International Journal of Sediment Research 31 (2016) 205–211

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International Journal of Sediment Research

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Original Research A study on limit velocity and its mechanism and implications for alluvial rivers

Yanhong Jia a, Zhaoyin Wang b,n, Xiangmin Zheng a, Yanfu Li c a East China Normal University, Shanghai 200241, China b State Key Laboratory of Hydroscience and Engineering of Tsinghua University, Beijing 100084, China c Nanjing Hydraulic Research Institute, Nanjing 210029, China article info abstract

Article history: Observations from field investigations showed that flow velocity greater than 3 m/s rarely occurs in Received 29 October 2014 nature, and high flow velocity stresses the bio-community and causes instability to the channel. For Received in revised form alluvial rivers without strong human disturbance, the flow velocity varies within a limited range, gen- 5 January 2015 erally below 3 m/s, while the discharge and wet area may vary in a range of several orders. This phe- Accepted 20 January 2015 nomenon was studied by analyzing hydrological data, including daily average discharge, stage, cross Available online 3 August 2015 sections, and sediment concentration, collected from 25 stations on 20 rivers in China, including the Keywords: , Yellow, Songhua, Yalu, Daling, and Liaohe Rivers. The cross-sectional average velocity was cal- Limit velocity culated from the discharge and wet area using the continuity equation. For alluvial rivers, the wet cross Alluvial river section may self-adjust in accordance with the varying flow discharge so that the flow velocity does not Self-adjustment exceed a limit value. In general, the average velocity increases with the discharge increase at low dis- Wet area Human activity charge. As the discharge exceeds the discharge capacity of the banks, any further increase in discharge does not result in a great increase in velocity. The average velocity approaches an upper limit as the discharge increases. This limit velocity, in most cases, is less than 3 m/s. Human activities, especially levee construction, disturb the limit velocity law for alluvial rivers. In these cases, the average velocity may be approximately equal to or higher than the limit velocity. The limit velocity law has profound morphological and ecological implications on alluvial rivers and requires further study. Rivers should be trained and managed by mimicking natural processes and meeting the limit velocity law, so as to maintain ecologically-sound and morphological stability. & 2015 International Research and Training Centre on Erosion and Sedimentation/the World Association for Sedimentation and Erosion Research. Published by Elsevier B.V. All rights reserved.

1. Introduction sediment transport rate, river width and depth, average flow velocity, hydraulic radius, channel slope and roughness. An alluvial channel is usually located in the middle or lower Based on discussions regarding the characteristics of different river reaches of a river, with its watercourse wandering and swaying slowly patterns, including mountain rivers, alluvial rivers, and estuaries, fi fl and nally forming a at and wide valley (Chang, 1990). Where the Chien et al. (1987) and Chien and Wan (1999) concluded that alluvial fl river carries a heavy sediment load and the land is at, the alluvial rivers have the ability of self-adjustment; that is, alluvial rivers can sediments may form a delta. An alluvial river is defined as a river with self-adjust in accordance with incoming water, sediment condition its boundary composed of sediment previously deposited in the valley, and boundary conditions. Riahi-Madvar et al. (2011) and Huang and or a river with erodible boundaries flowing in self-formed channels Nanson (2002) suggested that a self-formed river flowing through its (Wang et al., 2014). Over time the stream builds its channel with sediment it carries and continuously reshapes its cross sections to own alluvium tends to adjust its hydraulic geometry over time so that reach the depths of flow and channel slopes that generate the it can just transport the imposed sediment load without net deposi- sediment-transport capacity needed to maintain the stream channel tion or scour. Representative formulas expressing the self-adjustment (Wang et al., 2014; Huelin-Rueda et al., 2014). The river morphology of ability of alluvial rivers include Lacey's (1929) formula of equilibrium alluvial rivers is relevant to many variables, including discharge, theory, Leopold and Maddock's (1953) geometry formula of the rela- tions between velocity, water depth, river width, channel slope and

