Numerical Simulation of Fluid Flow in the Narrow Strait with Density Differences

Tarmizi Usman; Muhammad Ikhwan; Muhammad Zulfataya; Farhan Adami

doi:10.31764/jtam.v9i1.27252

Numerical Simulation of Fluid Flow in the Narrow Strait with Density Differences

Tarmizi Usman, Muhammad Ikhwan, Muhammad Zulfataya, Farhan Adami

Abstract

This study investigates the dynamics of fluid flow through a narrow strait connecting two large water bodies with different densities using numerical simulations. The research focuses on understanding how density-driven currents develop and interact in a confined channel, particularly the role of lateral density contrasts and the influence of gravitational and geostrophic forces. A semi-implicit numerical method is employed to efficiently model the complex flow dynamics while ensuring stability. The simulation results are analyzed using visualizations of the flow fields, which highlight the evolution of density-driven currents, vortex formation, and geostrophic adjustments over time. The findings reveal that denser water from the western basin flows toward the eastern basin, lowering the sea surface in the west and raising it in the east. Over time, the Coriolis force causes the bottom flow to deflect southward and the returning surface flow to shift northward, leading to geostrophic equilibrium. Transient vortices emerge within the strait, while stationary vortices form in the outflow regions, underscoring the interplay between gravitational forces, density contrasts, and rotational effects. These findings offer important insights into the hydrodynamic behavior of narrow straits, which are common in nature. The results can help improve the understanding of flow patterns in similar environments, such as fjords, estuaries, and channels, and may contribute to studies on sediment transport, nutrient mixing, and renewable energy potential in density-driven systems.

Keywords

Fluid Dynamics; Narrow Strait; Density Differences; Semi-Implicit Method; Geostrophic Adjustment; Renewable Energy.

Full Text:

DOWNLOAD [PDF]

References

Ackmann, J., Dueben, P. D., Palmer, T., & Smolarkiewicz, P. K. (2022). Mixed‐Precision for Linear Solvers in Global Geophysical Flows. Journal of Advances in Modeling Earth Systems, 14(9), 1–26. https://doi.org/10.1029/2022MS003148

Brutto, C., & Dumbser, M. (2023). A semi‐implicit finite volume scheme for a simplified hydrostatic model for fluid‐structure interaction. International Journal for Numerical Methods in Fluids, 95(1), 107–142. https://doi.org/10.1002/fld.5143

Chistyakov, A., Protsenko, E., Sidoryakina, V., & Protsenko, S. (2020). Mathematical modeling of 3D current flows for narrow shallow water bodies of complicated forms. E3S Web of Conferences, 224(02008), 1–8. https://doi.org/10.1051/e3sconf/202022402008

Dharmawan, K., Swastika, P. V., & Gandhiadi, G. K. (2024). Numerical Computation of One- and Two-Layer Shallow Flow Model. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 18(3), 1509–1518. https://doi.org/10.30598/barekengvol18iss3pp1509-1518

Frolkovič, P., Krišková, S., Rohová, M., & Žeravý, M. (2022). Semi-implicit methods for advection equations with explicit forms of numerical solution. Japan Journal of Industrial and Applied Mathematics, 39(3), 843–867. https://doi.org/10.1007/s13160-022-00525-y

Gomaa, M. A., Kasem, T. H. M. A., Huzayyin, O. A., Schlenkhoff, A., & Sasaki, J. (2023). Numerical simulation and PIV measurements of the wave-induced flow field near semi-circular breakwaters. SN Applied Sciences, 5(7), 175. https://doi.org/10.1007/s42452-023-05384-x

Haditiar, Y., Putri, M. R., Ismail, N., Muchlisin, Z. A., & Rizal, S. (2019). Numerical Simulation of Currents and Volume Transport in the Malacca Strait and Part of South China Sea. Engineering Journal, 23(6), 129–143. https://doi.org/10.4186/ej.2019.23.6.129

Haid, V., Stanev, E. V, Pein, J., Staneva, J., & Chen, W. (2020). Secondary circulation in shallow ocean straits: Observations and numerical modeling of the Danish Straits. Ocean Modelling, 148(April 2020), 101585. https://doi.org/https://doi.org/10.1016/j.ocemod.2020.101585

