IJLTEMAS International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS) IJLTEMAS 2278-2540 IJLTEMAS 25 10.51583/IJLTEMAS.2026.150700020 Curved Channels Exploring the Dynamics of Turbulent Flows: Mathematical Models and Stability in Curved Channels Satyapal Singh Dr. Department of Mathematics, B.S.A. (PG) College, Mathura, Affiliated to Dr. Bhim Rao Ambedkar University, Agra, 282004, India India 15 7 250 261 25 07 2026 30 07 2026 06 08 2026 Turbulent flows Curved channels RANS equations Flow stability Abstract

This study explores the dynamics of turbulent flows in curved channels, with a focus on developing and validating mathematical models that accurately represent flow behaviour and stability. Using Reynolds-Averaged Navier-Stokes (RANS) equations and turbulence models such as k-ε and k-ω, we conducted detailed numerical simulations to analyse the effects of channel curvature on turbulence intensity and flow stability. The simulations, implemented in CFD software, were validated against experimental data, ensuring robust and reliable findings. Additionally, linear and nonlinear stability analyses were performed to identify critical Reynolds numbers and assess the influence of curvature on flow transitions. The results highlight the significant impact of curvature on turbulence dynamics, providing valuable insights for engineering applications such as pipeline design and environmental flow management. Future research directions include refining turbulence models and conducting more comprehensive experimental validations.

 References Reynolds, O. (1883). An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philosophical Transactions of the Royal Society of London, 174 , 935–982. https://doi.org/10.1098/rstl.1883.0029 Richardson, L. F. (1922). Weather prediction by numerical process. Cambridge University Press. Kolmogorov, A. N. (1941). The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Doklady Akademii Nauk SSSR, 30 (4), 301–305. Schlichting, H. (1968). Boundary-layer theory (6th ed.). McGraw-Hill. Launder, B. E., & Spalding, D. B. (1974). The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 3 (2), 269–289. https://doi.org/10.1016/0045-7825(74)90029-2 Wilcox, D. C. (1988). Reassessment of the scale-determining equation for advanced turbulence models. AIAA Journal, 26 (11), 1299–1310. https://doi.org/10.2514/3.10041 Dean, W. R. (1927). XVI. Note on the motion of fluid in a curved pipe. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 4 (20), 208–223. https://doi.org/10.1080/14786440708564324 Berger, S. A., Talbot, L., & Yao, L. S. (1983). Flow in curved pipes. Annual Review of Fluid Mechanics, 15 (1), 461–512. https://doi.org/10.1146/annurev.fl.15.010183.002333 Ku, D. N. (1997). Blood flow in arteries. Annual Review of Fluid Mechanics, 29 (1), 399–434. https://doi.org/10.1146/annurev.fluid.29.1.399 Dietrich, W. E., & Smith, J. D. (1984). Bed load transport in a river meander. Water Resources Research, 20 (10), 1355–1380. https://doi.org/10.1029/WR020i010p01355 Batistella Lopes, M., Cocco Mariani, V., Cordeiro Mendonça, K., Beghein, C., & Kleinübing Larcher, J. H. (2021, July). Evaluating turbulence models to predict the particle deposition in curved ducts [Paper presentation]. 16th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Virtual Conference. Liu, J., Zuo, Z., Wu, Y., Zhuang, B., & Wang, L. (2015). A nonlinear partially-averaged Navier-Stokes model for turbulence flow simulations. Journal of Hydrodynamics, Ser. B, 27 (4), 627–635. https://doi.org/10.1016/S1001-6058(15)60526-1 Wang, J., & Shirazi, S. A. (2000). A simultaneous variable solution procedure for laminar and turbulent flows in curved channels and bends. Journal of Fluids Engineering, 122 (2), 323–329. https://doi.org/10.1115/1.1287723 Zhang, Q., Pan, C., Gu, W., & Zhou, F. (2023a). Structures of lateral flow and turbulence in a breaking tidal bore rushing through a curved channel of the Qiantang Estuary. Journal of Physical Oceanography, 53 (11), 2721–2740. https://doi.org/10.1175/JPO-D-23-0044.1 Ye, W., Luo, X., & Li, Y. (2020). Modified partially averaged Navier–Stokes model for turbulent flow in passages with large curvature. Modern Physics Letters B, 34 (21), Article 2050239. https://doi.org/10.1142/S0217984920502395 Humphrey, J. A. C., & Pourahmadi, F. (1983). Prediction of curved channel flow with an extended k-epsilon model of turbulence. AIAA Journal, 21 (10), 1372–1377. https://doi.org/10.2514/3.8255 Ali, S. Z., & Dey, S. (2024). Universal skin friction laws for turbulent flow in curved tubes. Physics of Fluids, 36 (9), Article 