n discharge, Yang and Song (1979) minimum unit stream power theory, Corresponding author. E-mail address: [email protected] (Z. Wang). and Chang's (1979) minimum stream power theory. Xie (1997) http://dx.doi.org/10.1016/j.ijsrc.2015.01.002 1001-6279/& 2015 International Research and Training Centre on Erosion and Sedimentation/the World Association for Sedimentation and Erosion Research. Published by Elsevier B.V. All rights reserved. 206 Y. Jia et al. / International Journal of Sediment Research 31 (2016) 205–211 summarized five characteristics of the self-adjustment ability of allu- enclosed by the boundary. Hydrological yearbooks provide data at vial rivers. the gauged sections. The cross-sectional average velocity was This paper proposes the limit velocity law, which is a noticeable calculated from the discharge and wet area using the continuity phenomenon in natural streams. Field investigations found that equation. Velocitydischarge curves from representative alluvial the flow velocity in natural alluvial rivers is generally not more rivers and mountain rivers were plotted to obtain the limit velo- than 3 m/s. Zhang et al. (2007) pointed out that due to the mild city law. The mechanisms of the limit velocity were analyzed from slope and wide floodplain of an alluvial river, the flow velocity is two aspects: one was based on the self-adjustment of the sedi- not more than 2–3 m/s. Aquatic life forms adapt well to the water ment transport capacity of alluvial rivers; and the other was based environment in which the flow velocity is not more than 3 m/s. on the relation between the limit velocity and critical velocity of Wang et al. (2007) analyzed the survival environments of 36 kinds the suspended load. During the process of this analysis, the curves of fish around the world, and found that 90% of adult fish cannot of cross sections, velocity and discharge, discharge and area, and survive when the flow velocity is more than 2 m/s; for example, critical velocity of suspended load motion and particle size fl Chinese sturgeon cannot survive when the ow velocity is more were used. than 1.5 m/s. To verify the field observation that the flow velocity in natural alluvial rivers is generally less than 3 m/s and to summarize the 3. Results flow velocity law for alluvial rivers, this paper analyzed observed hydrological data, and used the continuity equation to calculate 3.1. Concept of limit velocity flow velocity. The limit velocity law for alluvial rivers was derived based on results from the analyses. Furthermore, this paper ana- In general, the average velocity increases with an increase in lyzed why the limit velocity law exist in alluvial rivers, showed the the discharge when the discharge is low. As the discharge exceeds ecological and morphological implications of this law, and pro- the discharge capacity of the banks, any further increase in dis- posed the resistance principles of river training and management. charge does not result in a great increase in velocity. The average velocity approaches an upper limit, i.e. the limit velocity. The limit velocity, in most cases, is below 3 m/s. 2. Methods Fig. 1 shows the V–Q (which is the abbreviation for velocity– discharge) relation curves for alluvial rivers based on data from This study chose 25 stations on 20 rivers in China, including the the Caijiagou station on the Lalin River, the Wudaogou station on Yangtze, Yellow, Songhua, Yalu, Daling, and Liaohe Rivers. For each the Huifa River, the station on the , and the river, data were collected at one, two or three hydrological sta- Ayanqian station on the Nenjian River. The Lalin and Huifa Rivers tions. Hydrological data included the daily average discharge, daily are tributaries of the Songhua River. With an increase in the dis- average stage, cross sections, and sediment concentration. The charge, the average velocity approaches the limit velocity. As data were recorded from 1950 through 1988, except the data for shown in Fig. 1, the limit velocity is 1.30 m/s at the Caijiagou sta- the Liuhe and Xiliao Rivers, for which the period of the data was from 1935 through 1988. The monthly range of the data was tion, 1.73 m/s at the Wudaogou station, 2.00 m/s at the Jilin sta- determined by each river's physical state. The study was effective tion, and 1.86 m/s at the Ayanqian station. The limit velocity for only when the data were collected during the non-freezing period. the above alluvial rivers does not exceed 3 m/s. Therefore, the data of the Yangtze River were from January through December, the data of the were from May 3.2. Mechanisms of the limit velocity through December, and the data of the Songhua, Yalu, Daling, and Liaohe Rivers were from May through October, respectively. This study analyzed mechanisms of the limit velocity from two The boundary of a cross section comprises the channel aspects, including the mechanism based on the self-adjustment of the boundary and the water-surface profile. The wet area is the area sediment transport capacity of the alluvial rivers and the mechanism

