Publication Date:
2006-07-01
Description:
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 Reτ = 2 × 104 are considered. All the eigensolutions of the problem are damped, but initial perturbations with wavelengths λx 〉 λz 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, λz+ and λz/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 u event which does not grow but which forces streamwise velocity fluctuations by stirring the mean shear (uv 〈 O). The resulting v fluctuations grow significantly and last longer than the v ones, and contain nearly all the kinetic energy at the instant of maximum amplification. © 2006 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
