Stability Analysis of Shock Wave/Boundary Layer Interactions - Jean ...

Global Linear Stability TheoryTheoretical basics (2)SWBLI - Global Instability X. MERLE SINUMEF - ENSAM Paris 2008-07-15 5/19The stability analysis is based on the compressible Navier-StokesEquations,Flow quantities are then decomposed according toq(x,y,z,t) = Q(x,y) + ε˜q(x,y,z,t), ε ≪ 1with Q = ( U,V,W,P,T ) tand ˜Q =(ũ,ṽ, ˜w,˜p, ˜T) tThe mathematical form of the perturbation is:˜q(x,y,z,t) = 1 ∫ ∫(2π) 2 ̂q(x,y;β,ω)exp [i(βz − ωt)]dβdωF ω F βIf Im(ω) < 0, the base flow is linearly globally asymptotically stable,If Im(ω) > 0, the base flow is linearly globally asymptotically unstable.