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Vietnam Journal of Mechanics, NCS'.f of Vietnam Vol. 22, 2000, No 3 (149 - 166) EXPERIMENTAL RESULTS ON SAND TRANSPORT UNDER WAVES IN LARGE-SCALE WAVE FLUME Huu CHUNG Institute of Mechanics, NCST of Vietnam DANG ABSTRACT . The paper presents some results of a study based on the experiment carried · out in Delta Flume of Delft Hydraulics. The analysis of time-series of sand concentration and velocity are implemented for regular and irregular waves with different conditions on wave and grain size. From measured·concentrations and velocities the suspended transport components are calculated and some interesting information is obtained. At the same time some formulae for calculations of suspended sediment transport have been proposed and verified. A general evaluation on the total sediment transport rate over the water depth has been given on the basis of incorporating measurement, extrapolation and bedload prediction. 1. Introduction Sediment transport is a very complicated natural process and so far it is not fully understood yet. Therefore every different attempt to achieve knowledge on this phenomenon in some measure is always encouraged. The current-related transport component involves th~ convective sand transport carried by the mean currents such as tide, wind and wave-driven currents in the presence of short (high-frequency) surface waves acting as stirring agents. The wave-related sand transport is herein defined as the transport of sand particles by the oscillating fluid motion due to the high-frequency waves. The current-related transport over rippled beds has been studied in considerable detail (Van Rijn et al., 1993; Van Rijn and Havinga, 1995), but the wave-related transport is less well known. The wave-related transport over a flat bed has been studied in more detail based on numerous experiments in wave tunnels (see for· overview: Ribberink, 1998). Within this purpose the paper presents some results on the analysis of time series of concentration and 2DH velocity components under regular and irregular waves that were measured from the Delta Flume at the laboratory by the Dutch researchers of Delft Hydraulics in 1998. In this way, the different components of sediment transport are evaluated. At the same time on the basis of the analysis some remarks and methods for calculation of wave-related suspended sand transport have been proposed. By using extrapolation and bedload transport a general 149 evaluation on the relative importance of transport components in t hree layers has been given. A new acoustical instrument, Acoustical San d Transport Meter · (A,STM) was used for measuring both the velocity and the suspended sediment concentration simultaneously at five elevations above the bed. The tests in the Delta Flume were carried out as a part of t he European Large Installation Plan (LIP) with modern equipment. Therefore , in order to supply the detail of the experiment as well as the physical sense of measured data, their description and setting up are also presented. 2. Experimental design 2.1. Description of instruments The experiments were carried out in the Delta Flume of Delft Hydraulics.This is a large-scale flume that has a total length of 233 meters, a dep th of 7 meters and a width of 5 meters. On the bed a sand layer of 0.5 m was placed over a length of about 40m (see Fig.1). Regular and irregular waves were g enerate~ by a piston activated wave board on one side of the flume. The .instruments for measurement were mounted in a tripod, which was placed on the sand bed at location x = 125 m. For each test the instruments were operated for about 15 m inutes t o sample over a representative wave record . The following instruments were used in the fl.ti.me : • The two-dimensional five fold ASTM to measure instantaneous concentration and velocity components at five different positions in the vertical direction. • Two electromagnetic fl.ow meters (EMF) arrayed vertically and mounted to the flume wall for velocity. • Two optical back scatter sensors (OBS) for measurement of instantaneous concentration at two positions. • A pump sampling system (10 intake nozzles) also located along the delta flume wall (intake nozzles at about 0.3 m from the wall) . • Ripple profiler to measure bed form : The Sand