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Linear energy amplification in turbulent channels. (English) Zbl 1095.76021
Summary: We study the temporal stability of Orr-Sommerfeld and Squire equations in channels with turbulent mean velocity profiles and turbulent eddy viscosities. Friction Reynolds numbers up to $$\text{Re}_{\tau} = 2 \times 10^4$$ 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.

MSC:
 76E05 Parallel shear flows in hydrodynamic stability 76F10 Shear flows and turbulence 76M22 Spectral methods applied to problems in fluid mechanics
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