Investigation On The Bi-global Instability Of The Streaky Structures Induced By Fundamental Secondary Instability Modes In A Hypersonic Boundary Layer

The fundamental secondary instability mode can be observed in earlier stage of hypersonic boundary layers transition in recent direct numerical simulations and quiet tunnel experiments,which can excite streaky structures in boundary layers downstream.From the perspective of transition mechanism,the streaky structures play a crucial role in the transition process in boundary layers.Therefore,it is necessary to carry out research on the instability characteristics of the streaky structures.This paper investigated the generation mechanism and the inviscid instability of these streaky structures.In order to simplify the problem,a hypersonic boundary layer over a flat plate is focused on and the instability is analyzed by both the linear stability(LST)and secondary instability analysis(SIA).This paper investigated the influence of the amplitude of the disturbance on the dominant secondary instability modal when the primary instability disturbance is the second mode.And based on the results of the secondary instability analysis in the case of a larger primary instability disturbance amplitude,the streaky structures boundary layer generated by a fundamental secondary instability mode disturbance is constructed according to the linear model.Then,the inviscid bi-global instability analysis is applied to investigate these streaky structures in this paper.The instability characteristics are analyzed in different streaky boundary layers with different amplitude,and the effect of the amplitude of the streaky structures is also investigated.The research conclusions of this paper are as follows:1.The dominated secondary instability mode is affected by the amplitude of the two-dimensional primary secondary mode disturbance.When the amplitude is small,the subharmonic mode dominates the classical secondary instability and the peak values of the eigen-functions are near the critical layer;on the contrary,when the primary mode disturbance is large enough,the fundamental mode is the dominant one and its eigenfunction has a large value in the boundary layer.By the Fourier analysis of the eigenfunction of the fundamental mode,it is found that the zero-order component of the fundamental mode is the largest.It suggests that the main component of the fundamental mode disturbances is the stationary.2.There are multiple inviscid bi-global mode can be found in streaky boundary layers,which is similar to that in the two-dimensional supersonic boundary layers.The multiple modes are caused by very different mechanism.The modes with lower frequencies are the inflection instability modes which are corresponding to the shear of the boundary layers.These modes often have a smaller growth rates and they are similar to the first modes in supersonic two-dimensional cases.By contrast,the modes with higher frequencies have greater growth rates.These modes come from the compressible characteristic,i.e.a non-inflection inviscid instability.They are similar to the higher modes in compressible two-dimensional boundary layers.In summary,the multiple modes in streaky boundary layers can be seen as the extension of the same phenomena in compressible two-dimensional boundary layers.3.The amplitude of the streaky structures has a very different effect on the multiple modes instability.The amplitude has a stabilized effect on the first modes with the amplitude is smaller.When the amplitude is larger enough,though the origin first mode has few growth rate,some new “the first mode” type disturbance can be found in the boundary layers and these new disturbances are destabilized by amplitude of the streak.For the higher modes type disturbances,the amplitude usually destabilize them and some new similar higher modes type disturbances can be found when the amplitude is larger enough.