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An acoustic Doppler velocimeter (ADV) for the characterisation of turbulence in concentrated fluid mud
Continental Shelf Research 20 (2000) 1551}1567
An acoustic Doppler velocimeter (ADV) for the characterisation of turbulence in concentrated #uid mud Nicolas Gratiot*, Mathieu Mory, Daniel Auche`re Laboratoire des Ecoulements Ge& ophysiques et Industriels (Lab. de l'UJF, de l'INPG et du CNRS), Domaine Universitaire, BP 53, 38041 Grenoble Ce& dex 9, France Received 12 May 1999; received in revised form 22 December 1999; accepted 5 January 2000
Abstract The paper describes a velocimeter, based on the back-scattering of ultrasonic waves by particles, designed for measuring instantaneous turbulent velocities in a concentrated #uid mud mixture. The acoustic Doppler velocimeter (ADV) needs no calibration and is therefore a potentially useful tool for measuring velocities in the laboratory or in the "eld. We investigate its reliability for measurements in concentrated cohesive sediment suspensions, where the particle size is usually unknown due to the occurrence of #occulation, and where there is considerable acoustic wave absorption. Measurements in a resonant standing wave demonstrate the ability of the apparatus to measure unsteady velocities. The data validation rate ranges between 20 and 80 Hz for a cohesive sediment concentration in the range 20}140 g l\. Experiments were performed with two di!erent natural mud mixtures. It is observed that using an ADV does not require prior determination of particle and #oc properties. It is furthermore demonstrated that the amplitude of the back-scattered signal received by the transceiver results mainly from a single re#ection on particles, whereas echoes experiencing multiple re#ections are strongly damped. The use of an ADV for measuring turbulence properties is "nally assessed for low Reynolds turbulence, which occurs in Concentrated Benthic Suspension layers. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Acoustic; Velocimeter; Fluid mud; Turbulence
* Corresponding author. Tel.: #33-47-68-25-068; fax: #33-47-68-25-001. Present address: Ecole Nationale en GeH nie des Technologies Industrielles, UniversiteH de Pau et des Pays de l'Adour, rue Jules Ferry, 64000 PAU, France. E-mail address: [email protected] (N. Gratiot). 0278-4343/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 2 7 8 - 4 3 4 3 ( 0 0 ) 0 0 0 3 7 - 6
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1. Introduction During the few last decades, investigations in estuarine and coastal areas have shown the occurrence of near-bed layers in which concentrations of up to 200 g l\ can be measured. These #uid mud layers, also called concentrated benthic suspensions (CBS), are separated by a sharp interface (lutocline) from the upper water layer where the sediment suspension is dilute (Mehta, 1989). Several studies (Odd et al., 1993) have pointed out the importance of CBS for cohesive sediment transport. However, only a few surveys provide "eld observations of the CBS layer including suspended sediment concentration and velocity measurements (Trowbridge and Kineke, 1994). The di$culty in obtaining velocity measurements within the CBS layer stems from its thickness, which usually does not exceed a few centimetres, and the high concentration (20}200 g l\). Various methods have been considered for measuring #ow velocity in natural sediment suspensions. Using a hot "lm probe led to failure resulting from particle impingement on the sensor (Fukuda and Lick, 1980). Laser Doppler anemometry does not operate in #uid mud because the incident laser beams are rapidly attenuated and the light di!used by the particles is spread when the sediment concentration exceeds a few hundred milligrams per litre (Baker and Lavelle, 1984). Micropropeller current meters are often used in "eld surveys, but they only provide an estimate of the mean current. Turbulent velocity measurements have been made using radioactive tracers (Berlamont, 1989), dyed material (Sakakiyama and Bijker, 1989), and electromagnetic current meters (Sternberg et al., 1991; de Witt and Kranenburg, 1996). The electromagnetic current meter has proved to be a useful tool in shallow water environments and in "eld deployments, but one of its limitations is due to its spatial resolution (van der Ham, 1999; Soulsby, 1980). Ultrasonic probes are an attractive technology for measuring unsteady velocities as they are non-intrusive remote sensing systems. Various systems have been developed, some of which allow the three velocity components to be measured simultaneously at a single point while others provide instantaneous measurements of velocity pro"les. Their