Technical Papers
Nov 29, 2017

One-Dimensional Particle Tracking with Streamline Preserving Junctions for Flows in Channel Networks

Publication: Journal of Hydraulic Engineering
Volume 144, Issue 2

Abstract

A pseudo-three-dimensional particle tracking model of drifter paths has been developed to study the movement of scalars through a complex network of tidal channels and junctions. To better simulate dispersion caused by bifurcation and merging at junctions, a localized model is proposed in which particles move along potential flow streamlines through junctions. The model is applied to the Sacramento–San Joaquin Delta in the California Central Valley, and the approach reproduces the observed ultimate fate of the endangered native fish Delta smelt more accurately than a model that fully randomizes particle positions at junctions. The new model also reproduces the very large dispersion that has been previously inferred from Delta-wide heat balances; this large dispersion appears to be associated with flow splits at junctions. Overall, the streamline-following model is likely to be more accurate for long-term planning and management simulations of such complex estuaries than more commonly used cross-sectionally averaged Lagrangian transport equation solvers, which randomize concentration distributions of scalars at junctions, and thereby do not reproduce the increased dispersion mechanisms.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

Initial funding for this work was provided by the CALFED science program. Later support for VKS was provided by the Singapore Stanford Partnership; Stanford University through a Leavell Fellowship for the Sustainable Built Environment; and by the National Marine Fisheries Service, National Oceanographic and Atmospheric Administration. The authors are grateful to Dr. Eli Ateljevich at DWR for his assistance with using the DSM2 suite of models. The authors also acknowledge the constructive feedback of two anonymous reviewers; an anonymous associate editor; and Chief Editor, Thanos Papanicolaou, for greatly improving the quality of the manuscript.

