Characterizing ship-induced hydrodynamics in a heavy shipping traffic waterway via intensified field measurements

Li-lei Mao,Yi-mei Chen*,Xin Li

Department of Port,Waterway and Coastal Engineering,Southeast University,Nanjing 211189,China

Received 25 January 2020;accepted 18 September 2020

Available online 3 December 2020

Abstract Ship-induced hydrodynamics play an important role in shaping the cross-sectional profile of inland waterways and produce a large amount of pressure on the fluvial environment.This study aimed at quantifying the characteristics of ship-induced waves and currents in a heavy shipping traffic waterway via intensified field measurements conducted in the Changzhou segment of the Grand Canal,in Jiangsu Province,China.Based on the processed hydrodynamic data,waves and currents caused by single ships and multiple ships were investigated.For single ships,the shipinduced wave heights estimated with empirical formulas were not consistent with the observations.Categorized by the loading conditions of barges,the drawdown height was characterized by the ratio of ship speed to its limit speed.The maximum non-dimensional ship-induced wave height was parameterized by a nonlinear combination of the depth Froude number and a blockage coefficient.For multiple ships,when ships closely followed each other or interlaced each other's paths,it was difficult to characterize the superposition of several ship wakes.The magnitudes of current velocities induced by single ships and multiple ships were respectively nine and six times as large as those of natural flow.This may result in more severe sediment(re)suspension than natural flows.? 2020 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:Ship-induced waves;Drawdown;Field measurements;Current velocity;Sediment(re)suspension;Grand Canal

1.Introduction

As inland shipping traffic demands increase,heavy shipping traffic puts a large amount of pressure on the fluvial environment by producing waves and currents,leading to riverbank(or shoreline)erosion,sediment(re)suspension,increases of water turbidity,changes of the ecological environment,and damage to fixed or floating structures(Parchure et al.,2007;Roo and Troch,2013;Fleit et al.,2016;Kurdistani et al.,2019).Jiangsu Province is one of the most developed inland shipping traffic regions in China with more than 2 200 navigable rivers.The waterway surveys conducted in 2003,2012,and 2017 in Jiangsu Province revealed that ship traffic is one of the major inputs of energy in inland waterways,in the form of hydrodynamic field disturbance.Generally,inland waterways are not subjected to tidal excursion,and the fetch length of generated wind waves is restricted by their widths(Houser,2010;Roo and Troch,2015).Therefore,the waves and altering currents induced by ship passages are the most frequent and dominant forces shaping the cross-sectional profile of inland waterways.

When ships travel across the water surface,the variations of pressure at the water-air interface produce a series of waves(Soomere,2007).In deep water,the ship-induced wave pattern is a classical Kelvin wake wave,characterized by transverse and divergent waves(Soomere,2009),and the entire ship-induced disturbance system is regarded as the secondary wave system(Bertram,2000).In shallow water regions,the ship-induced wave pattern is determined by the interaction between the hydrodynamic field,the channel bathymetry,and the channel margins(Bellafiore et al.,2018).Nonlinear wake components,such as precursor solitons and depression waves(also called Bernoulli waves),may occur(Soomere,2007).At the ship bow and stern,pressure is increased whereas water level depression occurs along the ship hull.This is referred to as the primary wave system(Bertram,2000)or drawdown(G¨oransson et al.,2014).To maintain flow continuity,the velocity distribution between the moving ship and the riverbank changes accordingly,resulting in return currents opposite to the ship sailing direction(Bhowmik et al.,1995).In contrast to those in unrestricted waters,ships sailing in inland waterways cause a more pronounced potential flow around the ship hull due to the limited width and depth,and they also lead to an increased sinkage and trim because of the low underkeel clearance(Roo and Troch,2015).To minimize the impacts of ship wakes on inland waterways,the characteristics of waves and the associated currents induced by heavy shipping traffic should be clarified.

The direct and most effective way to characterize the shipinduced hydrodynamics is field measurements during ship passages at a specific site.Such on-site measurements have been conducted in many studies focusing on observations of waves induced by individual ships(Nanson et al.,1994;Osborne and Boak,1999;Chwang and Chen,2003;Ravens and Thomas,2006;Verney et al.,2007;Dam et al.,2008;Roo and Troch,2013,2015;Parnell et al.,2016).Based on the collected data,many formulas have been established to calculate the ship-induced waves and currents.However,those formulas have limitations in practice due to specific regional characteristics of data,and more calibration data are required to obtain reliable results in a specific study area.