application in assessing sediment #uxes in marine environments is di$cult because ultrasonic waves are absorbed in sediment-laden #ows. Instantaneous sediment #ux pro"les were nevertheless successfully measured in the laboratory with quartz-like particles having concentrations as high as 28 g l\ (Shen and Lemmin, 1997). In the "eld, despite the heterogeneity of the natural material, acoustic backscattering has been used to measure the mean velocity in a tidal #ow (Lhermitte, 1983) and in an estuarine environment (Thorne et al., 1998). Most systems have been used up to now in sand-like sediment-laden #ows. This article considers the case of natural cohesive sediments having high concentration values (in the range 20}160 g l\). This investigation was conducted in the course of a laboratory study of the occurrence and properties of CBS layers, for which it was desirable to measure turbulent unsteady velocities. The aim of the study presented in this paper was to examine the ability of an ADV system to measure instantaneous velocities in concentrated #uid mud. A standard ADV system was used, the principle of operation of which is based on analysis of the back-scattered phase change
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observed from pulse to pulse. Because this apparatus was built in our laboratory, the settings could be conveniently modi"ed. Several di$culties have to be considered when applying ultrasonic methods in #uid mud. First of all, acoustic waves are subject to absorption and multiple scattering. Secondly, particle sizes may change as a result of #occulation in cohesive sediment suspensions. They are usually not known precisely. An attempt was made to determine whether an ADV can operate without prior determination of #oc size and whether the quality of operation depends on the composition of the mud. Because the apparatus is not new in itself, the operating principle is only brie#y described in Section 2. The focus in Section 3 is then on the reliability of this apparatus for measurements in cohesive sediment suspensions. Unsteady velocity measurements were performed in a standing wave #ow. They are presented in Section 4. The precision of measurement, rate of data acquisition, and quality of measurement as a function of sediment concentration were determined. Measurements in turbulent #ows were "nally carried out. The statistical properties of the turbulence measurements are presented in Section 5.
2. Principle of operation of the ADV The ADV system is based on a Doppler Sonar concept described previously by Lhermitte (1983). The latter showed that such an apparatus is appropriate for measuring mean vertical pro"les of the longitudinal velocity in a tidal channel. Our application case is very di!erent as the aim here is to measure velocities in highly concentrated #uid mud, with su$cient spatial and temporal resolutions to measure turbulence. The ADV operating principle di!ers from more classical ADV systems which deduce the velocity from measurements of the Doppler frequency shift 2u v/c of the re#ected signal, u being the pulsation of the emitted pulse. Even if a long transmitter pulse is analysed, this method is not applicable for low velocities because determining the Doppler frequency using Fourier analysis is not very accurate. Analysing the back-scattered echoes in terms of changes in the time shift ¹ "2vt/c of pulse-to( pulse back-scattered signals, as done by our apparatus and described by Lhermitte (1983), provides a much better resolution of velocity. As the volume of measurement is not in"nitely small, the received signal is a combination of echoes back-scattered by a randomly distributed set of particles. The pulse-to-pulse Doppler system requires several successive echoes to remain coherent. This condition is satis"ed if the volume of measurement and the period of repetition ¹ between two successive pulses are P su$ciently small to consider that the motion is approximately of solid body type inside the measurement volume. Furthermore the velocity must be constant over a period that covers a su$cient number of successive echoes. The speci"cations of the ADV, as shown in Fig. 1, were determined with regard to the previous conditions. In order to reduce the volume of measurement, the beam is convergent, focusing the sound wave in a focal zone F where the beam cross-section X is almost constant. Its value is of the order of 1.5 mm, corresponding to the transverse distance where the wave energy is !6 dB the value of the wave energy on the axis of
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Fig. 1. Transducer speci"cations: (a) Multigate pro"ling system; (b) Shape of the emitted pulse; (c) Size of measurement volume.
