Fig. 2

(a) Evolution of growth rates of varicose modes obtained by PSE3D for various frequencies ranged from 35 kHz to 165 kHz with step of 10 kHz. The arrow indicates the increasing direction of frequency. The solid lines represent the second-varicose modes, while the dashed lines represent the first-varicose modes. The thick lines denote the largest components of the first- and second-varicose modes. (b) Comparison of spectra obtained by DNS (the transitional simulation) and PSE3D at x=289 mm. The spectrum of DNS is obtained by Fourier analysis of the time series at the largest root-mean-square (rms) point in the center line of the primary streak, which is believed to be contributed by only varicose modes. The peak value of the PSE3D results is fixed to be equal to that of the DNS results. The spectrum obtained by the classical PSE (not accounting for the spanwise variations of the mean flow) for the laminar boundary layer (i.e., in absence of Görtler vortices) is also shown (black lines). The solid black line and dashed black line stand for the planar and oblique results (with the spanwise wavelength of 6 mm), respectively. Note that the dashed-line results have been magnified by ten