This study aims at analyzing the hydrodynamics induced by different categories of ships in a heavy shipping traffic waterway.To achieve this goal,field measurements were carried out at a straight section of the Changzhou segment of the Grand Canal in China,and the wave and current parameters were observed during ship passages.Afterward,the shipinduced wave height and current velocity were characterized using the collected data and classical empirical formulas.Finally,factors impacting the ship-induced hydrodynamics in heavy shipping traffic waterways were analyzed,and improved and applicable formulas for the study area were developed.

2.Material and methods

2.1.Ship wakes in an inland waterway

In deep and unconfined water,the Kelvin wake wave can propagate over a long distance as the maximum transverse and divergent wave heights decrease with the distance to the sailing route(Roo,2013).Generally,the depth Froude number(Fh),expressed as follows,is used to distinguish different waves propagating from the ship hull:

whereVsis the ship speed,gis the gravitational acceleration,andhis the water depth.In shallow water,the limited ship speed leads toFhless than 1.Thus,the Kelvin wake wave effects are reduced,and the lateral depression waves propagate as highly nonlinear and asymmetric waves(Soomere,2007).This drawdown effect in an inland waterway largely depends on the ratio of the ship cross-sectional area to the waterway cross-sectional area,which is defined as

wheremis the blockage coefficient,Asis the immersed midship cross-sectional area,andAwis the waterway crosssectional area.As this ratio increases,the drawdown effect is strengthened(Houser,2010;G¨oransson et al.,2014).

To characterize the ship-induced primary and secondary wave patterns,ship types should be considered.In inland waterways,shipping traffic can be categorized into two groups(Roo,2013):displacement ships and planing ships.The first group,including cargo ships,often sails at a low speed with a large underwater volume and water displacement,resulting in a pronounced primary wave pattern.The second group,including yachts and pleasure boats,can sail at a super-critical speed(Fh≥1)with a small underwater volume,resulting in a dominant secondary wave pattern.Many empirical formulas have been developed to describe the primary and secondary waves.

For the primary wave,Kriebel and Seelig(2005)proposed a numerical model to calculate the drawdown height based on existing empirical formulas and field data.The drawdown height(sd)is defined as the vertical distance between the maximum and minimum water elevations during the drawdown phase,and it is calculated with the ship and waterway geometric parameters and a modified Froude number(F*)(Kriebel et al.,2003):

wheredis the ship's draft;C1andC2are two coefficients,withC1=0.002 6Cb-0.001 andC2=-215.8d/L+26.4,respectively;andF*=Flexp（αd/L）.Cbis a ship block coefficient,withCb=?/（LBd）;?is the water displacement;Lis the ship length;Bis the ship width;Flis the length Froude number,withFl=Vs（gL）-0.5;andαis the empirical coefficient dependent on the ship hull form,withα=2.35（1-Cb）.

For the secondary wave,many models have been developed to estimate the maximum ship-induced wave height(Hm)based on field and laboratory measurements.According to field observations and laboratory tests conducted by the Nanjing Hydraulic Research Institute in the southern segment of the Grand Canal in Jiangsu Province,China(Zhou and Chen,1996),a maximum wave height formula proposed by Blaauw et al.(1984)was chosen to calculateHmin the Grand Canal in Jiangsu Province:

whereAis a coefficient that depends on the shape of the ship hull(for loaded pushing units,A=0.8;for empty pushing units,A=0.35;and for conventional inland motor vessels,A=0.25),andsis the distance from the ship side to the calculated point.Eq.(4)indicates that the secondary wave height is mainly dependent onFhand the shape of the ship hull.