the beam. Measurements are made in this section of length F "8.8 cm in front of the X beam probe. The depth of the volume of measurement is dependent on the frequency f and the number of periods n of the emitted pulse. The value is presently of the 2 order of 0.5 mm as f "5 MHz and n +3. This speci"cation gives a volume of 2 measurement of nearly 1 mm. It may be noticed that the volume of measurement is smaller than those of classical electromagnetic current meters (a few cm) usually used to measure velocity in estuaries. An option of our system, by gating the back-scattered signal in "ve successive time windows, enables the velocities to be determined at "ve distances along the beam. The minimum value for the periodicity ¹ of wave packet emissions is determined P by considering the position of measurement, because a back-scattered echo has to be received before sending the next pulse. During this study, pulse emission periods of ¹ "0.128 ms and ¹ "0.256 ms were used. The corresponding maximum distances P P of measurement from the probe are c¹ /2+10 cm and c¹ /2+20 cm. There is also P P a maximum distance of measurement from the probe on account of the ultrasonic wave absorption properties of the sediment mixture (see Section 3). The time shift increase between two successive back-scattered echoes of two wave packets emitted at a time interval ¹ is P 2v ¹ (i#1)!¹ (i)" ¹ . ( ( c P
(1)
Time shift values are digitised for successive wave packets and stored in a "le. As an example, a 29 ms record of the changes in time shift of the back-scattered echoes for 226 successive wave packets is shown in Fig. 2. It displays a saw tooth behaviour as
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Fig. 2. Typical record of changes in time shift versus time. The software validates the calculated velocity if the correlation between a minimum of n"10 data and a "tted straight line is su$cient.
the phase of the back-scattered echo is between 0 and T . While the velocity can be deduced from Eq. (1), the velocity averaged over a time interval of duration N¹ is P instead determined numerically by "tting a straight line to a minimum of n successive time shift data (N"50 and n"10 for the example in Fig. 2), in order to reduce the variability in measurements. Fitting a straight line to at least n successive time shift data requires that ¹ (i#n)!¹ (i) should be less than T . This condition "xes the ( ( upper bound of the measurement velocity range, v((¹ /n¹ ) (c/2)+12 cm s\, (2) P as derived from Eq. (1) for n"10 and T "0.128 ms. The estimated velocity is P validated as being in su$ciently good correlation, as obtained for instance for the data contained in the "rst two saw teeth in Fig. 3. The third saw tooth displays more scatter; the estimated data cannot be validated when N¹ is too large as compared to P the typical time scale of variation of the velocity. If we consider the vertical deviation e of datas to the straight line, the velocity is validated as long as the standard deviation p is lower than 0.06T (see Fig. 3). C 3. Limitations for using an ADV in concentrated 6uid mud mixtures Speci"c questions arise in relation to the use of an ADV in cohesive sediment mixtures. In the "eld, the size of cohesive sediment #ocs can change drastically within the #uid mud because of the steep velocity gradients and because of the changes in concentration. Acoustic systems have already been used in cohesive sediment suspensions (Land et al., 1997). The e$ciency of back-scattering is linked to the nature of the sediments. The intensity and propagation of an acoustic wave packet is a!ected by
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Fig. 3. Output voltage of the back-scattered echo received at time t after emission of a wave packet. d "ct/2 is the position of the back-scattering if only a single re#ection occurs. Grey line: no sediment in the Q domain 0(d (5 cm. Dark line: #uid mud mixture in the domain 0(d (5 cm; 4a) C"70 g l\, 4b) Q Q C"194 g l\.The zero-mean voltage has been o!set to improve readability.
