STUDY THE MIGRATION OF THE TIDAL LIMIT AND

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1 Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 4-, 8, Darmstadt STUDY THE MIGRATION OF THE TIDAL LIMIT AND THE TIDAL CURRENT LIMIT OF THE YANGTZE RIVER UNDER ITS EXTREME HIGH AND LOWER RUNOFF Hongyan Shen, Jianyong Li,Shichang Yan State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering College of Ocean, Hohai University, Nanjing Abstract: Anqing-Xuliujing Reach (simplified as An-Xu Reach) locates in the tidal reached river of the Lower Yangtze River, connecting the river mouth and then entering into the sea. It is under the action of the runoff from the upper and that of the tide from the lower, making its hydrodynamic condition and then its river bed process complicated. This paper establishes a two-dimension flow numerical model for An-Xu Reach to study the migration law of the tidal limit and the tidal current limit under the typical water discharge condition in the Yangtze River. The established -D numerical model is applied to simulate the tide upward process along the Lower Yangtze River under the annual extreme discharge respectively corresponding to its certain accumulated frequency. The result shows that when the discharge smaller than 4 m/s, the tidal current limit would be above Anqing and the tidal current limitl would be above Nanjing, both upper than the traditional location Datong and Zhenjiang. And the relationship of the extreme discharge respectively with the tidal current limits locations is obtained here and a fitting formula was given out. I. INTRODUCTION The Yangtze River is the longest in China and the third in the world, shorter than the Nile in Africa and the Amazon in America. An-Xu Reach locates in the lower part of the Yangtze Rive with the total length of 6km starting from Anqing Gauge to Xuliujing Gauge. Its domain basin covers the marvelous alluvial plain of East China and the Yangtze Delta. That is, it flows downward through Anhui province and Jiangsu province, and then meets with the Huangpu River of ShangHai City at Wusong Mouth, ultimately entering the East China Sea. Its flow is driven both by the runoff of the Upper Yangtze River and by the tidal force propagating from the Pacific Ocean so that it takes on the distinct characteristics of the estuarine hydrodynamic. According to the counterbalance between the runoff force and the tide force, An-Xu Reach is subdivided into two parts, the estuarine river-flow reach and the estuarine tidalcurrent reach. The former, the river reach from the tidal limit to the tidal current limit, is mainly controlled by the runoff discharge and the tide begins to have influence on its flow and enhanced downward. It characterized as the water level changing periodically with the tide ebbing and flooding while the flow current orienting to the downward all the time. As to the later, the tidal influence take over the dominant role and the runoff force becomes minor. Its flow is periodically in the opposite direction as the tidal ebbing and flooding and the water level changes more obviously. Up to now, it is traditionally acknowledged that the tidal limit lies at Datong and the tidal current limit lies at Jiangyin. Accordingly, the estuarine river flow reach of Tongcheng Reach is the river segment from Datong Gauge Station to JiangYin and the estuarine tidal-current reach is that from JiangYin to Xuliujing Gauge Station. However, the position of the tidal limit and the tidal current limit migrate upward and downward according to the discharge from the upper river and the tidal energy entering into the estuary. Generally, they migrate upward with the small discharge and the macro-tide and downward with the large discharge and the micro-tide. Therefore the quantity of the discharge and the amplitude of the tide have great impact on their position. The river discharge mainly response to the rainfall quantity in its domain area of the same period while the tidal depends on the movement of the celestial bodies so that the discharge changes greater and less regular. Before the first half of the last century the water circulation is basically in its natural condition, the discharge of the Yangtze River had enjoyed a certain regular and its tidal limit and tidal current limit migrated in a certain range and changes little from year to year. But since the middle of the last century, many dams and water reservoirs have built in the upper of the Yangtze 9