Fig. 1. V–Q relations of typical alluvial rivers. Y. Jia et al. / International Journal of Sediment Research 31 (2016) 205–211 207 based on the relation between the limit velocity and critical velocity of The velocity increases faster with discharge in a small channel the suspended load. than in a large channel. Therefore, the points in Fig. 4 greatly scatter. Nevertheless, the velocity does not surpass a limit velocity 3.2.1. Self-adjustment of sediment transport capacity in alluvial between 2.5 and 3 m/s for channels with different bankfull areas. rivers In mountain rivers, the development of cross sections is con- The channel cross section of alluvial rivers generally consists of strained by bed rocks and bank rocks. At a gorge section the a channel and a wide floodplain. As shown in Fig. 2, the width of velocity may be higher than 2.5 m/s during extremely high flood the floodplain is 3500 m at the Caijiagou station and 830 m at the events. However, the river reach with high velocity sections are Ayanqian station. rather short. Fig. 5 shows the average velocity along the course As shown in Fig. 3, with discharge approaching a certain value, from Yichang to Chongqing and Yibin on the Yangtze River at the Q–A (which is the abbreviation of discharge–area) relation discharges of 30,000 and 60,000 m3/s, which equal the normal curves of the alluvial rivers are linear and pass through the origins flood discharge and abnormal flood discharge, respectively. The of the Q and A axes. The gradients represent the limit velocities. velocity was calculated based on the discharge and cross sectional This indicates that once the discharge exceeds the discharge areas at different sections. As shown in Fig. 5(a), although the capacity of the banks, any further increase in the discharge does velocity at several locations is higher than 2.5 or 3 m/s, the average not result in a great increase in the velocity because the channel velocity for all reaches is well below 2.5 m/s. In Fig. 5(b), the adapts to the increased discharge by only increasing its wet area. number of the locations at which the velocity is higher than 2.5 or For alluvial rivers, water flows in a channel when the discharge 3 m/s is higher than that in Fig. 5(a). This indicates that the velo- is low, whereas water flows into the floodplain which results in a city in the mountain river increases with increasing discharge; larger wet area when the discharge exceeds a certain value. As a even the average velocity can exceed 2.5 m/s. However, in alluvial result, the average velocity approaches an upper limit, generally rivers, due to their self-adjustment abilities, when the discharge less than 3 m/s. As seen in the above analysis, due to the char- exceeds a certain value, the average velocities will not exceed the acteristics of channel cross sections and the self-adjustment abil- limit of 2.5 or 3 m/s. ity, limit velocities exist for alluvial rivers. Fig. 4 shows the velocity–discharge relations of the Yellow 3.2.2. Relation between limit velocity and critical velocity of sus- River at the Huayuankou and Gaocun hydrological stations (Liu, pended load motion 2007). The Yellow River carries an extremely high sediment load; The critical velocity of suspended load motion refers to the therefore, it is very dynamic. The cross sections vary every year critical velocity at which the sediment exchanges from bed load and the bank-full wet areas consequently vary. In general the main motion to suspended load motion. When the flow velocity is channel has been shrinking in recent years due to sedimentation greater than the critical velocity, the sediment is suspended and and less high flood events which cause scouring of the channel. easily transported downstream by the flow. When the flow

Fig. 2. Cross sections of typical alluvial rivers.

Fig. 3. Q–A relations of typical alluvial rivers. 208 Y. Jia et al. / International Journal of Sediment Research 31 (2016) 205–211

Fig. 4. V–Q relations for the Yellow River at the Huayuankou and Gaocun hydrological stations (Liu, 2007). (a) Huayuankou station (1971–1990). (b) Gaocun station (1964 and 1996).