absorption, scattering by suspended particles, or by the presence of gas bubbles. Furthermore, it can change drastically, depending on the size and shape of the particles (Richards et al., 1996). For the purpose of experimental studies with natural mud mixtures, where the #oc properties are not known, we checked whether accurate velocity measurements required prior knowledge of #oc properties. Absorption and multiple re#ections of acoustic waves are two processes that have to be considered for using ultrasonic methods within #uid mud mixtures. On the one hand, the increase in ultrasonic wave absorption with increasing mud concentration implies a reduction in the magnitude of the back-scattered signals. This process sets a bound to the maximum distance of velocity measurement but it does not appear by itself to preclude using an ADV in a concentrated #uid mud mixture. On the other
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hand, it is very important to quantify the contribution of the echoes received after multiple re#ections in the magnitude of the back-scattered signal, since the ADV operating principle assumes a single re#ection for each echo analysed. Experiments were conducted in a small tank to assess the occurrence of single or multiple re#ections and to quantify absorption. The tank contained two chambers (A and B, respectively) separated by a thin "lm of plastic. Chamber A was "lled with #uid mud mixture while chamber B contained clear water. The probe was plunged into A and emitted a single pulse in the direction of B. Back-scattered acoustic echoes were recorded versus time. Fig. 3 presents the variation versus time in the magnitude of echoes produced in #uid mud mixtures at two di!erent concentrations (70 and 194 g l\). To interpret the diagrams, d "ct/2 is used instead of time; it is the distance Q from the probe where the echo received at time t was back-scattered if a single re#ection occurred. The acoustic propagation celerity is assumed to be constant and uniform in A and B (c"1500 m s\). We will show later that this condition is validated. As the probe is acting both as emitter and receiver, the emission of acoustic wave packets considerably disturbs the piezoelectric sensor; measurements are not available for a short time after emission, which corresponds to a distance of approximately 5 mm. When the two chambers contain clear water, back-scattering is insigni"cant in the domains 5 mm(x(48 mm and x'52 mm (parts A and B of the tank, respectively), as the absence of scatterers hinders re#ection. An echo of small amplitude is, however, observed at a distance of 50 mm. This is the re#ection of the acoustic pulse on the thin plastic "lm separating the two chambers. When sediments are contained in section A, we can quantify the relative importance of multiple re#ection echoes in the amplitude of the received signal by comparing the magnitude of echoes for x'50 mm and x(50 mm (dark plots) in Fig. 3. If a signi"cant proportion of the echoes is related to multiple re#ection events, the magnitude of the signal should be comparable on both sides of x"50 mm. Actually, the magnitude of echoes for x'50 mm is as low as it is when measured in clear water (gray lines in Fig. 3), where no sediment is present. The graphs in Fig. 3 do not indicate that multiple re#ections are not occurring, but that there is considerable absorption of acoustic waves when multiple re#ections do occur. The magnitude of echoes resulting from multiple re#ections is as low as the magnitude of echoes in clear water, and the magnitude of echoes resulting from a single re#ection predominates in the back-scattered signal. For a low sediment concentration (Fig. 3(a)), the received output voltage of echoes is high and has an almost constant amplitude for x(50 mm. In that case, the absorption is small and the magnitude of the acoustic pulse is not a!ected by sediment loading. The distance for which the amplitude of the signal drops corresponds to the distance of the plastic "lm. It is exactly the distance of the echo when the two chambers contain clear water. This indicates that the acoustic propagation celerity is constant. For a higher sediment concentration (Fig. 3(b)) the magnitude of the echoes decreases rapidly in front of the probe. For the highest concentration considered (194 g l\), echoes are no longer detected at more than 35 mm from the probe. To identify the e!ects of mud properties on ADV measurements, experiments were performed using two di!erent natural muds, extracted from the Gironde estuary (France) and from the Tamar estuary (UK). The mineralogical compositions of
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N. Gratiot et al. / Continental Shelf Research 20 (2000) 1551}1567 Table 1 Mineral composition of mud in the Tamar and Gironde
D in lm Grain size distribution (% by weight)
sand (63}100 lm) mud ((63 lm)
Gironde 12
Tamar 15.0
3 97
7.8 92.2
Gironde mud and Tamar mud were determined by de Croutte et al. (1996) and Feates et al. (1999), respectively. They are given in Table 1. Gironde mud contains about 30% of quartz. As quartz is known to be a good ultrasonic re#ecting surface, the presence of a signi"cant quantity of quartz suggests there should be a good ADV response. While Gironde mud was chemically treated with potassium permanganate and passed through a 100 lm sieve, Tamar mud was neither treated nor sieved. The ADV system was used in di!erent mixtures with sediment concentrations in the range 20}160 g l\. The mud properties (in particular for Tamar mud) in the tank were representative of those occurring in the "eld. For the high concentrations considered, it is to be expected that "ne sediments and #ocs are both present in the measurement volume.