2 Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 4-, 8, Darmstadt River and its water is intercepted and regulated, influencing the time and space distribution of its discharge. In the paper, a two-dimensional numerical model is established to simulate the flow in An-Xu Reach. By analyzing the results, it aims to figure out the change of the position of its tidal limit and its tidal current limit in the lower Yangtze River under the current measured discharge data at Datong Hydrological Station. II. MODEL DESCRIPTION An-Xu Reach is broad and shallow so that its physical quantities can be assumed to be of little change over the depth and its hydrodynamic model applies a state of the two-dimensional general orthogonal boundary-fitted grid in Descartes coordinates. The tow-dimensional depth averaged shallow equations in the curvilinear grid are shown as follows: ) Continuity Equation ( C Hu ) ( C Hv ) h + = CC () ) Momentum equation in -direction: ( C Huu ) ( C Hvu ˆ ) ( C Hvu ) ( CHvv ) Hu + + = CC ( CHτ) ( C Hτ ) ( C Hτ) ( CHτ) gu u + v + f v + + C C CC () ) Momentum equation in -direction: ( CHvu ) ( CHvv ) ( CHvu ) ( CHuu ) Hv + + CC ( CH τ) ( CH τ) ( CH τ) ( CH τ ) gv u + v = + f u + + C C CC () where, u~ and v~ are the depth averaged velocity components in and direction respectively and are the computing coordinates; C andc are the lamé's coefficient in the orthogonal curvilinear C = x + y C = xξ + yξ coordinates,, ;his the water level;h is the water depth;f is the coriolis force coefficient;cis the resistance coefficient;gis the gravity acceleration; τ τ τ τ is the shear stress as follows: τ τ v u C = υ t + C C C = τ C v C u = υt + C C C C (5) (6) τ u v C = υ t + C C C (4) ν where, t is the viscosity coefficient III. DISCRETIZATION OF THE EQUATIONS This paper applies the method of DSI [] to discretize the N-S equations. The DSI method improve the ADI method by applying the implicit velocity form in the direction and the explicit 9

3 Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 4-, 8, Darmstadt velocity form in the direction in the first half step and the opposite in the later haft step, shown as follows. In -direction( the first half step): ( CHu ) ( CHv ) * h + = (7) CC ( C Hvu ) ( C Hvv ) ( C Hvu ) ( CHuu ) Hv + + = CC gv u + v + f u C C ( CH τ) ( CH τ) ( CH τ) ( CH τ ) + + CC (8) In direction( the later half step): ( ) ( ) h n + C Hu C Hv + = CC (9) ( CHuu ) ( CHvu ˆ ) ( CHvu ) ( CHvv ) Hu + + CC ( CH τ) ( CH τ ) ( CH τ) ( CH τ) gu u + v = + f v + + C C CC () IV. PARAMETERS IN THE MODEL In the two dimensional numerical modal, the roughness coefficient is actually a synthesized index. It reflects not only the roughness of the river bed, but takes the effect of flow plane configuration, river hydraulic factors, geological size and formation of sections and the characteristics and composition of river bed into consider, as well as the errors caused by the discharge and its gradient []. What s more, the density of the grid also influences its value. In the present model, the domain area is somewhat long so that the roughness is different over the width and the length of the river, given as: nbi d dcr ri = nd i =,... k i ni + d > dcr d () Where, nb i is the roughness on the marginal bank; d cr is the critical depth between the marginal and the main channel; n i is thought to be determined by the roughness while nd i is the part dependent on the water depth; K is the number of the sections along the river length. V. TREATMENT OF THE MOVING BOUNDARY At the close boundary, its normal velocity is traditionally taken as zero, that is, there is no mass passing through the close boundary, which is easy to be handled. During the simulation, with the influence of the tide, some interior nods in the computing domain will be flooded in the flooding period and be exposed in the ebbing period. In order to properly embodying the phenomena of the drying and wetting of these nods, the model applies the dynamic boundary technique. The dynamic boundary technique is to select a certain depth as the critical depth, below which the nods is considered as dry and its depth is set to be equal to the critical depth with no velocity. Its water level is given by extrapolating the water level of the neighboring nods that are not dry. When the actual depth of the nod is 9