Hu, D., Li, S., Yao, S., & Jin, Z. (2019). A Simple and Unified Linear Solver for Free-Surface and Pressurized Mixed Flows in Hydraulic Systems. Water, 11(10), 1979. https://doi.org/10.3390/w11101979

Ikhwan, M., Wafdan, R., Haditiar, Y., Ramli, M., Muchlisin, Z. A., & Rizal, S. (2021). Simulation and Analysis of Marine Hydrodynamics Based on the El Niño Scenario. Global Journal of Environmental Science and Management, 7(4), 543–554. https://doi.org/10.22034/gjesm.2021.04.04

Kämpf, J. (2009). Ocean Modelling for Beginners. In Ocean Modelling for Beginners: Using Open-Source Software. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-00820-7

Kämpf, J. (2010). Advanced Ocean Modelling Using Open Source Software. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-10610-1

Kemper, J., Riebesell, U., & Graf, K. (2022). Numerical Flow Modeling of Artificial Ocean Upwelling. Frontiers in Marine Science, 8. https://doi.org/10.3389/fmars.2021.804875

Kurogi, M., & Hasumi, H. (2019). Tidal control of the flow through long, narrow straits: a modeling study for the Seto Inland Sea. Scientific Reports, 9(1), 11077. https://doi.org/10.1038/s41598-019-47090-y

Liu, H., Pang, C., Yang, D., & Liu, Z. (2021). Seasonal variation in material exchange through the Bohai Strait. Continental Shelf Research, 231(Dec 2021), 104599. https://doi.org/https://doi.org/10.1016/j.csr.2021.104599

Pal, D., Mahananda, M., Hanmaiahgari, P. R., & Kaushik, M. (2017). Experimental Investigation of Turbulent Hydrodynamics in Developing Narrow Open Channel Flow. In V. Garg, V. P. Singh, & V. Raj (Eds.), Development of Water Resources in India (pp. 429–440). Springer International Publishing.

Pudjaprasetya, S. R., & Swastika, P. V. (2023). Two-Layer Exchange Flow with Time-Dependent Barotropic Forcing. In E. Franck, J. Fuhrmann, V. Michel-Dansac, & L. Navoret (Eds.), Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems (pp. 269–277). Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-40860-1_28

Rossi, V. M., Longhitano, S. G., Olariu, C., & Chiocci, F. L. (2023a). Straits and seaways: controls, processes and implications in modern and ancient systems. Geological Society, London, Special Publications, 523(1), 1–15. https://doi.org/10.1144/SP523-2022-271

Rossi, V. M., Longhitano, S. G., Olariu, C., & Chiocci, F. L. (2023b). Straits and seaways: end members within the continuous spectrum of the dynamic connection between basins. Geological Society, London, Special Publications, 523(1), 85–109. https://doi.org/10.1144/SP523-2022-159

Setiawan, I., Haditiar, Y., Ikhwan, M., Nufus, Z., Syukri, M., Ismail, N., & Rizal, S. (2020). Modeling Of M2-Tide In The Western Waters Of Aceh, Indonesia. Journal of Sustainability Science and Management, 15(8), 122–135. https://doi.org/10.46754/jssm.2020.12.011

Shahane, S., & Vanka, S. P. (2022). A Semi-Implicit Meshless Method for Incompressible Flows in Complex Geometries. SSRN Electronic Journal, 472(111715), 1–14. https://doi.org/10.2139/ssrn.4041121

So, R. M. C. (2022). Effects of Numerical Methods on the Calculation of Developing Plane Channel Flow. Journal of Applied Mathematics and Physics, 10(06), 2086–2104. https://doi.org/10.4236/jamp.2022.106142

Sun, Z., Chen, Z., Hu, H., & Zheng, J. (2015). Ship interaction in narrow water channels: A two-lane cellular automata approach. Physica A: Statistical Mechanics and Its Applications, 431(August 2015), 46–51. https://doi.org/10.1016/j.physa.2015.02.079

Tibaut, J., Ravnik, J., & Schanz, M. (2023). Numerical simulation of fluid flow with a fast Boundary‐Domain Integral Method. PAMM, 22(1), 1–6. https://doi.org/10.1002/pamm.202200196

DOI: https://doi.org/10.31764/jtam.v9i1.27252