4. Unsteady velocity measurements in a concentrated 6uid-mud mixture The accuracy of measurements was determined for 10 di!erent mixtures with sediment concentrations of up to 160 g l\. Velocity measurements were carried out in a resonant standing wave within a tank of "nite length (Fig. 4). Furthermore, in this unsteady #ow, it is possible to quantify the ability of the ADV to make unsteady #ow measurements, by determining the data measurement rate. In the linear regime, a simple theory relates free surface motions to the velocity "eld in the water layer. The accuracy of the ADV was estimated by comparing velocity measurements to the theoretical estimates of velocity variations deduced from measurements of free surface motions, as no other technique was available for comparing velocity measurements among themselves. Fig. 4 shows a sketch of the experimental set-up, consisting of a small #ume of length ¸"25.0 cm and width 9.0 cm. The water depth was set to h"5.0 cm. Gravity waves were generated mechanically by oscillating a vertical plate located in the middle of the #ume with the period of oscillation of resonant standing waves
¹"2
p¸ , g tanh(ph/¸)
(3)
where g denotes the acceleration due to gravity. The plate was removed when surface waves were established and their amplitude appeared to be qualitatively constant. After approximately 10 s, secondary modes were dissipated and the resonant wave mode was then predominant. The oscillation amplitude decreased slowly due to
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Fig. 4. Resonant gravity wave facility. Free surface oscillations are measured using an ultrasonic wave gauge. The ADV is immersed in a separate chamber.
Fig. 5. Time-dependent changes in free surface displacements for a resonant standing wave: (䉭) experimental data, (*) model function given by Eq. (4).
bottom and side-wall friction. The time record of the free surface displacements measured using an ultrasonic wave gauge at a "xed location in the #ume is shown in Fig. 5. The time-dependent changes in free surface motions were in good agreement with a function of the form g(x, t)"a e\?R cos(px/¸) cos(ut) (4) (u"2p/¹), which is superimposed on the data. This indicates that the wave energy is entirely contained in the resonant standing wave mode. Exponential decay accounts for viscous dissipation. While the wave frequency was determined theoretically, the initial amplitude a and the wave decay rate a were estimated from the free surface displacement record for each condition investigated. The transducer was placed in a section of the tank separated by a Plexiglas wall from the part of the tank where the gravity wave #ow was generated (see Fig. 4). The
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section where the transducer was located was "lled with tap water, to ensure the propagation of acoustic waves through the Plexiglas wall between the probe and the position of measurement. Any #ow disturbance due to the ADV probe was therefore eliminated. Just before generating the gravity wave, the #uid mud mixture was fully mixed by hand. Obviously, the sediment settles slowly when mechanical mixing is stopped. The interface separating #uid mud and clear water was clearly visible in our experiments. The slow downward displacement of the interface provided an estimate of the settling velocity w . The latter quantity was found to be less than 1 mm s\ A (generally 0.3 mm s\). We therefore estimate that the concentration at the position of velocity measurement did not drop below the mean concentration before t'h /w +40s (h is the water depth above the measurement volume; the position of N A N measurement was located 1 cm above the bottom). The velocity was measured during the time interval 20 s(t(30 s after the gravity wave was generated. The wave height remained of su$cient magnitude during this time interval. The variation in mud concentration with time, if it occurred, must have increased as a consequence of settling. The averaged mud concentration was measured from bottle samples taken from the initial #uid mud mixture. For the free surface displacements given by Eq. (4) the variation in the horizontal velocity component predicted by the linear potential theory is a gk cosh k(z#h) u(x, z, t)"! e\?R sin(kx) sin(ut), u cosh kh
(5)