4 Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 4-, 8, Darmstadt larger than the critical depth, it enters into the regular program computing. VI. MODEL DOMAIN AND VALIDATION Fig. shows the model domain of An-Xu Reach in the lower Yangtze River. The upper inflow open boundary lies adjacent to Anqing Gauge Station and the lower outflow open boundary lies adjacent to the Xuliujing Gauge Station, shown in the figure below. As there are no filed discharge data at Anqing Gauge Station and little inflow or outflow between Anqing and Datong, the boundary condition of the upper inflow is given as the time series of the runoff discharge measured at the Datong Gauge Station. According to the statistics data of discharge measured at Datong Gauge Station, the average discharge is 9,m/s in year,close to the average annual discharge 8,7m /s (from 95 to ) [4]. So in the present study its simulation covers the time spanning from Feb. st to Mar.st,. The average flow discharge during the computing period is of relatively small quantity, about,4m /s. The lower flow boundary condition is given as the water level at Xuliujing Gauge Station of the corresponding time series. Additionally, it covers the whole process from the spring tide with the largest tidal range of m to the neap tide with the smallest tidal range of m. So that it can figure out the degree of the tidal intrusion upwards to An-Xu Reach in the lower Yangtze River combining the various tides with the smaller runoff discharge. The model grid is 4 98 shown in Fig.. Its size ranges from 45m to 68m over the length and from 8m to 656m over the width. The average grid length is 9m and 47m respectively, see Figure. The gauge stations of Wuhu, Ma Anshan, Nanjing, Zhenjiang, and Jiangyin is chosen to serve for the validation spots in the model, shown as Fig. Figure. The model domain area of An-Xu Reach 94

5 Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 4-, 8, Darmstadt Figure 4. Grid sketch of An-Xu Reach Through the trial calculation, the result showed that the roughness coefficient is taken as from.4 to.8.fig.-7 show the comparison of water levels at Wuhu, Ma Anshan, Nanjing, Zhenjiang, and Jiangyin Gauge Station. The result shows that the damping of the tidal upwards the An-Xu Reach is well simulated H(m) Figure 5. Comparison of the water level at Wuhu H(m) H ( m ) Figure 7. Comparison of the water level at Nanjing H ( m ) cmomputed 9 Figure 8. Comparison of the water level at Zhenjiang - - Figure 6. Comparison of the water level at Ma anshan 95

6 Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 4-, 8, Darmstadt. 5 H ( m ) Figure 9. Comparison of the water level at Jiangyin VII. MIGRATION OF THE TIDAL LIMIT AND TIDAL CURRENT LIMIT Datong Gauge Station is the last gauge station distributed in the Yangtze River to measure its discharging runoff so that the discharge data measured here represents the water volume of the Yangtze River entering the sea. Its catchment area is km, 94.7% of the Yangtze River Basin. According to the discharge statistics data at Datong Gauge Station from 95 to 6, the largest discharge is 96m /s( ), the smallest is 46m /s( ) and the annual is 85m /s. the tidal limit and tidal current limit is traditionally regarded to be located at Datong ( 5 km above Xuliujing ) and Zhenjiang ( 5 km above Xuliujing ) in dry-season respectively. Figure. The accumulated frequency of the annual minimum disharge at Datong (95~6) This paper pays special attention to its dry season discharge. Fig.8 shows the accumulated frequency distribution of the annual minimum discharge at Datong Gauge Station. The typical annual minimum discharges corresponding to some certain accumulated frequencies are listed in Tab.. TABLE I. TYPICAL DISCHARGE OF VARIOUS ACCUMULATED FREQUENCY Accumulated frequency Annual maximum Annual minimum % 5% 5% 5% 75% 95% 99% Using the -D numerical flow model established here to simulate the water flow in the Lower Yangtze River under the typical discharge of various accumulated frequency listed in Tab., the result shows that during the spring tidal with m tidal range the tidal current limit is above Anqing. There still exist fluctuations in water level at Anqing when the discharge is 4 m /s. Meanwhile the tidal current limit location see Tab. TABLE II. LOCATION OF TIDAL CURRENT LIMIT Q(m) D(m) above Xuliujing as the horizontal direction, the relationship between the small discharge and the location of the tidal current limit could be obtained, see Fig 9.the fitting formula could be: D=-.4*Q+57.4 () Where D is the distance of the tidal current limit location above Xuliujing, km; Q is the dry-season discharge of the lower Yangtze River, m /s. if the discharge is larger than 4 m /s or smaller than 4 m /s, the formula may not be suitable. Analyzing the result, it could be seen that the location of the tidal current limit changed from km to 465km above Xuliujing, that is, from Nanjing to Tongguanshan, corresponding to the various small discharges. Taking the discharge as the vertical coordinate and the distance of the tidal current limit 96

