Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow
This study implemented kinematic wave and dynamic wave approximation of flood routing for a prismatic rectangular channel. The results of the two methods were compared by differences in maximum flow depth, and the applicability of kinematic wave equation was discussed. The influences of hydraulic an...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/12/9/2528 |
| _version_ | 1797554066499305472 |
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| author | Hanwu Zheng Er Huang Ming Luo |
| author_facet | Hanwu Zheng Er Huang Ming Luo |
| author_sort | Hanwu Zheng |
| collection | DOAJ |
| description | This study implemented kinematic wave and dynamic wave approximation of flood routing for a prismatic rectangular channel. The results of the two methods were compared by differences in maximum flow depth, and the applicability of kinematic wave equation was discussed. The influences of hydraulic and geometrical factors on the applicability of kinematic wave equation were considered. It was found that a portion of the numerical results violated existing criteria used to indicate the applicability of kinematic wave equation, particularly when geometrical and hydraulic factors were considered together. This is because the characteristics of upstream inflow were rarely or incompletely considered in these criteria. Therefore, the present study proposed a new criterion. The theoretical influence of all factors was considered using three parameters, namely, <inline-formula><math display="inline"><semantics><mrow><msubsup><mrow><mi>K</mi><mi>F</mi></mrow><mn>0</mn><mn>2</mn></msubsup></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo>/</mo><msubsup><mi>T</mi><mn>0</mn><mo>′</mo></msubsup></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>Q</mi><mrow><mi>b</mi><mi>o</mi><mi>t</mi><mi>t</mi><mi>o</mi><mi>m</mi></mrow></msub><mo>/</mo><msub><mi>Q</mi><mrow><mi>p</mi><mi>e</mi><mi>a</mi><mi>k</mi></mrow></msub></mrow></semantics></math></inline-formula> (<inline-formula><math display="inline"><semantics><mrow><mi>K</mi><mo>,</mo><mo> </mo><msub><mi>F</mi><mn>0</mn></msub><mo>,</mo><mo> </mo><msub><mi>η</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo>,</mo><mo> </mo><msubsup><mi>T</mi><mn>0</mn><mo>′</mo></msubsup><mo>,</mo><mo> </mo><msub><mi>Q</mi><mrow><mi>b</mi><mi>o</mi><mi>t</mi><mi>t</mi><mi>o</mi><mi>m</mi></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math display="inline"><semantics><mrow><msub><mi>Q</mi><mrow><mi>p</mi><mi>e</mi><mi>a</mi><mi>k</mi></mrow></msub></mrow></semantics></math></inline-formula> represent the kinematic wave number, Froude number, the time span of discharge exceeding 90% of maximum discharge in hydrograph, wave travel time in the channel, base flow discharge, and peak discharge, respectively, while the subscript 0 represent the value of reference discharge). The influences of these three parameters were illustrated by the momentum equation of one-dimensional Saint-Venant equation. The numerical results showed that the value of <inline-formula><math display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo>/</mo><msubsup><mi>T</mi><mn>0</mn><mo>′</mo></msubsup><mo> </mo><msup><mrow><mrow><mo>(</mo><mrow><mi>K</mi><msubsup><mi>F</mi><mn>0</mn><mn>2</mn></msubsup></mrow><mo>)</mo></mrow></mrow><mi>D</mi></msup></mrow></semantics></math></inline-formula> could be used to determine the relative error <inline-formula><math display="inline"><semantics><mrow><msub><mi>ξ</mi><mi>h</mi></msub></mrow></semantics></math></inline-formula> of kinematic wave equation. In addition, for each <inline-formula><math display="inline"><semantics><mrow><msub><mi>Q</mi><mrow><mi>b</mi><mi>o</mi><mi>t</mi><mi>t</mi><mi>o</mi><mi>m</mi></mrow></msub><mo>/</mo><msub><mi>Q</mi><mrow><mi>p</mi><mi>e</mi><mi>a</mi><mi>k</mi></mrow></msub></mrow></semantics></math></inline-formula> the value of <inline-formula><math display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo>/</mo><msubsup><mi>T</mi><mn>0</mn><mo>′</mo></msubsup><mo> </mo><msup><mrow><mrow><mo>(</mo><mrow><msubsup><mrow><mi>K</mi><mi>F</mi></mrow><mn>0</mn><mn>2</mn></msubsup></mrow><mo>)</mo></mrow></mrow><mi>D</mi></msup></mrow></semantics></math></inline-formula> used to depict the same relative error <inline-formula><math display="inline"><semantics><mrow><msub><mi>ξ</mi><mi>h</mi></msub></mrow></semantics></math></inline-formula> was different. This new criterion was validated using two real case studies, and it showed a good performance. |
| first_indexed | 2024-03-10T16:25:32Z |
| format | Article |
| id | doaj.art-771aaf7017894640a98a32af78d62430 |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-10T16:25:32Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Water |
