# zbMATH — the first resource for mathematics

On the new concept of turbulence modeling in fully developed turbulent channel flow and boundary layer. (English) Zbl 1325.76097
Cannon, John (ed.) et al., Mathematical and physical theory of turbulence. Proceedings of the international turbulence workshop, Orlando, FL, USA, May 19–23, 2003. Boca Raton, FL: Chapman & Hall/CRC (ISBN 0-8247-2323-6/hbk; 978-1-4200-1497-6/ebook). Lecture Notes in Pure and Applied Mathematics 250, 183-193 (2006).
Summary: The new concept of turbulence modeling is proposed as an attempt to simulate the effect of turbulence on the flows as realistically as possible. The turbulence effect is fundamentally not the diffusion phenomena that the concept of eddy viscosity models is based on. It is rather the convection phenomena that are responsible for the turbulence effect on the flows. This can be observed from the time-averaged Navier-Stokes equations that the extra terms, which are called the gradients of the Reynolds stresses, are derived from the convection term of the Navier-Stokes equations. The current work aims to present the new concept on modeling the gradients of the Reynolds shear stresses that does not rely on the eddy viscosity concept. The gradients of the Reynolds shear stresses are modeled in terms of the gradients of the product of the root-mean-square of the velocity fluctuations times a model constant. The direct numerical simulation (DNS) data of the fully developed turbulent channel flow and the turbulent boundary layer with constant pressure are used to evaluate the proposed concept in comparison with the eddy viscosity concept. The proposed concept shows much closer agreement with the DNS data, especially in the regions of viscous sublayer and buffer layer. Furthermore, it is found that the model constant is independent of Reynolds numbers and equal to $$-1/2$$ for both flows.
For the entire collection see [Zbl 1098.76004].
##### MSC:
 76F40 Turbulent boundary layers 76F65 Direct numerical and large eddy simulation of turbulence