Floquet analysis of fundamental,subharmonic and detuned secondary instabilities of Grtler vortices  

作　　者：REN Jie FU Song 

机构地区：[1]School of Aerospace Engineering,Tsinghua University

出　　处：《Science China(Physics,Mechanics & Astronomy)》2014年第3期555-561,共7页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.10932005 and 11202115)

摘　　要：Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental, subharmonic and detuned secondary instabilities. With the Gortler-vortices-distorted base flow, two classes of secondary disturbances, i.e. odd modes and even modes, are identified according to the eigenfunctions of the disturbances. These modes may result in different patterns in the late stages of the transition process. Li and Malik [ 1 ] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes I ＆ Ⅱ and odd modes I ＆ lI. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplifeation. The detuned modes are confirmed to be less amplifed than the fundamental （for the odd mode I） and subharmonic modes （for even modes I ＆ II and the odd mode II）.Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the Grtler instability up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental,subharmonic and detuned secondary instabilities. With the Grtler-vortices-distorted base flow,two classes of secondary disturbances,i.e. odd modes and even modes,are identified according to the eigenfunctions of the disturbances. These modes may result in diferent patterns in the late stages of the transition process. Li and Malik [1] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes Ⅰ & Ⅱ and odd modes Ⅰ & Ⅱ. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplification. The detuned modes are confirmed to be less amplified than the fundamental(for the odd mode Ⅰ) and subharmonic modes(for even modes Ⅰ & Ⅱ and the odd mode Ⅱ).

关 键 词：Goirtler vortices secondary instability Floquet theory 

分 类 号：V211[航空宇航科学与技术—航空宇航推进理论与工程]