Effects of viscoelasticity on the probability density functions in turbulent channel flow

The probability density functions (PDFs) of the velocity fluctuations and their derivatives of a viscoelastic turbulent channel flow are calculated and compared against those for a Newtonian fluid at a friction Reynolds number 180. The velocity fields in both cases are provided from previous and new direct numerical simulations In the viscoelastic case, the Giesekus model is used at a friction Weissenberg number 50, a mobility parameter 1/900, and viscosity ratio 0.9, corresponding to 37.4% drag reduction. The skewness and the flatness factors, which are also calculated and presented as functions of the distance from the wall, further reveal and quantify the non-Gaussian characteristics of the turbulent structures and how they are distributed in the flow domain. With the presence of viscoelasticity the non-Gaussian character of the PDFs is typically further enhanced. In particular, larger asymmetries and much longer tails are typically observed in the viscoelastic PDFs. This indicates higher intermittency in the viscoelastic turbulent flow versus the Newtonian one. along with strong correlations between all scales of turbulence. Furthermore, we have also seen significant qualitative changes regarding the distribution of the non-Gaussian characteristics of the PDFs as a function of the distance from the wall. The most notable differences are seen in the PDFs of the shear and spanwise velocity components in the buffer and log-law regions, as well as in most of the components of the first and second order velocity derivatives. It is also found that in the log-law layer the PDFs of the logarithm of the dissipation and the pseudodissipation rate, as well as of the enstrophy, are almost Gaussian. In contrast, in the viscous sublayer and the buffer layer, significant deviations from the Gaussian shape are observed. Whereas the deviations from Gaussianity are more enhanced with viscoelasticity next to the wall, with the PDFs even more negatively skewed, away from the wall sometimes (i.e., for the logarithm of the enstrophy) they are decreased. All these findings are pointing out to a fairly complex picture for the interaction of viscoelasticity with turbulence that makes the task of developing turbulent viscoelastic models even more challenging. (C) 2009 American Institute of Physics. [doi:10.1063/1.3258758]