Table of Contents
International Journal of Partial Differential Equations
Volume 2015, Article ID 105809, 15 pages
Research Article

Development of a Nonlinear Model Incorporating Strain and Rotation Parameters for Prediction of Complex Turbulent Flows

1Department of Civil Engineering, Khulna University of Engineering & Technology (KUET), Khulna 9203, Bangladesh
2Department of Urban Management, Kyoto University, Katsura Campus, C1-3, Kyoto 615-8540, Japan
3Faculty and Graduate School of Engineering, Hokkaido University, Sapporo 060-8623, Japan

Received 18 September 2014; Revised 24 December 2014; Accepted 10 January 2015

Academic Editor: Nikolai A. Kudryashov

Copyright © 2015 Md. Shahjahan Ali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The standard model has the deficiency of predicting swirling and vortical flows due to its isotropic assumption of eddy viscosity. In this study, a second-order nonlinear model is developed incorporating some new functions for the model coefficients to explore the models applicability to complex turbulent flows. Considering the realizability principle, the coefficient of eddy viscosity () is derived as a function of strain and rotation parameters. The coefficients of nonlinear quadratic term are estimated considering the anisotropy of turbulence in a simple shear layer. Analytical solutions for the fundamental properties of swirl jet are derived based on the nonlinear model, and the values of model constants are determined by tuning their values for the best-fitted comparison with the experiments. The model performance is examined for two test cases: (i) for an ideal vortex (Stuart vortex), the basic equations are solved numerically to predict the turbulent structures at the vortex center and the (ii) unsteady 3D simulation is carried out to calculate the flow field of a compound channel. It is observed that the proposed nonlinear model can successfully predict the turbulent structures at vortex center, while the standard model fails. The model is found to be capable of accounting the effect of transverse momentum transfer in the compound channel through generating the horizontal vortices at the interface.