As a ship sails in a waterway,the induced primary waves appear in a depression area at the water surface around the ship hull and move against the increased water velocity.The increased velocity augments the potential to produce high bed shear stress,significant sediment entrainment,and sediment(re)suspension.Ship-induced currents are usually used to assess the hydraulic impacts of shipping traffic on the fluvial environment in inland waterways(Wolter et al.,2004;Schludermann et al.,2014)and the bed shear stress that controls the(re)suspension processes.The magnitude of return current velocity depends on the displacement,blockage coefficient,distance between the sailing route and riverbank,and sailing speed(Mazumder et al.,1993;Hu¨Sig et al.,2000).In narrow waterways,a simplified formula is used to estimate the return current velocity(Vr),which is dependent on the ship sailing speed relative to flow velocity(Vsr)and blockage coefficient(PIANC,2008):

The return current velocity can reach the maximum value for deep-draft and wide-beam ships in narrow waterways.

2.2.Study site

In this study,the Changzhou segment of the Grand Canal of China was selected as the study site.It is located in the middle part of the southern segment of the Grand Canal in Jiangsu Province of China.It is an important part of the waterway network in the Yangtze River Delta and Jiangsu Province.The studied river segment starts at Heyuanli and terminates at the Zhihu Port,with a length of 48.82 km.To meet the requirements of city development and regional flood control,the urban section of the Changzhou segment was rerouted in 2005-2008.The urban part of the segment was designed as a trapezoidal cross-section with a water-surface width of 90 m,a bottom width of 70 m,and a water depth of 3.2 m.It is one of the segments in the Grand Canal,with the heaviest shipping traffic and the highest navigation density.As shown in Fig.1,the measurement site is located in a straight section of the urban segment.In the Changzhou segment of the Grand Canal,the most common ship vessels are self-propelled barges.Due to the heavy shipping traffic in the Changzhou segment,ships often closely follow each other or cross each other's paths with little clearance,resulting in the disturbance of different wave patterns.

Fig.1.Location of urban part of Changzhou segment of Grand Canal and measurement site.

2.3.Field measurements

Field measurements were conducted under normal river flow conditions.Due to the presence of several ship locks and artificial water-level controls,flow velocities were very low(measured as 0.054 m/s)at the measurement site.During the measurements,wave variables and instantaneous current velocities caused by passing ships were recorded.Fig.2 provides a schematic overview of the equipment deployment.All the equipment was installed in a cross-sectional array at one side of the waterway.The water-level fluctuations during the ship passages were collected by the wave height measurement system(CBY-II).As shown in Fig.2,ten wave gauges were arranged in two parallel rows,with five gauges in each row along a cross-shore transect.The sampling frequency of water surface elevation was 20 Hz.Two NORTEK acoustic Doppler velocimeters(ADVs)were deployed to record the threedimensional current velocities at a height of 25 cm above the riverbed with 6-m and 40-m distances to the riverbank.The two ADVs were attached by a bottom-resting steel frame,and their sampling frequency was 8 Hz.Ship speed is another important parameter,and it was obtained by two methods.The first method estimated ship speed by dividing a fixed distance by the ship passing time.The second method directly collected the ship speed data from a nearby monitoring station.The distance between the passing ship and the riverbank was measured with a laser rangefinder,which was set up on the riverbank,perpendicular to the river transect.

Fig.2.Schematic overview of equipment deployment on crosssectional measurement transect(units:m).

2.4.Data processing

In this study,water-level fluctuations,current velocities,and the properties of 220 ships passing through the waterway were recorded.These passing ships included 205 groups of barges,three fleets,and 12 yachts.Due to the heavy shipping traffic,several ship-induced waves were often superposed.To characterize the hydrodynamics induced by single ships,the data for 27 passing barges(passages No.1-27)and 12 passing yachts(passages No.28-39)were analyzed(Table 1).Generally,water-level fluctuations collected by the wave height measurement system should be processed with the signal analysis method to clarify the relative importance of ship-and windgenerated waves(Chwang and Chen,2003;Houser,2010),or the complex ship-induced wave patterns should be separated into the primary and secondary wave patterns(Velegrakis et al.,2007;Teschke et al.,2008;Roo and Troch,2013).Different wave periods make it possible to separate the ship-induced wave patterns.The primary wave pattern generally has a longer duration(TLP≥10 s,whereTLPis the primary wave duration)in comparison with the secondary wave pattern(2 s＜TSP＜10 s,whereTSPis the secondary wave duration)(Roo and Troch,2013).A fast Fourier transform method was adopted to convert the time-domain data into frequency-domain data.Afterward,the primary wave pattern was identified with a low-pass filter with a frequency(f)less than 0.1 Hz,whereas a band-pass filter(0.1 Hz＜f＜0.5 Hz)determined the secondary wave pattern.The identification of wave patterns was conducted with MATLAB software.During ship passages,the current speeds in different directions were recorded by the two ADVs that were deployed at different water depths.Generally,flow speed time-series obtained by ADVs should be filtered to improve the accuracy of data.Fleit et al.(2016)developed an advanced filtering method based on the quality of measured signals.This method requires a correlation limit of 70%and a signal-to-noise ratio(SNR)limit of 20 dB for the qualified recorded data.Therefore,measured data with values of correlation or SNR below the corresponding limits were excluded in this study.

