Probability Density Functions of Vorticities in Turbulent Channels with Effects of Blowing and Suction

This paper presents direct numerical simulation (DNS) result of the Navier-Stokes equations for turbulent channel flows with blowing and suction effects. The friction Reynolds number is Re-tau = 394 and a range of blowing and suction conditions is covered with different perturbation strengths, i.e. A = 0.05, 0.1, 0.2. While the mean velocity profile has been severely altered, the probability density function (PDF) for (spanwise) vorticity - depending on wall distance (y(+)) and blowing/suction strength (A) - satisfies the generalized hyperbolic distribution (GHD) of Birnir [The Kolmogorov-Obukhov statistical theory of turbulence, J. Nonlinear Sci. (2013a), doi: 10.1007/s00332-012-9164-z; The Kolmogorov-Obukhov theory of turbulence, Springer, New York, 2013b] in the bulk of the flow. The latter leads to accurate descriptions of all PDFs (at y(+) = 40, 200, 390 and A = 0.05, 0.2, for instance) with only four parameters. The result indicates that GHD is a general tool to quantify PDF for turbulent flows under various wall surface conditions.