Ripple Profi ler is ~ 2 MHz scanning sonar system comprising a pencil beam transducer on a rotating head. Thus for each head position a backscatter profile can be obtained, allowing a 2D image through the water to be built up . Data is t ransferred to a PC via serial link following capture using an on board 8 bit ADC. Besides , other instruments were also used in this experiment. During the first test series this sand bed had a D 50 of 0.33 mm, and during the second test series 150 . ·: . . .. the Dso was 0.16 mm. The ASTM frame was positioned on this sand bed. The water depth was 4.5 m in all experiments. The scheme for the positions of the measurement instrument is illustrated in Fig. 2. According to the manufacturer (Delft Hydraulics) the error amount for measured velocity value is 10% and 30% for the measured concentrations. VVave generator Beach slope of stones .5 m Sand bed 0.5m 1.23 m 121 m 125m 100 m 140 m Fig. 1. Sketch of experimental set-up EMF1 ASTM1 1.075m ASTM2 0.475m 0851 EMF2 ASTM3 ASTM4 0.225m 0852 A5TM5 0.125m 0.075m Fig. 2. Positions of instrwnents for measurement in the vertical direction 2.2. Experimental programme The experimental conditions presented in Table 1 include different sand sizes, wave types, wave heights and the orientation of ASTM and they are divided into five group. The orientation of the ASTM was changed during the test program in order to see the influence of measurement positions on the results . In this case the sensors are not located in the plane of orbital motion, so that the measurement volume is least disturbed by the sensors. However, in a field situation the direction of the Waves cannot be controlled, which may lead to an unfavourable orientation of the ASTM with respect to the plane of orbital motion. The measurement levels above the bed for most tests are presented in Fig. 2. There are some special cases (D4, D5, El, E2) for which the measurement levels were 0.175, 0.225, 0.325, 0.575 and l.175m. 151 Table 1. Measurement program Data Set Measurement No. I Number of test Grain size dso (mm) Wave height Hs (m) Orientation of ASTM (degree) 8 0.33 1.00 8 0.33 l.2S 7 0.16 1.00 9 0.16 1.2S 3 0.16 1.SO -90 -120 -90 -120 -120 -90 -120 -90 -90 Al, AlB, A2A, Dl, D2, D3, D4, DS BlA, B2A, BlB, El, E2, E3, E4, ES Gl, G2, G3, G4, Jl, J2, J3 Hl, H2, H3 , H4, HS, Kl, K2, K3, K4 Ml, M2, M4 II III IV v 3. Experimental results 3.1. Distribution of suspended sand concentrations and velocities In order to analyse the time series data from the experiment as well as from the field a software, namely TISERAT (Time Series Analysis Tool) has been developed with FORTRAN 90. Using this tool the instantaneous signal can be represented as the sum of time-averaged value and fluctuations for high and low frequencies as follows · c(z, t) = c +Cs+ C1_, u(z, t) = u +Us+ U1_ , v(z, t) = v +Vs+ V 1_ (3 .1) in which c(z., t), u(z, t), v(z, t) are instantaneous concentration and velocity components, respectively, the tilde sign "~" denotes a fluctuation, the subscript s denotes high frequency fluctuation and f. for low frequencies and the overbar "-" denotes time-averaged values. The u-component is aligned along the long axis of the flume, positive in the onshore direction, and the v-component is aligned across the flume. Typical vertical distributions of time-averaged concentration, cross-shore and longshore velocities are presented in Fig. 3 for tests B2A and K2. It can be seen from these figures that the vertical distributions of time-averaged concentration show a well known behaviour, i.e. the concentration of sediment is very high near the bed and decreases monotonically towards the surface. 152 ~ ~ l..... Te&t B2A 1.2 • ~ 02 "' \ .... •\ ~ o.~ 1 I\ 0.8 ~ 0.6 I:) 0.4 Test K2 "="' ~ 1.2 -.........__ 00 \ ~ 0.6 ~ 0.4 ~ 0.2 11) 0 - 0.5 N 1.5 -.- ................. o lime-averaged concenfr.#Jon 0.2 0.4 0.6 Time- aver3getl concenlrclfion (kg/m.1) (kg/m$} Test ~2A ·0.04 · 0.02 Test K2 0 Ci-ass- shore ~I L 0.02 I 1.2 1 • I 0 .8 0.6 0.4 0.2 0 -0.02 velocif!f (m/.s) , 0 Test82A Test.K2 1-----1~---+-..,<~-+--1 1-----11-----4~--+- 0.8 I---+-~'-+---+-~ 0.6 / .r 1----+----,,c.c.....-+-- -+ - - 0,4 !-----+~--+----+-- -0.01 -0.005 • 0 -0 .03 ·0.02 1.2. 1 / 0.8 0. 6 ~ 0.2 0 0.4 1 0.2 1-----=+----+---+-~0 -0.015 0.02 Cross - shore velucil!I {mls) ~---------1 . 