Table 1 Properties of single ship passages in this study.

3.Results

3.1.Blockage coefficient for a single ship

In the study area,ships sailing upstream generally have empty loads,whereas ships sailing downstream always have full loads.The actual draught of barges is dependent on their loading conditions.With constant shipping conditions,the immersed volume of a ship increases with loads.According to theChinese Navigation Standard of Inland Waterway(GB 50139-2014),the blockage coefficient should be lower than 1/6 in a restricted waterway or lower than 1/7 in a high-flow velocity waterway,soas to minimize the resistance of sailing ships.However,the measured segment was designed as an over-wide waterway with a 90-m width,which exceeds the waterway construction standard of China.Thus,the passing ships should have large blockage coefficients.Based on different cargo-carrying capacities of barges,the 27 barges were categorized into five groups with 300-t,400-t,500-t,600-t,and 800-t loading conditions,respectively.Fig.3 demonstrates the blockage coefficients of single barges analyzed in this study,which were categorized according to their loading conditions.As the ship's tonnage increases with the same loading conditions,themvalues presented an increasing trend.The values of the depth Froude number for barges and yachts ranged from 0.34 to 0.56 and from 0.29 to 0.82,respectively.It should be noted that yachts were not categorized by their loading conditions because they were regarded as planing vessels,and the blockage coefficient of the yachts was 0.009 45.

Fig.3.Blockage coefficients of single barges categorized according to their loading conditions.

3.2.Wave height induced by a single ship

As ship-induced waves propagate away from vessels,typical water-level fluctuations for a passing cargo ship at a specific position demonstrate a slight initial water-level rise(often referred to as the ship bow wave),followed by a large water-level drop.Both features are associated with the primary wave pattern,after which a group of secondary waves arrives(G¨oransson et al.,2014).Fig.4 presents the two typical waterlevel fluctuations recorded by Wave Gauge#5(WG#5)and the corresponding filtered wave patterns during the passages of SY818(No.1)and SHZTD106(No.31),respectively.As shown in Fig.4(a),the water-level fluctuations caused by passage No.1 had a significant water-level drop due to the large water displacement,thereby leading to pronounced drawdown effects.The drawdown duration and height were 22.2 s and 0.108 m,respectively.In contrast to passage No.1,the secondary wave pattern was more pronounced for passage No.31 with a large wave height of 0.484 m(Fig.4(b)),because the ship had a lower underwater volume and a higher sailing speed.

Fig.4.Recorded water-level fluctuations and their filtered wave patterns during ship passages.

Drawdown has a long extension.It can generate high velocities of water particles and produce high bed shear stress when propagating onto the shoals.This can alter the local hydrodynamic fields.In this context,the drawdown effect is often a major concern in confined waterways(G¨oransson et al.,2014).According to Eq.(3),a correlation analysis between the drawdown height and its associated parameters was conducted,and the correlation coefficient(r)was adopted to evaluate the influences of various parameters.Thervalues for the ship speed,ship's draft,and blockage coefficients were 0.651,0.229,and 0.317,respectively,indicating thatVshad a greater influence on the primary wave pattern.As shown in Fig.5,the measuredsdvalues of the 39 single passing ships and the calculated values from Eq.(3)were compared.It was found that the calculatedsdvalues were in poor agreement with the observations,with a pronounced systematic overestimation.This indicates that the empirical formula proposed by Kriebel et al.(2003)was not applicable to the case in this study.

