An Explicit Solution for Characterizing Non-Fickian Solute Transport in Natural Streams
Abstract
:1. Introduction
2. Materials and Methods
2.1. Model Description
2.1.1. Formulation for Non-Fickian Tracer Transport
2.1.2. Parameter Determination
2.2. Field Experiment
3. Results and Discussion
3.1. Verification by Synthetic Data
3.2. Validation by Field Data
3.3. Late-Time Behavior of the Breakthrough Curve
4. Conclusions
- The proposed formula was validated by comparison with analytical and numerical solutions, and the results were exact. Its performance in simulating non-Fickian transport in streams was also validatesd using field tracer data, and good agreement was achieved.
- Despite the accurate results of reproducing the overall breakthrough curves, significant differences in their late-time behaviors were found according to the memory function modeling. This indicates that the best-fit breakthrough curve does not imply the accurate storage effect modeling.
- The tailing effect was discussed by comparing the optimal memory functions and net residence time functions. The key role of residence time-dependent functions is to enable us to quantitatively identify the storage effect, which is fundamental for a deeper understanding of non-Fickian tracer transport in streams. Hence, insight in characterizing non-Fickian mixing in can be provided from the memory function modeling.
- According to the data and optimal parameters, the proper formula for the memory function was inconsistent. The exponential memory function had a structural limit in generating a heavy-tailed breakthrough curve.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Case | Sub-Reach | Length (m) | Discharge (m^{3}/s) | Velocity (m^{2}/s) | Area (m^{2}) | Width (m) | Depth (m) |
---|---|---|---|---|---|---|---|
C1 | SR1 (C1-S1–C1-S2) | 1200 | 12.63 | 0.610 | 20.69 | 57.36 | 0.361 |
SR2 (C1-S2–C1-S3) | 830 | 0.598 | 21.10 | 58.86 | 0.358 | ||
SR3 (C1-S3–C1-S4) | 2000 | 0.553 | 22.83 | 53.00 | 0.431 | ||
C2 | SR1 (C2-S1–C1-S2) | 954 | 2.17 | 0.322 | 6.17 | 20.75 | 0.305 |
SR2 (C2-S2–C1-S3) | 1798 | 0.317 | 6.06 | 15.45 | 0.388 | ||
SR3 (C2-S3–C1-S4) | 1105 | 0.315 | 6.74 | 16.75 | 0.395 |
Simulation Case | $\overline{\mathit{u}}$ (m) | ${\mathit{D}}_{\mathit{L}}$ (m^{2}·s^{−1}) | ${\mathit{T}}_{\mathit{m}}$ (s) | $\mathit{\alpha}$ (10^{−4}·s^{−1}) |
---|---|---|---|---|
C1-SR1 | 0.605 | 0.56 | 604.94 | 3.76 |
C1-SR2 | 0.644 | 0.59 | 536.39 | 2.92 |
C1-SR3 | 0.355 | 4.89 | 2187.74 | 1.54 |
C2-SR1 | 0.465 | 0.17 | 201.39 | 5.57 |
C2-SR2 | 0.420 | 1.73 | 827.86 | 2.01 |
C2-SR3 | 0.315 | 6.94 | 5767.09 | 1.35 |
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Kim, B.; Kwon, S.; Seo, I.W. An Explicit Solution for Characterizing Non-Fickian Solute Transport in Natural Streams. Water 2023, 15, 1702. https://doi.org/10.3390/w15091702
Kim B, Kwon S, Seo IW. An Explicit Solution for Characterizing Non-Fickian Solute Transport in Natural Streams. Water. 2023; 15(9):1702. https://doi.org/10.3390/w15091702
Chicago/Turabian StyleKim, Byunguk, Siyoon Kwon, and Il Won Seo. 2023. "An Explicit Solution for Characterizing Non-Fickian Solute Transport in Natural Streams" Water 15, no. 9: 1702. https://doi.org/10.3390/w15091702