095110. https://doi.org/10.1063/5.0222083 Kashyap, P. V., Duguet, Y., & Dauchot, O. (2024). Linear stability of turbulent channel flow with one-point closure. Physical Review Fluids, 9 (6), Article 063906. https://doi.org/10.1103/PhysRevFluids.9.063906 Kundu, S., & Chattopadhyay, T. (2022). Analysis and validation of mathematical models of secondary velocities along vertical and transverse directions in wide open-channel turbulent flows. Journal of Hydraulic Research, 60 (5), 770–785. https://doi.org/10.1080/00221686.2022.2053206 Liu, D., Lv, S., & Li, C. (2024). Impact of spur dike placement on flow dynamics in curved river channels: A CFD study on pick angle and river-width-narrowing rate. Water, 16 (16), Article 2236. https://doi.org/10.3390/w16162236 Mironov, V. L., & Mironov, S. V. (2024). Vortex model of plane turbulent air flows in channels. Journal of Applied Mechanics and Technical Physics, 65 (1), 58–68. https://doi.org/10.1134/S002189442401006X Mishra, A. A., & Girimaji, S. S. (2013). The dynamics of pressure in planar turbulent flows: Flow stability and modeling. In Proceedings of the ASME 2013 Fluids Engineering Division Summer Meeting (Vol. 1A, Paper FEDSM2013-16167). American Society of Mechanical Engineers. https://doi.org/10.1115/FEDSM2013-16167 Sharma, A., Lakkaraju, R., & Atta, A. (2023). Influence of channel bend angle on the turbulent statistics in sharply bent channel flows. Physics of Fluids, 35 (5), Article 055104. https://doi.org/10.1063/5.0149086 Sharma, A., Lakkaraju, R., & Atta, A. (2023). Insight into the particle-laden turbulent flow statistics in sharply bent channels. Physics of Fluids, 35 (9), Article 095119. https://doi.org/10.1063/5.0169374 Zhang, Q., Pan, C., Gu, W., & Zhou, F. (2023b). [Duplicate of entry #14. Retain only one and adjust in-text citations accordingly.] Journal of Physical Oceanography, 53 (11), 2721–2740. https://doi.org/10.1175/JPO-D-23-0044.1 Ali, N., Chand, A., Sharma, V., & Tariq, A. (2025). Flow mechanism across 180° sharp bend of matrix-cooled serpentine channel. International Journal of Heat and Fluid Flow, 112 , Article 109683. https://doi.org/10.1016/j.ijheatfluidflow.2024.109683 Bagheri, E., Wang, Z., Choueiri, G. H., & Hof, B. (2025). Collapse of turbulence in curved pipe flow. arXiv. https://doi.org/10.48550/arXiv.2511.17073 Bera, S., Shit, G. C., Reza, M., & Drese, K. S. (2024). Linear temporal instabilities and transient energy growth in rotating curved microchannel flow. Physics of Fluids, 36 (12), Article 124112. https://doi.org/10.1063/5.0246936 Ghani, W., Shah, S. R., & Kumar, B. (2024). Bed morphology and turbulent anisotropy in a curved flexible bed channel. Water Practice and Technology, 19 (4), 1421–1437. https://doi.org/10.2166/wpt.2024.108 Gopakumar, G. A. (2025). Direct numerical simulation of pulsating flow in curved pipes: Insights into aortic dissection in humans [Doctoral dissertation, University of Kentucky]. UKnowledge. https://doi.org/10.13023/etd.2025.516 Hu, C., Liu, Y., & Yu, M. (2025). Influence of Froude number on the development and evolution of secondary flows in a sharply curved bend: An experimental and numerical study [Manuscript submitted for publication]. SSRN. http://dx.doi.org/10.2139/ssrn.5251116 Lupi, V., Canton, J., Rinaldi, E., & Schlatter, P. (2024). Modal stability analysis of toroidal pipe flow approaching zero curvature. Journal of Fluid Mechanics, 987 , Article A21. https://doi.org/10.1017/jfm.2024.312 Pokharel, C., Kafle, J., & Bhatta, C. R. (2024). Impact of effective viscosity on blood flow through sinusoidal stenosed curved artery. Journal of Nepal Mathematical Society, 7 (2), 8–21. https://doi.org/10.3126/jnms.v7i2.73100 Soldati, G., Orlandi, P., & Pirozzoli, S. (2025). Reynolds number effects on turbulent flow in curved channels. Journal of Fluid Mechanics, 1003 , Article A12. https://doi.org/10.1017/jfm.2025.10012 Song, R., Xiao, H., Liu, Y., & Wu, Y. (2025). Spatial marching with subgrid-scale local exact coherent structures in non-uniformly curved channel flow. Journal of Fluid Mechanics, 1025 , Article A42. https://doi.org/10.1017/jfm.2025.10968 Farzad, H., Keshavarzi, A., Hamidifar, H., & Gualtieri, C. (2026). Turbulence in a bend in the presence of emergent vegetation and a 3D pool bedform. Water, 18 (3), Article 431. https://doi.org/10.3390/w18030431 Xie, P., Li, C. G., Lü, S. J., Jing, H. F., & Zhang, F. Z. (2024). Numerical simulation of effects of permeable spur dike on three-dimensional flow structure in curved channel with different curvatures. China Rural Water and Hydropower, (5), 31–40. https://doi.org/10.12396/znsd.231512