2 -0.02 0.8 --0.01 0 Long-shore veloc/ly- (m/s) Long - shqre velocif!J ( m/s) Fig. 3. Distribution of time-averaged concentrations and velocities The range of time-averaged concentration at the highest elevation is from 0.01 g/l (test BIB) to 0 .09g/l (test M4) and the range at the lowest (number 5) is 0.32 g/l (test H4) - 1.38 g/l (test E4). Although sometimes in the field the sedi:rnent concentration may be higher than this, especially during a storm, the ranges of concentration that were created in the Delta. flume are large enough to simulate most real cases. The maximum cross-shore time-averaged velocities in onshore direction are 0.02 m/s at position number 3 (near the bed) for the test Kl .and -0.04 m/s for 153 offshore at the position 2 of test H2. At the same time this value is also the maximum undertow velocity. The results of analysis of all the tests show that at the positions 1 and 2 the undertow currents always happen . . This phenomenon is due to the influence of vertical circulation in the flume with onshore fluid flux between wave crest and wave trough and offshore return of fluid in the lower part of the water column. For long shore current the distribution of velocity has the same direction at the defined time point. The tests G and J give the best time-averaged values in comparison with the other cases in standard deviation. This is easy to understand, because in the tests G and J the sand particle with D 50 = 0.16m, wave height is 1 m and especially the ripple height is small enough (r = 0.03 m ) and the ripple length is quite long (.X = 0. 72 m), yielding less variations in velocities and concentrations . Moreover, in some cases the duration of measurement is not long enough, such as 2 minutes for test BlB, 3 minutes for D4, 6 minutes for J3, 7 minutes for E2, H4 and 8 minutes for K3, M4. 3.2. Suspended sand transport components 3.2.1. Vertical distribution Based on the definitions (3.1) the net suspended sediment transport rates in cross-shore and longshore directions are as follows -;:;:;--;:;;;-- QY ,..._, ,.._, -;:;;:;-;:;;:;- ,.._,,..,, = vc + V C + VsCe + VeCs + ViPe 8 (3 .2) 8 in which the first terms of (3 .2) are transport components relating to mean current, and the other terms relate to waves. This paper concent rates on the cross-shore processes, so the· local longshore movement was not an alysed in· more detail. The calculations of vertical distributions of sand transport components for all the tests are illustrated in Fig. 4. It shows that with five data sets the components of interaction between high and low frequencies are very small and can be ignored, while the components due to purely high and low frequencies are relatively large, so the omission of these components may cause a large error in the prediction computation. At the elevations 1 (the highest above the bed) and 2 the undertow current always exists, so the time-averaged transport components corresponding to these · elevations are always offshore directed. From the above results it is easily seen that the suspended sediment transport mainly occurs in the near-bed layer with a thickness of about 0.3 to O.S-m, which is roughly equivalent to 10 to 20 t imes the ripple height. 154 Dataset I Data set II 1.4 1.2 .. 1 0.8 0.6 ........._ Off L ..., ~ .. 0 0.01 0.02 - .,,. ·.· 0 -0.01 -0.00!5 0 0.005 Suspended sed. 0.01 0.015 ·0.02 -0.01 Dataset IV Data set Ill 1.4 ? ....... .---1.4 ~-------1 . 2------+----~ ~ 1.2 '-..:. ~ ~ ~ ~ ~ ~ cu llJ (:> ~ ~ 11) "' 0.03 Svspended sed. transporf (k~/nfl/s) fransporf(lrg/m 2/s) t-.i ·0.01 0.01 0 0 .02 -0.02 0.03 Suspended sed. frcmsport{!cg/ m2/s) 0 0.02 0.04 Suspended sed. tr.ansport (lrg/m2js) Dataset V ---·1 .4 -.----...,.