Fig.5.Comparison between measured and calculated drawdown heights of 39 single passing ships.

The maximum ship-induced wave height is an important index for characterizing the secondary wave groups after the drawdown,which is usually estimated with the peak-to-peak method(Dam et al.,2008).Hmincreases with the depth Froude number before it reaches a threshold value(Dam et al.,2008).Fig.6 shows the relationships betweenFhandHmfor the 27 single barges and 12 single yachts.For the yachts with the same hull shape,FhandHmhad a significant correlation.However,the relationship for barges was not significant due to the various ship hull shapes.Therefore,Hmfor the 27 single barges and 12 single yachts calculated with Eq.(4)was based onFhand the coefficientA.The coefficientAreflects the characteristics of ship hull shape,and it was estimated with regression analysis using the measured data.Fig.7 compares the calculatedHmwith the observations for the 27 single barges and 12 single yachts with theAvalues of 0.581 and 0.465,respectively.This figure demonstrates that Eq.(4)was able to basically predictHmfor the barges,but the coefficientAmight not be sufficiently accurate to describe the ship hull shape for the 27 single barges.

Fig.6.Relationships between depth Froude number and maximum ship-induced wave height for 27 single barges and 12 single yachts.

Fig.7.Comparison between measured and calculated maximum ship-induced wave heights for 27 single barges and 12 single yachts.

Fig.8.Current velocity distributions in different directions during passages No.1 and No.31.

3.3.Current velocity induced by a single ship

Ships sailing along different routes at different sailing speeds alter current velocities in waterways.The flow direction at the measurement site was from west to east.Fig.8 shows the current velocity distributions when a barge and a yacht passed by.In the case of barge passage,flow in the westsouth direction was measured by ADV #1,whereas ADV #2 measured the east-south flow direction.For the yacht,ADV#1 measured the flow direction towards the east,and ADV #2 measured the flow direction towards the south.The recorded current velocities during the passages of the barge and yacht are shown in Fig.9.The current velocity had a significant increase when a ship sailed through the observed area,and the increase recorded by ADV #2 was less than that recorded by ADV#1.The maximum return current velocities measured by ADV #1 and ADV #2 reached 0.154 m/s and 0.090 m/s,respectively,during passage No.1 and reached 0.590 m/s and 0.335 m/s,respectively,during passage No.31.

Fig.9.Magnitudes of recorded current velocities during passages No.1 and No.31.

Due to the very low flow velocity with no sailing ships(measured as 0.054 m/s)and the limited fetch length of windinduced waves(Houser,2010),the recorded current velocities caused by passing ships were considered to be the return current velocities.Based on the assumptions of ship passages described in detail by Schiereck(2001),the Bernoulli equation along a streamline between the cross-sections of a waterway with and without a ship could be derived.Accordingly,the return current velocity caused by the passing ships could be expressed by the drawdown height,ship speed,and blockage coefficient(Roo,2013),which is regarded as the theoretical value.Correlation analysis between the measured return current velocity and its related parameters was performed.For ADV #1,the correlation coefficients forsd,Vs,andmwere 0.337,0.199,and 0.402,respectively.In the case of ADV #2,they were 0.414,0.297,and 0.495,respectively.Fig.10 compares the theoreticalVrfor the 27 passing barges with theVrvalues calculated by Eq.(5).This figure demonstrates that the calculatedVrwas not consistent with the theoretical values.It should be noted that Eq.(5)only considers the ship speed and blockage coefficient but neglects the limited speed for sailing ships in inland waterways.

Fig.10.Comparison of theoretical and calculated return current velocities for 27 passing barges.

3.4.Waves and currents induced by multiple ships

Interaction between ships often occurs when ships meet or overtake one another.In inland-restricted waterways,this interaction can be very strong because the ships are very close to each other,thereby mainly impacting the maneuverability or course-keeping of ships(Zou and Larsson,2013).At the measurement site,the shipping traffic is quite heavy,and the ships often follow each other or cross each other's paths.Due to the arrangement of the measurement instruments,a channel with a limited width was selected in this study.Therefore,consecutive and interlacing passages of more than one ship were observed at the study site.Compared to those induced by a single ship,the hydrodynamics induced by multiple ships were more complex due to the interaction of waves and currents.Meanwhile,the relative positions between the consecutive and interlaced ships were changed,thereby producing different distances between ships and riverbanks.