Fig. 5. Average velocity in the Yangtze River from Yibin to Yichang at discharges of 30,000 m3/s (a) and 60,000 m3/s (b).

velocity is lower than the critical velocity, the sediment is in bed in which: load motion or rests on the bed. During the transition between bed load motion and suspended load motion, some adjustments Us—critical velocity of suspended load motion, m/s; 3 are made to the water flow and sediment transportation, and γs—specific weight of sediment grains, N/m ; changes occur to the wet area, which affects the flow velocity. γ—specific weight of water, N/m3; Based on a series of experimental data, Sha (1965) developed g—gravitational acceleration, N/kg; an empirical formula for determining the critical velocity of sus- ν—kinetic viscosity of the liquid, m2/s; pended load motion according to the similarity principle of d—sediment diameter, m; movement. Fan derived a theoretical formula for the critical ω—fall velocity of particle, m/s; velocity of suspended load motion based on the mechanism of Rb—hydraulic radius, m. sediment transport. For flows with high Reynolds numbers, Fan's formula produces consistent results for suspended load motion. According to Eqs. (1), (2) and (3), the relations between the For flows with low Reynolds numbers, the formula also produces critical velocity of suspended load motion and particle size at the similar results as the measured data (Water Conservancy and water depth of 1 m, 5 m, 10 m and 15 m are plotted respectively in Hydropower Discharge Engineering and High-Speed Flow Infor- Fig. 6. For a certain water depth, the greater the particle size, the mation Network, 2002). Therefore, Fan's formula, as shown in higher the critical velocity of suspended load motion is. When the Eqs. (1) and (2), was chosen in this study for calculating the critical critical velocity of suspended load motion is given, the maximum velocity of suspended load motion. The fall velocity of sediment particle size that the water can pick up decreases as the water particles, ω, was calculated using Formula of Wuhan Institute of depth increases. Hydraulic and Electric Engineering (WIHEE), as shown in Eq. (3). Fig. 6 shows the critical velocity of suspended load motion,  corresponding to the coarsest sediment to be suspended, when ω 0:2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiUs ¼ d Rb ð Þ the water level equals the full depth of the main channel. The full γ γ f 2 1 s υ d γ gd depth of the main channel was obtained by dividing the full wet area of the main channel by its width. Two hydrological stations 8 ÀÁ: < ωd 0 1 ωd 3 on the alluvial rivers were selected for the analysis, as shown in ωd 3:82 υ υ o5 10 f ¼ ÀÁ : ð2Þ Table 1. It found that when the water level equals the full depth of 2 υ : ωd 0 12 ωd 3 3:530:678 υ υ Z5 10 the main channel, the critical velocity of suspended load motion, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi corresponding to the coarsest sediment to be suspended, is close  fl υ 2 γ γ υ to the limit velocity. This means that when the ow velocity in a ω ¼ 13:95 þ1:09 s gd13:95 ð3Þ fi d γ d river is lower, ner grains of suspended load are picked up. As the flow velocity increases, the size of particles suspended becomes Y. Jia et al. / International Journal of Sediment Research 31 (2016) 205–211 209 greater until it reaches a point that the coarsest sediment is sus- 3.3.1. Ecological implications pended. If the flow velocity in a river continues to increase, the Rivers are the carriers of life and provide habitats to creatures. particles, whose size is greater than the coarsest