| spelling | doaj.art-771aaf7017894640a98a32af78d624302023-11-20T13:17:07ZengMDPI AGWater2073-44412020-09-01129252810.3390/w12092528Applicability of Kinematic Wave Model for Flood Routing under Unsteady InflowHanwu Zheng0Er Huang1Ming Luo2State Key Lab of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, ChinaState Key Lab of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, ChinaState Key Lab of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, ChinaThis study implemented kinematic wave and dynamic wave approximation of flood routing for a prismatic rectangular channel. The results of the two methods were compared by differences in maximum flow depth, and the applicability of kinematic wave equation was discussed. The influences of hydraulic and geometrical factors on the applicability of kinematic wave equation were considered. It was found that a portion of the numerical results violated existing criteria used to indicate the applicability of kinematic wave equation, particularly when geometrical and hydraulic factors were considered together. This is because the characteristics of upstream inflow were rarely or incompletely considered in these criteria. Therefore, the present study proposed a new criterion. The theoretical influence of all factors was considered using three parameters, namely, <inline-formula><math display="inline"><semantics><mrow><msubsup><mrow><mi>K</mi><mi>F</mi></mrow><mn>0</mn><mn>2</mn></msubsup></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo>/</mo><msubsup><mi>T</mi><mn>0</mn><mo>′</mo></msubsup></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>Q</mi><mrow><mi>b</mi><mi>o</mi><mi>t</mi><mi>t</mi><mi>o</mi><mi>m</mi></mrow></msub><mo>/</mo><msub><mi>Q</mi><mrow><mi>p</mi><mi>e</mi><mi>a</mi><mi>k</mi></mrow></msub></mrow></semantics></math></inline-formula> (<inline-formula><math display="inline"><semantics><mrow><mi>K</mi><mo>,</mo><mo> </mo><msub><mi>F</mi><mn>0</mn></msub><mo>,</mo><mo> </mo><msub><mi>η</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo>,</mo><mo> </mo><msubsup><mi>T</mi><mn>0</mn><mo>′</mo></msubsup><mo>,</mo><mo> </mo><msub><mi>Q</mi><mrow><mi>b</mi><mi>o</mi><mi>t</mi><mi>t</mi><mi>o</mi><mi>m</mi></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math display="inline"><semantics><mrow><msub><mi>Q</mi><mrow><mi>p</mi><mi>e</mi><mi>a</mi><mi>k</mi></mrow></msub></mrow></semantics></math></inline-formula> represent the kinematic wave number, Froude number, the time span of discharge exceeding 90% of maximum discharge in hydrograph, wave travel time in the channel, base flow discharge, and peak discharge, respectively, while the subscript 0 represent the value of reference discharge). The influences of these three parameters were illustrated by the momentum equation of one-dimensional Saint-Venant equation. The numerical results showed that the value of <inline-formula><math display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo>/</mo><msubsup><mi>T</mi><mn>0</mn><mo>′</mo></msubsup><mo> </mo><msup><mrow><mrow><mo>(</mo><mrow><mi>K</mi><msubsup><mi>F</mi><mn>0</mn><mn>2</mn></msubsup></mrow><mo>)</mo></mrow></mrow><mi>D</mi></msup></mrow></semantics></math></inline-formula> could be used to determine the relative error <inline-formula><math display="inline"><semantics><mrow><msub><mi>ξ</mi><mi>h</mi></msub></mrow></semantics></math></inline-formula> of kinematic wave equation. In addition, for each <inline-formula><math display="inline"><semantics><mrow><msub><mi>Q</mi><mrow><mi>b</mi><mi>o</mi><mi>t</mi><mi>t</mi><mi>o</mi><mi>m</mi></mrow></msub><mo>/</mo><msub><mi>Q</mi><mrow><mi>p</mi><mi>e</mi><mi>a</mi><mi>k</mi></mrow></msub></mrow></semantics></math></inline-formula> the value of <inline-formula><math display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo>/</mo><msubsup><mi>T</mi><mn>0</mn><mo>′</mo></msubsup><mo> </mo><msup><mrow><mrow><mo>(</mo><mrow><msubsup><mrow><mi>K</mi><mi>F</mi></mrow><mn>0</mn><mn>2</mn></msubsup></mrow><mo>)</mo></mrow></mrow><mi>D</mi></msup></mrow></semantics></math></inline-formula> used to depict the same relative error <inline-formula><math display="inline"><semantics><mrow><msub><mi>ξ</mi><mi>h</mi></msub></mrow></semantics></math></inline-formula> was different. This new criterion was validated using two real case studies, and it showed a good performance.https://www.mdpi.com/2073-4441/12/9/2528flood routingkinematic wave approximationdynamic wave approximationnumerical method |
| spellingShingle | Hanwu Zheng Er Huang Ming Luo Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow Water flood routing kinematic wave approximation dynamic wave approximation numerical method |
| title | Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow |
| title_full | Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow |
| title_fullStr | Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow |
| title_full_unstemmed | Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow |
| title_short | Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow |
| title_sort | applicability of kinematic wave model for flood routing under unsteady inflow |
| topic | flood routing kinematic wave approximation dynamic wave approximation numerical method |
| url | https://www.mdpi.com/2073-4441/12/9/2528 |
| work_keys_str_mv | AT hanwuzheng applicabilityofkinematicwavemodelforfloodroutingunderunsteadyinflow AT erhuang applicabilityofkinematicwavemodelforfloodroutingunderunsteadyinflow AT mingluo applicabilityofkinematicwavemodelforfloodroutingunderunsteadyinflow |