Table 2 summarizes the sailing conditions of different consecutive and interlaced ship paths.In Case 1,the distance between ships 1 and 2 was very short.Thus,the water-level drop lasted for approximately 60 s.Afterward,highfrequency secondary waves appeared.In contrast to Case 1,ships 3 and 4 in Case 2 were not in the same sailing line,with distances to the riverbank of 40 m and 45 m,respectively.The first water-level drop occurred with a duration of 40-60 s,and after 20 s,the second one appeared.As for Case 3,the recorded wave-level fluctuations caused by ships 5 and 6 had a very low magnitude due to the large distance to the riverbank.Therefore,no significant water-level drop was observed.The water-level fluctuations caused by two consecutive ships are more complex in comparison with those caused by a single ship,due to the uncertainty of ship distributions in time and space.When ships sail towards each other,they usually decelerate before their paths interlace.In cases 4 and 5,there were two ships sailing towards each other.No significant water-level drop was recorded in Case 4.By contrast,thewater-level drop lasted for 40 s in Case 5.Following the first water-level drop in Case 5,another mild water-level drop appeared.Case 6 included three ships.Ship 12 moved upstream and was closer to the riverbank where the measurement instruments were set up,and ships 11 and 13 consecutively traveled downstream.In this case,a water-level drop was observed.However,there was not a significant increase in wave height due to the low sailing speed.

Table 2Sailing conditions of different consecutive and interlaced ship paths.

Moreover,the return currents induced by multiple ships are difficult to describe.In the six different cases described above,a more significant increase in the current velocity occurred near the riverbank.As the distance between ships 1 and 2 was short,the recorded maximum current velocity caused by the two ships reached 0.320 m/s,which was higher than those of the other two cases(cases 2 and 3)with consecutive ships.Cases 2 and 3 had low wave-level fluctuations.Accordingly,the recorded current velocities had a slight increase.Due to the low sailing speed,the recorded maximum current velocities during the passage of ships with interlaced paths were not large.The recorded maximum current velocities in cases 4,5,and 6 were 0.170 m/s,0.150 m/s,and 0.190 m/s,respectively.In addition,the magnitudes of maximum current velocities induced by single ships and multiple ships were respectively nine and six times as large as those under the condition with no sailing ships.

4.Discussion

In this study,the characteristics of ship-induced hydrodynamics,including the ship-generated wave height and associated current velocities during ship passages,were investigated in the Changzhou segment of the Grand Canal,a typical inland-restricted waterway.The magnitude and behavior of the ship-induced hydrodynamics depend on the characteristics of passing ships and their sailing environment.The ship-induced hydrodynamics cause sediment(re)suspension and bank erosion processes(Parchure et al.,2007),thereby producing a large amount of pressure on the fluvial environment.

Fig.11.Relationship between sd and Vs/Vl categorized by loading conditions for 27 barges.

Eq.(3)gave poor results for the 27 barges in this study,although it includes the major relevant parameters.The primary wave pattern changed with the increased sailing speed,and could be characterized with the ratio of ship sailing speed to its limit speed(Vs/Vl).Fig.11 shows the relationship betweensdandVs/Vlcategorized by the loading conditions for the 27 barges.The induced drawdown height is expected to increase withVs/Vlfor a ship with the same tonnage and loading conditions.As shown in Fig.11,the increasing trend of drawdown height was found in most cases.When a ship approached its limit speed(Vs/Vl=1),a significant increase insdoccurred(Roo and Troch,2015).However,for all 27 barges in this study,the values ofVs/Vlwere lower than 1.The maximum drawdown height reached 0.17 m for the 800-t fullloaded ship withVs/Vl=0.93.