sediment to be Floodplains and riparian wetlands have high biodiversity and suspended, will also be picked up, however, the cross sectional depend on flows from rivers. Studies have shown fundamental area of the river will increase as a result and the flow velocity will feedback loops and mutual adjustments that exist between bio- reduce. Therefore, the critical velocity of suspended load motion, logical and physical processes within alluvial systems (Fisher et al., corresponding to the coarsest sediment to be suspended, will 2007; Corenblit et al., 2007; Corenblit et al., 2011; Collins et al., never be exceeded. The sediment particles, whose size is gre- 2012; Davies & Gibling, 2013). Flow velocity is known to be par- ater than the coarsest sediment to be suspended, will fall back ticularly important because it determines the rate at which onto the river bed. Thus, the maximum particle size of the sus- nutrients and oxygen reach aquatic species, and it also affects the pended load will not exceed the current maximum value for the lift and drag force on aquatic species (McDonnell, 2000; Yi et al., suspended load. 2014a). According to studies on bio-communities in river ecosys- The limit velocity roughly equals to the critical velocity for the tems, flow velocities should be kept below 3 m/s in order for coarsest sediment to be suspended. This equivalence in an alluvial survival of most aquatic animals, even for flood flows (Yi et al., river also demonstrates the mechanism of limit velocity in a river. 2014b). Most aquatic animals live in lentic or slow water flows. When the water depth equals the full depth of the main channel, The suitability index, SI, is defined as the suitability of physio- sediment whose size is smaller than the coarsest sediment to be chemical conditions of a habitat for species to live and spawn. suspended may be picked up; when the flow velocity in a river is SI¼1 represents the best conditions and SI¼0 represents the close to but not exceeding the limit value, the size of sediment worst. In fact, SI¼0 implies that species cannot live in the habitat. picked up by the river flow will increase until reaching a point that The SI for Chinese sturgeon is best for a flow velocity of 0.2–0.6 the coarsest sediment is suspended. The sediment suspended is m/s and SI reduces to zero for velocities higher than 1.5 m/s (Wang easily transported downstream by the flow. The remaining sedi- et al., 2007). Wang et al. (2007) listed critical velocities for dif- ment will mix with bed load and participate in bed evolution. ferent values of SI for 36 species of fish in rivers around the world. They showed that if the flow velocity is higher than 2 m/s, the 3.3. Implications of the limit velocity adults of 90% of the species cannot live, about 85% of the species cannot spawn, and juvenile fish of all species cannot live. Flow The limit velocity law has both ecological and morphological conditions for the survival of aquatic life forms are that the flow implications. velocity does not exceed 3 m/s, which is the limit velocity of alluvial rivers. The flow velocity in rivers remains mostly within the range of 0.3–3 m/s, which is the velocity most suitable for many fish spe- cies to live. On the other hand, natural rivers develop complex channels to reach the highest stability. In other words, the natural complex channel shapes may accommodate the normal discharge variation and their channel shapes remain unchanged. During floods, the discharge may be ten times higher than the average discharge, however, the complex channel shapes provide enough

