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Probability density functions of vorticities in turbulent channels with effects of blowing and suction. (English) Zbl 1401.76073

Summary: 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 \({\mathrm{R}}\mathrm{e}_\tau = 394\) 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 B. Birnir [J. Nonlinear Sci. 23, No. 4, 657–688 (2013; Zbl 1282.76112); The Kolmogorov-Obukhov theory of turbulence. A mathematical theory of turbulence. New York, NY: Springer (2013; Zbl 1273.76001)] 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.

MSC:

76F55 Statistical turbulence modeling
76D05 Navier-Stokes equations for incompressible viscous fluids
76F65 Direct numerical and large eddy simulation of turbulence
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