References

Anderson, J., and Mierzwa, M. (2002). An introduction to the Delta Simulation Model II (DSM2) for simulation of hydrodynamics and water quality of the Sacramento-San Joaquin Delta, Delta Modeling Section, Office of State Water Project Planning, California Dept. of Water Resources, Sacramento, CA.
Banas, N. S., Hickey, B. M., MacCready, P., and Newton, J. A. (2004). “Dynamics of Willapa Bay, Washington: A highly unsteady, partially mixed estuary.” J. Phys. Oceanogr., 34(11), 2413–2427.
Bennett, W. A. (2005). “Critical assessment of the delta smelt population in the San Francisco estuary, California.” San Francisco Estuary Watershed Sci., 3(2), in press.
Bouchez, J., Lajeunesse, E., Gaillardet, J., Frane-Lanord, C., Dutra-Maia, P., and Maurice, L. (2010). “Turbulent mixing in the Amazon River: The isotropic memory of confluences.” Earth Planet. Sci. Lett., 290(1–2), 37–43.
Brunner, G. W. (1995). “HEC-RAS river analysis system.” Hydraulic reference manual, version 1.0, Hydrologic Engineering Center, Davis, CA.
CDFW (California Department of Fish and Wildlife). (2015a). “1981–2012 daily salvage data.” ⟨ftp://ftp.dfg.ca.gov/salvage/⟩ (Oct. 26, 2017).
CDFW (California Department of Fish and Wildlife). (2015b). “20-mm townet data.” ⟨ftp://ftp.dfg.ca.gov/Delta%20Smelt/⟩ (Oct. 26, 2017).
Danckwerts, P. V. (1953). “Continuous flow systems: Distribution of residence times.” Chem. Eng. Sci., 2(1), 1–13.
Debnath, I., and Chatterjee, A. K. (1979). “Nonlinear mathematical model of the propagation of tides in interlacing channels.” Comput. Fluids, 7(1), 1–12.
DeLong, L. L., Lewis, L., Thompson, D. B., and Lee, J. K. (1997). “The computer program FourPt (version 95.01): A model for simulating one-dimensional, unsteady, open-channel flow.”, USGS, Reston, VA.
Dimou, K. N., and Adams, E. E. (1993). “A random-walk, particle tracking model for well-mixed estuaries and coastal waters.” Estuar. Coast. Shelf Sci., 37(1), 99–110.
Driscoll, T. A. (1994). Schwarz-Christoffel toolbox user’s guide, version 2.3, Univ. of Delaware, Newark, DE.
Driscoll, T. A., and Vavasis, S. A. (1998). “Numerical conformal mapping using cross-ratios and Delaunay triangulation.” SIAM J. Sci. Comput., 19(6), 1783–1803.
DSM2 version 6 [Computer software]. California Dept. of Water Resources, Sacramento, CA.
Fischer, H. B. (1972). “A Lagrangian method for predicting pollutant dispersion in Bolinas Lagoon, Marin County, California.” U.S. Government Printing Office, Washington, DC.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imerger, J., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic Press, New York.
Fleenor, W. E., and Bombardelli, F. (2013). “Simplified 1-d hydrodynamic and salinity transport modeling of the Sacramento-San Joaquin Delta: Sea level rise and water diversion effects.” San Francisco Estuary Watershed Sci., 11(4), 1–22.
Fortran version 90 [Computer software]. Intel, Inc., Santa Clara, CA.
Gartrell, G. (1993). “Quantification of uncertainties in a water quality model with application to the Sacramento-San Joaquin Delta.” Hydraulic engineering, H. W. Shen, H. W. Su, and F. Wen, eds., Vol. 2, ASCE, Reston, VA, 1628–1634.
Gleichauf, K. T., Wolfram, P. J., Monsen, N. E., Fringer, O. B., and Monismith, S. G. (2014). “Dispersion mechanisms of a tidal river junction in the Sacramento-San Joaquin Delta, California.” San Francisco Estuary Watershed Sci., 12(4), in press.
Gross, E. S., MacWilliams, M. L., Holleman, C. D., and Hervier, T. A. (2010). POD 3-D tracking modeling study: Particle tracking model testing and applications report, Interagency Ecology Program, West Sacramento, CA.
Hsu, C.-C., Wu, F.-S., and Lee, W.-J. (1998). “Flow at 90° equal-width open-channel junction.” J. Hydraul. Eng., 186–191.
Huang, J., Weber, L. J., and Lai, L. G. (2002). “Three-dimensional numerical study of flows in open-channel junctions.” J. Hydraul Eng., 268–280.
Hunter, J. R., Craig, P. D., and Phillips, H. E. (1993). “On the use of random walk models with spatially variable diffusivity.” J. Comput. Phys., 106(2), 366–376.
Hutton, P. H., and Enright, C. (1993). “Simulating THM precursors transport with DWRDSM.” Hydraulic engineering, W. Shen, H. W. Su, and F. Wen, eds., ASCE, Reston, VA.
Jobson, H. E. (2001). “Modeling water quality in rivers using the branched Lagrangian transport model (BLTM).”, USGS, Reston, VA.
Kacimov, A. R. (2000). “Application of conformal mapping to diverging open channel flow.” J. Eng. Math., 37(4), 397–400.
Ketcheson, D. I., MacDonanld, C. B., and Gottleib, S. (2008). “Optimal implicit strong stability preserving Runge-Kutta methods.” Appl. Numer. Math., 59(2009), 373–392.
Kimmerer, W. J. (2004). “Open water processes of the San Francisco estuary: From physical forcing to biological responses.” San Francisco Estuary Watershed Sci., 2(1), in press.
Kimmerer, W. J., Gross, E. S., and MacWilliams, M. L. (2009). “Is the response of estuarine nekton to freshwater flow in the San Francisco estuary explained by variation in habitat volume?” Estuaries Coasts, 32(2), 375–389.
Kimmerer, W. J., MacWilliams, M. L., and Gross, E. S. (2013). “Variation of fish habitat and extent of the low-salinity zone with freshwater flow in the San Francisco estuary.” San Francisco Estuary Watershed Sci., 11(4), in press.
Kimmerer, W. J., and Nobriga, M. L. (2008). “Investigating particle transport and fate in the Sacramento-San Joaquin Delta using a particle tracking model.” San Francisco Estuary Watershed Sci., 6(1), in press.
Liu, L., and Ateljevich, E. (2011). “Methodology for flow and salinity estimates in the Sacramento-San Joaquin Delta and Suisun Marsh.” 32nd Annual Progress Report, California Dept. of Water Resources, Sacramento, CA.
MacWilliams, M. L., and Gross, E. S. (2007). Un-TRIM San Francisco Bay-Delta model calibration report, California Dept. of Water Resources, Sacramento, CA.
MacWilliams, M. L., Monismith, S. G., Ateljevich, E., and Enright, C. (2016). “An overview of multi-dimensional models of the Sacramento-San Joaquin Delta.” San Francisco Estuary Watershed Sci., 14(4), in press.
MATLAB [Computer software]. MathWorks, Natick, MA.
Monismith, S. G., et al. (2009). “Thermal variability in a tidal river.” Estuaries Coasts, 32(1), 100–110.
Monsen, N. E. (2000). “A study of sub-tidal transport in Suisun Bay and the Sacramento-San Joaquin Delta, California.” Ph.D. thesis, Stanford Univ., Stanford, CA.
Moyle, P., Bennett, W., Fleenor, W., and Lund, J. (2010). Habitat variability and complexity in the upper San Francisco estuary, delta solutions, Center for Watershed Sciences, Univ. of California, Davis, CA.
Nichols, F. H., Cloern, J. E., Luoma, S. N., and Peterson, D. H. (1986). “The modification of an estuary.” Science, 231(4738), 567–573.
NRC (National Research Council). (2010). A scientific assessment of alternatives for reducing water management effects on threatened and endangered fishes in California’s Bay Delta, National Academy Press, Washington, DC.
Okubo, A. (1973). “Effects of shoreline irregularities on streamwise dispersion in estuaries and other embayments.” Neth. J. Sea Res., 6(1), 213–224.
Perry, R. W., et al. (2013). “Sensitivity of survival to migration routes used by juvenile Chinook salmon to negotiate the Sacramento-San Joaquin River Delta.” Environ. Biol. Fishes, 96(2–3), 381–392.
Perry, R. W., et al. (2014). “Using a non-physical behavioural barrier to alter migration routing of juvenile Chinook salmon in the Sacramento-San Joaquin river delta.” River Res. Appl., 30(2), 192–203.
Prandtl, L. (1935). “The mechanics of viscous fluids.” Aerodynamic theory, W. F. Durand, Vol. 3, Springer, Berlin, 34–208.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical recipes in Fortran, 2nd Ed., Cambridge University Press, Cambridge, U.K.
Ramamurthy, A. S., Qu, J., and Vo, D. (2007). “Numerical and experimental study of dividing open-channel flows.” J. Hydraul. Eng., 1135–1144.
Ridderinkhof, H., and Zimmerman, J. T. F. (1992). “Chaotic stirring in a tidal system.” Science, 258(5085), 1107–1111.
Rose, K. A., Kimmerer, W. J., Edwards, K. P., and Bennett, W. A. (2013). “Individual-based modeling of delta smelt population dynamics in the upper San Francisco estuary. I: Model description and baseline results.” Tran. Amer. Fish. Soc., 142(5), 1238–1259.
Ross, O. N., and Sharples, J. (2004). “Recipe for 1-D Lagrangian particle tracking models in space-varying diffusivity.” Limnol. Oceanogr.-Meth., 2(9), 289–302.
Sanz-Serna, J. M. (1992). “Symplectic integrators for Hamiltonian problems: An overview.” Acta Numerica, 1, 243–286.
Sridharan, V. K. (2015). “Scalar transport in channel networks: Development of a particle tracking model to study the movement of scalars in the Sacramento-San Joaquin Delta.” Ph.D. thesis, Stanford Univ., Stanford, CA.
STARWalker version 1.0 [Computer software]. Stanford Univ., Stanford, CA.
Thomson, D. J., and Montgomery, M. R. (1994). “Reflection boundary conditions for random walk models of dispersion in non-Gaussian turbulence.” Atmos. Environ., 28(12), 1981–1987.
Venutelli, M. (2002). “Stability and accuracy of weighted four-point implicit finite difference schemes for open channel flow.” J. Hydraul. Eng., 281–288.
Visser, A. (1997). “Using random walk models to simulate the vertical distribution of particles in a turbulent water column.” Mar. Ecol. Prog. Ser., 158, 275–281.
Wang, B., Fringer, O. B., Giddings, S. N., and Fong, D. A. (2009). “High-resolution simulations of a macrotidal estuary using SUNTANS.” Ocean Modell., 28(1), 167–192.
Wolfram, P. J., Fringer, O. B., Monsen, N., Gleichauf, K., Fong, D., and Monismith, S. G. (2016). “Modeling intra-junction dispersion at a tidal river junction.” J. Hydr. Div., in press.
Wright, P. (2001). “Fixing the delta: The CALFED Bay-Delta program and water policy under the Davis administration.” Golden Gate Univ. Law Rev., 31(4), 331–350.
Zhang, Y., Ye, F., Stanev, E. V., and Grashorn, S. (2016). “Seamless cross-scale modeling with SCHISM.” Ocean Modell., 102, 64–81.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 144Issue 2February 2018

