Statistical theory of vortex merger in the two-dimensional mixing layer

1978 ◽  
Vol 21 (2) ◽  
pp. 153 ◽  
Author(s):  
Ryuji Takaki ◽  
Leslie S. G. Kovasznay
Keyword(s):  
Statistical Theory ◽  
Mixing Layer ◽  
Two Dimensional ◽  
Vortex Merger

Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime

1995 ◽  
Vol 291 ◽  
pp. 57-81 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Travelling Waves ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Layer ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
New Type ◽  
Two Stages

We consider the nonlinear spatial evolution in the streamwise direction of slightly three-dimensional disturbances in the form of oblique travelling waves (with spanwise wavenumber kz much less than the streamwise one kx) in a mixing layer vx = u(y) at large Reynolds numbers. A study is made of the transition (with the growth of amplitude) to the regime of a nonlinear critical layer (CL) from regimes of a viscous CL and an unsteady CL, which we have investigated earlier (Churilov & Shukhman 1994). We have found a new type of transition to the nonlinear CL regime that has no analogy in the two-dimensional case, namely the transition from a stage of ‘explosive’ development. A nonlinear evolution equation is obtained which describes the development of disturbances in a regime of a quasi-steady nonlinear CL. We show that unlike the two-dimensional case there are two stages of disturbance growth after transition. In the first stage (immediately after transition) the amplitude A increases as x. Later, at the second stage, the ‘classical’ law A ∼ x2/3 is reached, which is usual for two-dimensional disturbances. It is demonstrated that with the growth of kz the region of three-dimensional behaviour is expanded, in particular the amplitude threshold of transition to the nonlinear CL regime from a stage of ‘explosive’ development rises and therefore in the ‘strongly three-dimensional’ limit kz = O(kx) such a transition cannot be realized in the framework of weakly nonlinear theory.

A thermo-chemical exploration of a two-dimensional reacting supersonic mixing layer

1997 ◽  
Vol 9 (11) ◽  
pp. 3513-3522 ◽  
Author(s):  
Debasis Chakraborty ◽  
H. V. Nagaraj Upadhyaya ◽  
P. J. Paul ◽  
H. S. Mukunda
Keyword(s):  
Mixing Layer ◽  
Two Dimensional ◽  
Supersonic Mixing ◽  
Supersonic Mixing Layer
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