7 Figure. Relationship between dry-season discharge and location of the tidal current limit VIII. CONCLUSIONS The -D numerical flow model established here is the first time to simulate the whole lower Yangtze River. As the simulated area is large and the typographic varies greatly, it is a tough work to generalize the depth information, physical characteristics and dry-wet boundary condition. The flow driven both by the runoff and tidal force, the hydrodynamic condition is also complicated and difficult to reproduce properly. Based on the simulation result under different dryseason discharge, the tidal limit and tidal current limit would be upward as the dry-season discharge reduces. When the discharge is 46 m /s (the lowest in current record from 95-6), the tidal current limit would be 465.4km above Xuliujing, almost reaching Tongguanshan Reach. As the dams built in the upper Yangtze River, the dry-season would be elongated and the tidal current limit would be upstream and stayed for a longer time, aggravating the salt-water intrusion. This paper aims to study the tidal limit and tidal current limit location to value the influence of the change in dry-season discharge of the Lower Yangtze River to its hydrodynamics and then the water quality for the domestic, industrial and agriculture using. typographic varies greatly, it is a tough work to generalize the depth information, physical characteristics and dry-wet boundary condition. The flow driven both by the runoff and tidal force, the hydrodynamic condition is also complicated and difficult to reproduce properly. Based on the simulation result under different dryseason discharge, the tidal limit and tidal current limit would be upward as the dry-season discharge reduces. When the discharge is 46 m /s (the lowest in current record from 95-6), the tidal current limit would be 465.4km above Xuliujing, almost reaching Tongguanshan Reach. As the dams built in the upper Yangtze River, the dry-season would be elongated and the tidal current limit would be upstream and stayed for a longer time, aggravating the salt-water intrusion. This paper aims to study the tidal limit and tidal current limit location to value the influence of the change in dry-season discharge of the Lower Yangtze River to its hydrodynamics and then the water quality for the domestic, industrial and agriculture using. REFERENCE [4] Li RongHui, A preliminary study on extended shallow water equations and its application, thesis of Hohai University, [5] Yuan Shiqiong Roughness calculation in the natural river VOLNO. Hydropower Station Design, 997. [6] Chen Xiqing, Chen Jieyu Proposal to Study and Control of the Decrease tendency in Discharge of the Changjing River Entering the Sea in the Dry Season. Science and Technology Review, [7] Zhang Erfeng, Chen Xiqing Changes of water discharge between Datong and the Changjiang Estuary during the dry season.acta GEOGRAPHICA SINICA VOL.58, NO. MAR., REFERENCE [] Li RongHui, A preliminary study on extended shallow water equations and its application, thesis of Hohai University, [] Yuan Shiqiong Roughness calculation in the natural river VOLNO. Hydropower Station Design, 997. [] Chen Xiqing, Chen Jieyu Proposal to Study and Control of the Decrease tendency in Discharge of the Changjing River Entering the Sea in the Dry Season. Science and Technology Review, [] Zhang Erfeng, Chen Xiqing Changes of water discharge between Datong and the Changjiang Estuary during the dry season.acta GEOGRAPHICA SINICA VOL.58, NO. MAR., IX. CONCLUSIONS The -D numerical flow model established here is the first time to simulate the whole lower Yangtze River. As the simulated area is large and the 97

Available online at ScienceDirect. Procedia Engineering 154 (2016 )

Available online at ScienceDirect. Procedia Engineering 154 (2016 ) Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 154 (2016 ) 574 581 12th International Conference on Hydroinformatics, HIC 2016 Research on the Strength and Space-time Distribution