Fig. 6. Relations between critical velocity of suspended load motion and Fig. 8. Reclamation of floodplain with grand levees and narrowed flood channels particle size. with roughness elements.

Table 1 Comparison between the critical velocity of suspended load motion and limit velocity of typical alluvial rivers.

River Hydrological station Full depth of the main The coarsest sediment to be sus- Critical velocity of suspended load Limit velocity channel (m) pended (mm) motion (m/s) (m/s)

The Lalin River The Caijiagou station 6 0.2 1.3 1.3 The Nenjiang River The Ayanqian station 5.9 0.5 1.81 1.9

Fig. 7. Typical complex channel shapes of alluvial rivers. 210 Y. Jia et al. / International Journal of Sediment Research 31 (2016) 205–211

Fig. 9. Cross section (a), V–Q relation (b), and the Q–A relation (c) of the Hankou station on the Yangtze River. water conveyance capacity and keep the velocity below a critical and lower reaches, flood wave propagation will be slowed. Thus value to prevent aquatic life from being hurt. flood safety can be improved owing to the low scouring energy and enhanced levees. Moreover, the aquatic habitat will become 3.3.2. Morphological implications stable and the value of the SI of the river habitat will increase to The concept of limit velocity is useful in alluvial river training one (Wang et al., 2007). and management. Fig. 7 shows the typical complex channel shapes of channels and floodplains. Engineers consider the floodplain to be any part of the valley floor subject to occasional floods that 4. Conclusions threaten life and property. As flood discharge exceeds the bankfull discharge, the wet area of the cross sections sharply increases with A noticeable phenomenon exists in natural streams: the flow stage, thus, the flow velocity remains equal to or lower than the velocity varies in a limited range, generally from zero to 3 m/s, limit velocity. while the discharge varies in a range of several orders of magni- In many cases, man-made structures constrain the channel tude from zero to thousands or several tens of thousands of m3/s, within a narrow levee-defined valley and reclaim the floodplain depending on the size of the river. In alluvial rivers, the velocity for agriculture and residential development. Fig. 8 shows an varies within a small range, while the stream flow may spread example of floodplain reclamation. Grand levees are constructed over the channel and the floodplain. In general, the average to constrain the flood water within a narrower valley. This will velocity increases with an increase in the discharge when the influence the limit velocity law. As shown in Fig. 9, the cross discharge is small. As the discharge exceeds the bank-full dis- section at the Hankou station on the Yangtze River has flood charge, any further increase in the discharge does not result in an protection embankments. Although the channel is wide (over increase in the velocity. The average velocity approaches a limit, 1800 m), the V–Q curve shows that with an increase in discharge, which is called the limit velocity. The limit velocity, in most cases, the flow velocity does not approach an upper limit. Moreover, the is below 3 m/s. Q–A relation does not exhibit a linear distribution with an inter- This paper analyzed two aspects regarding the mechanisms of cept of zero, which indicates that as the wet area changes to adapt to the change in water flow, the flow velocity changes accordingly the limit velocity. On one hand, the limit velocity exists in alluvial fl and does not approach the limit velocity. This practice does not rivers because the wet cross section increases linearly with ow fl really provide better flood safety. The smooth banks have much discharge while the ow velocity remains below the limit velocity. lower roughness than banks with natural vegetation, so a high On the other hand, the limit velocity roughly equals to the critical velocity current may directly attack the banks and break the velocity for the coarsest sediment to be suspended. As the velocity levees. In order to keep the flow velocity below the limit velocity, exceeds the limit velocity, the cross-section of river may be fl large stones are placed on the smooth banks to create high resis- changed and thus the ow velocity is reduced. tance. Other roughness elements, such as trees and shrubs on the The limit velocity law has profound morphological and ecolo- fl floodplain, are useful in increasing the resistance and controlling gical implications for alluvial rivers. River ow velocity remains – the flow velocity. With these elements which increase the mostly within the range of 0.3 3 m/s, which is the velocity most roughness, the overbank flood flow has higher stage but lower suitable for aquatic life to live. When channel improvements or velocity, thus, the channel and floodplain may remain stable. One impoundments are used to restrict the natural process of overbank consequence of high roughness is high flood stages, which may be flow, the limit velocity law is broken and the velocity during high solved by raising the grand levees. In general, high velocity rather floods is much higher than 2.5 m/s. Under this condition, many than high stage poses a threat to levees. organisms are stressed and the ecosystem is impaired. Moreover, In summary, rivers should be trained and managed to reduce high flow velocity scours the bed and banks, thus, the risk of bank flow velocity, even during floods. Actions to remove obstacles from failure is high. The limit velocity law should be taken into con- the river to enhance the flow velocity disrupt the limit velocity law sideration during levee design. To enhance the bank roughness for and are not suitable for the health of river ecosystems. The con- controlling high velocity current, large stones can be placed on the cept of resistance construction should be introduced in river smooth banks to create high resistance. Floodplain vegetation is training and management projects. If the resistance structures are another type of resistance against flood flow. Such vegetation constructed on the entire river system including the upper, middle behaves as an obvious obstacle to flood propagation. Y. Jia et al. / International Journal of Sediment Research 31 (2016) 205–211 211

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文章名

作者 11,作者 21,作者 32,作者 43 1 单位 1 信息 2 单位 2 信息 3 单位 3 信息



摘要 第一作者照片  宽度 3cm,高约 摘要文字例:泥沙运动特征的变化及其对港口航道的影 4.3cm 响是大型海岸工程实施时需要考虑的主要问题。由于海 岸生态系统往往对泥沙冲淤的变化非常敏感,生态评估 也逐渐成为工程规划及方 案可行性论证研究的重要内 容。本文利用泥沙数学模型,以深圳湾为例研究了五种 填海方案造成的海湾来沙量、含沙量和泥沙冲淤分布的 第一作者名 变化,讨论了泥沙淤积速率的变化对港口航道和红树林  生态系统的影响,并通过岸线方案的对比指出了在分别  考虑各种泥沙评价指标时对 应的五种填海方案的优 报告人即第一作者简介 劣。定量分析表明,不同评价指标对应的方案优劣次序 

有所差异,协调多种指标要求的综合优化岸线可以通过 比较各种方案后给出

 关键词 关键词文字





注:论文已发表于 期刊 卷 期( ~ 页)/论文未公开发表过。