**Turbulent flow of non‐newtonian systems**

A theoretical analysis for turbulent flow of non‐Newtonian fluids through smooth round tubes has been performed for the first time and has yielded a completely new concept of the attending relationship between the pressure loss and mean flow rate. [1]

**Symmetry-preserving discretization of turbulent flow**

We propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators, i.e., the convective operator is represented by a skew-symmetric coefficient matrix and the diffusive operator is approximated by a symmetric, positive-definite matrix. [2]

**The dispersion of matter in turbulent flow through a pipe**

The dispersion of soluble matter introduced into a slow stream of solvent in a capillary tube can be described by means of a virtual coefficient of diffusion (Taylor 1953 *a*) which represents the combined action of variation of velocity over the cross-section of the tube and molecluar diffusion in a radial direction. [3]

**Probability Density Function of Scalar Length Scales in Turbulent Flow**

In this Brief Communication scalar length-scale and time-scale distributions are proposed to determine by considering the statistics of the scalar field and its gradient. For this purpose, a relationship between the scalar length-scale probability density function and the joint probability density function for the scalar field and its gradient in the form of the integral relation is established. [4]

**Large Eddy Simulation of Turbulent Channel Flow Using Smagorinsky Model and Effects of Smagorinsky Constants**

A large eddy simulation (LES) of a turbulent channel flow is performed by using the Smagorinsky subgrid scale model and the effects of Smagorinsky constants in LES are discussed. The computation is performed in the domain of δ δ2δ2 π ××π with 32 6432 × × grid points at a Reynolds number Reτ = 590 based on the channel half width, δ and wall shear velocity, uτ. The performance of the Smagorinsky model is tested in LES for three values of Smagorinsky constant, CS = 0.065, 0.1 and 0.13, and for all three cases the computed essential turbulence statistics of the flow field are compared with Direct Numerical Simulation (DNS) data. [5]

Reference

[1] Dodge, D.W. and Metzner, A.B., 1959. Turbulent flow of non‐Newtonian systems. *AIChE Journal*, *5*(2), pp.189-204.

[2] Verstappen, R.W.C.P. and Veldman, A.E.P., 2003. Symmetry-preserving discretization of turbulent flow. *Journal of Computational Physics*, *187*(1), pp.343-368.

[3] Taylor, G.I., 1954. The dispersion of matter in turbulent flow through a pipe. *Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences*, *223*(1155), pp.446-468.

[4] Chorny, A. (2015) “Probability Density Function of Scalar Length Scales in Turbulent Flow”, *Physical Science International Journal*, 9(2), pp. 1-6. doi: 10.9734/PSIJ/2016/22455.

[5] Uddin, M.A. and Mallik, M.S.I., 2015. Large Eddy Simulation of Turbulent Channel Flow using Smagorinsky Model and Effects of Smagorinsky Constants. *Journal of Advances in Mathematics and Computer Science*, pp.375-390.