initial perturbation amplitudes have significant influences on the development of the coherent structures.The former can alter the oscillation amplitude of the streaks and further influence the development of the coherent structure during the early stage by changing the stretching term of streamwise vorticity（+（?）u/（?）x）,the latter can alter the density of the streaks and further influence the development of the coherent structure during the later stage by changing the stretching term of streamwise vorticity（+（?）u/（?）x）.（relevant content has been published in the journal of Applied Mathematics and Mechanics）（2）Evolutions of subharmonic varicose low-speed streaks are investigated by changing the value of the Reynolds number and the initial perturbation amplitude.The results show that:the initial perturbation amplitude to maintain the turbulence for subharmonic varicose low-speed streaks are larger compared to that of subharmonic sinuous low-speed streaks,as a consequence,the subharmonic varicose low-speed streaks are more stable than subharmonic sinuous low-speed streaks.The tilted streamwise vortex tubes and ’V’-like streamwise vortex tubes can be induced by the subharmonic varicose low-speed streaks simultaneously,and the vortical structure can also lead to the positive feedback process between low-speed streaks and streamwise vortices.During the self-sustaining process of the turbulence,the subharmonic varicose low-speed streaks cannot be kept permanently but transform into the subharmonic sinuous low-speed streaks.Similar to the subharmonic sinuous low-speed streaks,the variation of the Reynolds number and the initial perturbation amplitude has an impact on the development of the coherent structure during the early and the later stage,respectively.（relevant content has been accepted in the journal of Applied Mathematics and Mechanics,and the reviewers’ comments is ’The finding is very interesting and this implies the dominated role of the SS low-speed streaks in near-wall turbulence.The topic of investigation is I suppose worthy and the paper is generally well written and well documented,which contains some new interesting results.’）（3）The hairpin vortex induced by subharmonic sinuous low-speed streaks is described by λ_ci method,and the evolutions of hairpin vortex are also investigated by changing the value of the Reynolds number and the initial perturbation amplitude.The results show that:The hairpin vortex and the hairpin packet can be the induced by the subharmonic sinuous low-speed streaks.The formation of a hairpin vortex is generated from the ’X’-like streamwise vortices,and then shapes in ’Λ’-and ’Ω’-pattern alternatively.The pattern of the hairpin vortex（’Λ’ and ’Ω’-pattern）is depended on the shape（pointed shape and ellipsoid shape）of the spanwise collision between subharmonic sinuous low-speed streaks,which is the result of the shearing between the high-and low-speed fluids.Furthermore,the formation of the hairpin packet is depended on the collision between two subharmonic sinuous low-speed streaks.When the Reynolds number and the initial perturbation amplitude are small,regeneration of the secondary hairpin vortex can be accompanied by the decay of the primary hairpin vortex and a hairpin packet composed of several hairpin vortices can not be formed,and vice versa.（relevant content has been published in the journal of Fluid Dynamics Research,and the reviewers’ comments is ’The observation of detailed vortex dynamics of the spanwise subharmonic structures might lead to new knowledge for the interpretation of the near-wall hairpin vortex generation.’）...