History

Received: Sep 8, 2016
Accepted: Jul 11, 2017
Published online: Nov 29, 2017
Published in print: Feb 1, 2018
Discussion open until: Apr 29, 2018

Permissions

Request permissions for this article.

Authors

Affiliations

Vamsi K. Sridharan, Ph.D., A.M.ASCE https://orcid.org/0000-0003-1457-6900 [email protected]
Assistant Project Scientist,Univ. of California, Santa Cruz, Institute of Marine Sciences; Affiliate, Fisheries Ecology Division, Southwest Fisheries Science Center, Southwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, 110 McAllister Way, Santa Cruz, CA 95060 (corresponding author). ORCID: https://orcid.org/0000-0003-1457-6900. E-mail: [email protected]
Stephen G. Monismith, Ph.D., A.M.ASCE
Professor, Dept. of Civil and Environmental Engineering, Stanford Univ., The Jerry Yang and Akiko Yamazaki Environment and Energy Bldg., 473 Via Ortega, Stanford, CA 94305.
Derek A. Fong, Ph.D., A.M.ASCE
Senior Research Engineer, Dept. of Civil and Environmental Engineering, Stanford Univ., The Jerry Yang and Akiko Yamazaki Environment and Energy Bldg., 473 Via Ortega, Stanford, CA 94305.
James L. Hench, Ph.D.
Associate Professor, Nicholas School of the Environment, Duke Univ. Marine Laboratory, 135 Marine Lab Rd., Beaufort, NC 28516.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share