An Analytical Solution for Advection-Diffusion Equation with Advection–Dominated Term using Multiple-Scale Expansion Methods
DOI:
https://doi.org/10.35895/jpsi.1.2.123-135.2025Keywords:
advection, advection, Green’s function, Green’s function, multiple-scale expansion, multiple-scale expansion, suspended sediment transport, suspended sediment transportAbstract
In this study, we solved the advection-diffusion sediment transport equation by taking into account the settling velocity and employing a multiple-scale expansion to approximate the dominant advection. We obtained an analytical solution in terms of the Green’s function. The model results showed that, during one tidal cycle, TSS was concentrated at the surface and eventually transported to the sea. The pattern of TSS distribution was consistent with both constant and linear time-dependent river discharge. The simulation revealed that the concentration of TSS offshore was higher than near the estuaries, in agreement with our observations.
References
Alkhatib, M., Jennerjahn, T.C., Samiaji, J. (2007). Biogeochemistry of the Dumai River estuary, Sumatra, Indonesia, a tropical blackwater river, Limnol. Oceanogr., 52(6), 2410–2417.
Amiruddin, A.M., Ibrahim, Z.Z., Syazwan Aizat Ismail, A.S. (2011). Water Mass Characteristics in the Strait of Malacca using Ocean Data View. Research J. Enviro. Sci., 5: 49-58.
Brakenhoff, L., Schrijvershof, R., van der Werf, J., Grasmeijer, B., Ruessink,G., van der Vegt, M. (2020). From Ripples to Large-Scale Sand Transport: The Effects of Bedform-Related Roughness on Hydrodynamics and Sediment Transport Patterns in Delft3D, J. Mar. Sci. Eng. 8, 892; doi:10.3390/jmse8110892
Carslaw, H.S., Jaeger,J. (1960). Conduction of Heat in Solids, Claredon, Oxford.
Colosimo, I., de Vet, P.L.M., van Maren, D.S. Ad J. H. M. Reniers, Johan C. (2020). Winterwerp and Bram C. van Prooijen, The Impact of Wind on Flow and Sediment Transport over Intertidal Flats, J. Mar. Sci. Eng. 8, 910; doi:10.3390/jmse8110910.
Dejak, C., Mazzei Lalatta, I., Messina, E. & Pecenik, G. (1987). A two-dimensional diffusion model of the Venice Lagoon and relative open boundary conditions. Ecol. Modelling, 37: 21-45.
Eke, C.D., Anifowose, B., Van De Wiel, M.J., Lawler, D., Knaapen, M.A.F. (2021). Numerical Modelling of Oil Spill Transport in Tide-Dominated Estuaries: A Case Study of Humber Estuary, UK. J. Mar. Sci. Eng. 9, 1034. https:// doi.org/10.3390/jmse9091034.
Holmes, M.H. (2011). Introduction to perturbation methods, Springer-Verlag, Berlin, 451 pp.
Lissa J. MacVean & Mark T. Stacey. (2011). Estuarine Dispersion from Tidal Trapping: A New Analytical Framework, Estuaries and Coasts, 34:45–59 DOI 10.1007/s12237-010-9298-x.
Mei, C.C., Chian C., Ye F. (1998). Transport and Resuspension of Fine Particle in a Tidal Boundary Layer near a Small Peninsula, J. Phys. Oceanorg, 28, 2313-2332.
Mubarak., Nurhuda, A., Sulaiman, A. (2016). On the Vertical of Suspended Sediment Transport in Dumai Estuary, International Journal of Applied Environmental Sciences, 11, (4), pp. 1025-1035.
Officer, B. (1978). Physical Oceanography of Estuaries. John Willey & Son, New York.
Rifardi., Mubarak., Elizal., Nurhuda, A., Aristi, F. (2020). Sediment transport model from Dumai River estuary to the Rupat Strait, Riau Province, Indonesia. AACL Bioflux, Volume 13, Issue 6, 3447-3459.
Rifardi & Badrun, Y. (2017). Sandbar Formation in the esjid River Estuary, Rupat Strait, Riau Province, Indonesia, Indonesian J. Geoph, 49, 65 - 72.
Tas, S.A.J., Dirk S. van Maren, D.S., Reniers, A.J.H.M. (2020). Observations of Cross-Shore Chenier Dynamics in Demak, Indonesia, J. Mar. Sci. Eng. 8, 972; doi:10.3390/jmse8120972
Vongvisessomjai, S. & Chatanantavet, P. (2006). Analytical model of interaction of tide and river flow, Songklanakarin J. Sci. Technol. Vol.28 No.6 Nov.
Wang, X.H. (2002). Tide-Induced Sediment Resuspension and the Bottom Boundary Layer in an Idealized Estuary with a Muddy Bed, J. Phys. Oceanorg, 32, 3113-3132.
Wang,T., Geyer, W.R., Engel,P., Jian W., Feng, S. (2015). Mechanism of tidal oscillatory salt transport in a partially stratified estuary, J. Phys. Oceanorg, 45, 2773-2790.
Wu, Z., Zhao,J., Yin, J., Li, H. (2001). Nonlinear Diffusion Equation, World Scientific, Singapore, 479pp.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Albert Sulaiman, Mubarak Mubarak (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
