Numerical Study Of Transition In Channel Flow

Recent studies have shown that when the Reynolds number is low,the turbulence presents an elongated banded structure with a certain tilt angle to the streamwise direction.With the development of the flow field,the size of the banded turbulent structure does not increase in the streamwise direction,but grows laterally in the spanwise direction,making the length of the turbulent band longer.In this paper,direct numerical simulation of the flow field at low Reynolds number is carried out to analyze the motion properties and turbulence generation mechanism of the turbulent band at low Reynolds number.The results show that the turbulent structure continuously invades the laminar flow region at the downstream end,and gradually decays at the upstream end.The asymmetry between the two ends results in the transverse growth of the turbulent band.Through the stability analysis of the local mean flow near the downstream end,it is found that local spanwise instability is the main reason for the development and self-sustainment of the turbulent band at low Reynolds number.In addition,in the presence of multiple bands,the interaction between bands will determine the pattern that bands can form,which is of great significance to the study of channel transition.Therefore,precise control on the position and orientation of turbulent bands is very important.Inspired by the instability mechanism at the head of the band,we present a method that can trigger turbulent bands directly at low Reynolds numbers.The key is to impose a moving localised force which induces a local flow with sufficiently strong spanwise velocity inflection.More importantly,we can generate any band patterns with desired relative position and orientation,which solves the disadvantages of traditional method,and greatly facilitates the subsequent numerical analysis.With this method,a series of simulation is presented in this paper,the propagation speed of the downstream end and the advection speed of the low-speed streaks in the bulk are discussed and investigated.Based on these results,a calculation method for the tilt angle of turbulent bands is proposed.