Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (3): 359-368.doi: https://doi.org/10.1007/s10483-014-1796-8

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Nonlinear evolution of Klebanoff type second mode disturbances in supersonic flat-plate boundary layer

 YU Min, LUO Ji-Sheng   

  1. Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China
  • Received:2013-01-31 Revised:2013-05-22 Online:2014-03-26 Published:2014-02-18

Abstract: Studying the evolution of 3D disturbances is of crucial theoretical importance for understanding the transition process. The present study concerns the nonlinear evolution of second mode unstable disturbances in a supersonic boundary layer by the numerical simulation, and discusses the selectivity of 3D disturbances and possibility to transition. The results indicate that a Klebanoff type nonlinear interaction between 2D and 3D disturbances with the same frequency may amplify a band of 3D disturbances centered at a finite spanwise wavenumber. That is, certain 3D disturbances can be selectively and rapidly amplified by the unstable 2D disturbances, and certain small-scale 3D structures will appear.

Key words: thick-walled cylinder and spherical shell, strain gradient, nonlocal, viscoplasticity, supersonic flat-plate boundary layer, nonlinear interaction, secondary instability, selectivity of 3D disturbance

2010 MSC Number: 

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