----~ -+- Net sus.sed.transport -a- Time-averaged transport __._ High frequency transport -0.02 0 0.02 0.04 Svspended sed. fransporf{kg/m2/s) ~ Low frequency transport Fig. 4. Distribution of cross-shore sediment transport components for combined tests 3.2.2 . Depth-integrated transport rates as a function of wave height The relationship between sediment transport rates integrated over the depth . ' 155 and wave height is presented in Fig. 5 based on the calculations for 35 tests of irregular waves. It shows that the time-averaged suspended sediment transport rates are in the offshore direction, while the suspended sediment transport rates - for high frequency go together in the same direction of wave propagation in the onshore. These remarks are similar with those of previous studies, such as Vincent and Green, 1990; Osborne and Greenwood, 1992; Osborne and Vincent, 1996; Grasmeijer and Van Rijn, 1999, Van Rijn et al., 1993 and Van Rijn, 1998. At the same time the results also show that the significant wave height plays an important role in transport rates, which increase according to the growth of wave height. The influence of particle diameter is also seen clearly. Under the action of waves, coarser sand particles are brought further toward the land and the mean current brings the finer sand in the opposite direction. Note that the standard deviations due to averaging tests of the same conditions on wave and grain size are quite · large because of the local influence of ripples. ~ Measur. Time-ave.trans.,d =0.33mm -A- Measur. High fre.trans.d50 =0.33mm Measur.Time-ave.'trans.,d 50 =0.16mm Measur. High fre.trans.d50 =0.16mm Extra.High fre.trans.ci =0.33mm 50 Extra.High fre.trans.d50=0.16mm 50 --a-: ---*--'QI-- -- e- -- .. ./"~ ~ • / :) ' 7-/ .V onshore :-----_ ~ 0 0.l -- 0.4 0.6 • 0.8 1 T rt-- 1.2 Signiriant w.:11/e height ( m) Fig. 5. Relationship between the significant wave height and depth-integrated transport 156 " _J H I~ offshore -4 __,~ ~ 1.4 1.6 4. Prediction of wave related suspended sand transport (high frequency) 4.1. Houwman's method Houwman and Ruessink (1996) found that the high-frequency suspended sediment transport plays an important role in the net transport ~nd 't,annot be neglected. In their approach the mean sediment concentration at a certain height above the bed is thought to be the time-averaged value of two sediment concentration peaks per wave cycle, one during the onshore directed wave motion and the other during the offshore directed wave motion. AccorA)ng to the velo~ity moments approach the shape of the sediment concentration peaks can be assumed to be equal to the shape of lu(t) 13 . If it is also assumed that each half wave cycle can be described with the linear wave theory with different amplitudes but with equal duration it follows T/2 - c(z) 3 3 )2 = k ( Uon + Uof f T f 3 sin wt dt (4 .1) 0 In equation (4.1), the left term is the time-averaged sediment concentration at height z above the bed, U0 n and U 0 ff refer to the onshore and offshore peak , orbital velocity, T and w are the wave period -and angular frequency respectively and k is a constant. The oscillatory suspended sediment t ransport at a certain height z ·above the bed can be related to the fourth order moment u · lu3 1 . The wave-averaged oscillatory sediment transport rate Q(z) through a layer dz is then described by: U4 - U4 .· · ~ff dz Q(z) = k'c(z) ~n uon T k' = ~ /2 (4 .2) + uof f J sin4wt dt ( T 0 0 /2 J 3 )-l ~ 0.441786 sin wt (4.3) Figure 6 shows the comparison of this expression with measurements; indicating that the Houwman formuia tends to overestimate the measured values. However, by replacing the coefficient k' in Houwman's formula the result becomes much better as will be seen .below. 157 Dataset I ~ ~ ~ ~ ~ "' Dataset II -1.20 II >-1.00 i-0.80 i-0.60 ,_0.40 I ~0.20 "€' \::, .. ~ .... . . o.oo -0.01 0.00 ~ ~ 0.01 0.02 ~ . ~0 . 60 ~ '-OAO I L. 'II ~ ~ "I 0.04 0.03 -1.00 I '-'0.80 ~ ---.., -1.20 ~.__ 0.20 . '-0.00 -O.Q1 WO' Ve- re/1fed SllS. fransporf (kgjm2/S) ,.....,.,, 0.00 0.01 0.03 0.02 --- 0.04 Wave - re/3fetl sus. fransport(lrgjm2js) Data ~t Ill '€' ~ ~ ~ ~ ~150 1.00 -~ t - 1.20 ~1.00'. ..q ~o .so ~ '-0.60 ~ ~ 'I) 1-.j '- ~ ~ 0.50 ~ Data set IV . ~ 0.01 0.02 I L ~--:- I'--.- "-0.20 -0.00 -0 .01 0 .00 ·~ 0.00 0 .00 -0.01 ~ 0.40 - 1'j 0.03 f!Vove-re/afed svs. transport (lrg/m2/s) 0.01 Wave-re/afed 0.02 0.03 0.04 sus. fr.ansporf ( lcg/m2j.s) Data setV ......- Measured ~ ~ -<:> ~ ~ I'll 1.20 J 1.00 0.80 0.60 0.40 .A o.zo __._ Houwman's I ......_ Polinomial I j_, "' 0.00 -0.01 0.00 -*- k'=2 tM0.01 0.02 0 .03 ~k'=3 0.04 _.__ k'=4 Wave -related sus. frcmsporf(kg/m2/s) Fig. 6. -+- k'=5 Comparison between measured and predicted wave-related suspended transports 4.2. The proposed methods · 4.2.1. Polynomial of degree 3 Based on the tests that were carried out from the Delta flume, the polynomials of degree 3 by the least-squared method were derived. This method is found to 158