The ship-induced wave height calculated by Eq.(4)is largely determined byFhand the coefficient related to the ship hull shape.However,the calculatedHmdid not agree with the observations.Schoellhamer(1996)provided another way that combinesFhandmto characterizeHm.As a result,the nondimensional ship-induced wave height(Hm/h)was found to be linearly correlated toFh2.4m1.6,with a correlation coefficient of 0.992 in a shallow microtidal estuary.Rapaglia et al.(2011)also established a relationship betweenHm/hand the combined factors in the Venice Lagoon,and the best empirical relationship was found to beFh3.5m1.6with a correlation coefficient of 0.755.In this study,the 27 barges had different hull shapes and were on various geometric scales.For these barges,theFhandmvalues varied from 0.34 to 0.56 and from 0.024 to 0.108,respectively.The regression analysis in this study(Fig.12)indicates that the maximumHm/hwas linearly correlated toFh3.8m0.7with a correlation coefficient of 0.810.The maximumHm/hincreased withFhandm,andHm/hwas more sensitive toFhthan tom.This finding indicates that the ship sailing speed has significant impacts on the ship-induced wave height.This relationship can be adopted to estimate the ship-induced wave height in the Changzhou segment of the Grand Canal.

Fig.12.Relationship between maximum Hm/h and Fh3.8m0.7.

The short-term effects of the passages of single ships or multiple ships may cause sediment(re)suspension and sediment transport towards the riverbank,and the long-term effects might result in morphological changes of the waterway.In heavy shipping traffic waterways,the ship-induced waves and currents play an important role in sediment(re)suspension and riverbank erosion processes.Mobilization of sediment from the riverbed is related to bed shear stress(Verney et al.,2007),which is a function of the water density,wave friction factor,and maximum drawdown velocity(G¨oransson et al.,2014).As presented above,the barges and yachts with a higher sailing speed resulted in higher current velocities.For a single ship,the maximum current velocities in passages No.1 and No.31 reached 0.154 m/s and 0.590 m/s,respectively.The recorded maximum current velocities caused by ships with consecutive and interlaced paths were not as large as expected.The maximum current velocity caused by consecutive ships of three groups occurred in Case 1,with a value of 0.320 m/s.For ships with interlaced paths,the maximum current velocity was 0.190 m/s.However,in comparison with the flow velocity under normal flow conditions with no shipping traffic,current velocities induced by multiple ships were augmented,and were six times as high as the normal flow velocity(0.054 m/s).When the bed shear stress exceeded a critical threshold value,sediment(re)suspension and riverbank erosion can occur.

5.Conclusions

In this study,the characteristics of waves and currents induced by passing ships were clarified using the observed data from field measurements in a heavy shipping traffic waterway.In addition to the effects of single-ship passages,the impacts of multiple-ship passages were investigated as well.The main conclusions can be summarized as follows.

(1)Based on the hydrodynamic data measured during the single ship passages of 27 barges and 12 yachts,the classical model(Eq.(3))was not able to accurately estimate the drawdown height induced by a single ship.The results show that the drawdown height had an increasing trend as the ratio of ship sailing speed to its limit speed(Vs/Vl)was augmented for ships with the same tonnage and loading conditions.The maximum drawdown height reached 0.17 m for an 800-t fullloaded barge withVs/Vlequal to 0.93.

(2)Based on Eq.(4),the maximum ship-induced wave height for the 27 barges and 12 yachts was estimated,with a coefficient of ship hull shape(A)of 0.581 and 0.465,respectively.The comparison between the calculated and observedHmshows that Eq.(4)was able to basically estimateHmfor the barges.However,the adopted values for coefficientAwere not sufficiently accurate to describe the ship hull shape of the barges.Therefore,a linear relationship was established between the maximum non-dimensional ship-generated wave height and a nonlinear combination of the depth Froude number and blockage coefficient(Fh3.8m0.7),with a correlation coefficient of 0.810.The simulation results show that this relationship was able to describe the effect of the ship hull shape more accurately.

(3)Water-level fluctuations and current velocities caused by multiple ships are more complex,and they depend on the spatiotemporal distribution of ships.The magnitudes of current velocities induced by single ships and multiple ships were respectively nine and six times as large as the flow velocity with no sailing ships.These current velocities may result in sediment(re)suspension from the riverbed and riverbank erosion.This effect might also change the cross-sectional profile of inland-restricted waterways over long periods.

Declaration of competing interest

The authors declare no conflicts of interest.