Linear energy amplification in turbulent channels

We study the temporal stability of the Orr-Sommerfeld and Squire equations in channels with turbulent mean velocity profiles and turbulent eddy viscosities. Friction Reynolds numbers up to Re-tau= 2 x 10(4) are considered. All the eigensolutions of the problem are damped, but initial perturbations with wavelengths lambda(x) > lambda(z) can grow temporarily before decaying. The most amplified solutions reproduce the organization of turbulent structures in actual channels, including their self-similar spreading in the logarithmic region. The typical widths of the near-wall streaks and of the large-scale structures of the outer layer, lambda(+)(z) = 100 and lambda(z)/h = 3, are predicted well. The dynamics of the most amplified solutions is roughly the same regardless of the wavelength of the perturbations and of the Reynolds number. They start with a wall-normal v event which does not grow but which forces streamwise velocity fluctuations by stirring the mean shear (uv < 0). The resulting u fluctuations grow significantly and last longer than the v ones, and contain nearly all the kinetic energy at the instant of maximum amplification.