Fig. 1

Comparison of instantaneous growth rates of present results with those of Luo and Wu[5] at different phases of Stokes layer with λ=k=1, ψ=0, R=780, h1=h2=16, and α=0.3"

Fig. 2

Comparisons of most unstable transient eigenvectors of present results with those of Luo and Wu[5] at selected phases t/T=0, 0.2, 0.4, 0.64, 0.8, 0.9, 1.0, and 1.1 (from left to right) with same parameters as in Fig. 1"

Fig. 3

Second-order derivatives of base-flow velocity U to y at time t/T=0 (color online)"

Fig. 4

Growth rates of two most unstable modes and corresponding wave numbers varying with δ for R=780"

Fig. 5

Vorticities of two most unstable modes at δ=0.1 and t/T=0.2 for R=780: (a) Mode 1 and (b) Mode 2 (color online)"

Fig. 6

Production and dissipation of two most unstable modes at δ=0.1, α=0.51, and t/T=0.2: (a) production and (b) dissipation (color online)"

Fig. 7

Dissipation of Mode 1 at δ=0.1, α=0.51, and t/T=0.2 (color online)"

Fig. 8

Effects of Stokes-layer interactions on production and dissipation of Mode 1: (a) production and (b) dissipation, where α=0.51, t/T=0.2 for δ=0.1; α=0.8, t/T=0.19 for δ=0.42; α=1.7, t/T=0.11 for δ=0.9 (color online)"

Fig. 9

Effects of Stokes-layer interactions on production and dissipation of Mode 2: (a) production and (b) dissipation, where parameters are same as in Fig. 8 (color online)"

Fig. 10

Comparison of eigenvalues in viscous and inviscid cases at δ=0.1, t/T=0.2, R=780, and α=0.51"

Fig. 11

Comparison of unstable eigenvectors of two most unstable modes in viscous and inviscid cases with same parameters as in Fig. 10: (a) Mode 1; (b) Mode 2, where solid lines are for viscous case (dark), and dashed lines are for inviscid case (red) (color online)"

Table 1

Eigenvalues of two most unstable modes in viscous and inviscid cases"

Fig. 12

Instantaneous growth rates varying with time for different δ at R=780 (color online)"

Fig. 13

Instantaneous growth rates of α=0.76 and α=0.51 at δ=0.4 for R=780"

Fig. 14

Comparison of instantaneous growth rates between cases of λ=0.5 and λ=1.0 for R=780, δ=0.1, and α=0.51"

Fig. 15

Comparison of eigenvectors in cases of λ=1.0 (solid) and λ=0.5 (dashed) at selected phases of t/T=0, 0.25, 0.5 (from left to right): (a) and (b) , where R=780, δ=0.1, and α=0.51"

Table 2

Three defined cases"

Fig. 16

Maximum growth rates of Cases 1 and 3 varying with λ for R=780"

Fig. 17

Instantaneous growth rates of Cases 1 and 2 varying with time for R=780, δ=0.4, and λ=2"

Fig. 18

Comparison of eigenvectors in Cases 1 (solid) and 2 (dashed) at selected phases t/T=0, 0.25, 0.5 (from left to right): (a) and (b) , where R=780, δ=0.4, and λ=2"

Fig. 19

Maximum growth rates varying with δ for different λ at R=780"

Fig. 20

Maximum growth rates varying with ϕ for R=780"

Fig. 21

Instantaneous growth rates varying with time at δ=0.3 and ϕ=0.25 for R=780"

Fig. 22

Most unstable eigenvectors at time t/T=0.2: (a) and (b) , where R=780, δ=0.3, ϕ=0.25, and α=0.57"

Fig. 23

Most unstable eigenvectors at time t/T=0.45: (a) and (b) , where parameters are same as in Fig. 22"

Fig. 24

Maximum growth rates varying with k for R=780"

Fig. 25

Instantaneously most unstable eigenvectors at time t/T=1.69: (a) and (b) , where R=780, δ=0.3, and α=0.59"

Fig. 26

Instantaneously most unstable eigenvectors at time t/T=0.85: (a) and (b) , where R=780, δ=0.3, and α=0.72"