where h is the mean depth of the water layer inside the tank, z is the vertical co-ordinate (here at the position of measurement) and z"!h is on the bottom. Solution (5) veri"es u(0, t)"u(¸, t)"0 on the boundaries of the tank. Free surface and velocity measurements were not actually performed simultaneously in order to avoid any disturbance of the #ow by the wave gauges immersed in the tank. Considering Eq. (5), a function of the form u (x, z, t)"u e\?R sin(ut#h), (6) was superimposed on the experimental data after adjusting the initial amplitude u and phase h, while the wave height decay rate a was determined from the wave gauge records. Fig. 6 shows the time records of the velocity measured for three sediment concentrations (43, 50 and 100 g l\) of Gironde or Tamar mud. The best agreement between the experimental data and Eq. (6) is observed for the lowest concentrations, i.e. C"43 and C"50 g l\. For the higher concentration C"100 g l\, a few signi"cant errors arise when the velocity is maximum, but wave motion and wave decay are satisfactorily accounted for in the experimental data records. We believe that the variations at maximum velocity are measurement errors rather than turbulence production, because they are mainly observed for the higher concentration. Turbulence resulting from internal wave breaking is less likely to occur for the higher concentration. Each record displays short time intervals containing no data; these correspond to periods during which the software did not validate the velocity measurements. The data
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Fig. 6. Horizontal velocity measurement in a resonant standing wave #ow. Gironde mud is used for the plots in (a) and (b). Tamar mud is used for the plot in (c). (a) C"100 g l\, (b) C"50 g l\, (c) C"43 g l\. (䉫, ;, *): ADV measurements, (*) model.
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Fig. 7. Isoline of the rate of validation of velocity measurements (data per second) versus suspended sediment concentration C and versus distance of measurement from the sensor d . Q
records display slight asymmetries, which are not understood. The wave model used for comparison is linear and does not include secondary-mode oscillations. Although the observed asymmetry is not signi"cant, it is surprising that the asymmetry in Figs. 6(a) and (b) is opposite in direction to that in (c). No di!erence was observed in the accuracy of the measurements and in the rate of measurement between the Gironde and Tamar mud mixtures. Fig. 7 quanti"es the variations in measurement validation rate. The isoline plots were interpolated from a set of 60 cases for di!erent distances of measurement d from the probe and for di!erent concentrations of Tamar #uid mud Q mixtures. The maximum validation data rate is 78.1 Hz as ¹ "0.256 ms (N"50). As P expected, the rate of data validation increases for decreasing concentration and decreasing distance of measurement from the probe. It is therefore established that the ADV system can measure unsteady velocities in #uid mud mixtures with concentrations of up to 140 g l\ with a data validation rate better than 20 data s\.
5. Measurements of turbulent velocity in a concentrated 6uid mud mixture The determination of turbulent velocities in #uid mud layers is a necessary step for assessing the vertical transfer of sediments between the muddy bed and the dilute suspension in estuarine environments. The investigations described in Section 4 demonstrated the ability of an ADV to make accurate measurements of unsteady velocities in concentrated #uid mud mixtures. The rate of validation, in the range 20}75 data s\, is not high, but it may be su$cient for turbulence measurements in concentrated Benthic suspensions in the "eld, where the velocity is quite low. A limitation on using an ADV for turbulence measurements in concentrated #uid mud
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mixtures is the size of the measurement volume. For our system, this is typically 0.5 mm in the direction of propagation of ultrasonic waves and 1.5 mm in the perpendicular direction (see Section 2). The ADV operates on the principle that solid-body motion is achieved inside the measurement volume. The size of the measurement volume must therefore be smaller than the smallest scale of turbulence. In order to investigate the ability of the ADV to measure turbulence properties, turbulence velocity variations were recorded in a simple sediment mixing experiment and some of the statistical properties of the turbulence were determined. The sediment was mixed in a square tank, 0.3 m wide and 0.2 m deep, by a rapidly rotating propeller. The propeller was set to a su$ciently rapid speed to maintain all the sediment in suspension. Velocity measurements were made in #uid mud mixtures of various concentrations (20, 50, 80 and 100 g l\). Before the velocity was measured, the water and sediment were mixed for about 10 min and visual observations were made through the transparent bottom of the tank to ensure that no sediment remained deposited there. Fig. 8. presents a time history record measured by the ADV, covering a period of 128 s. Each velocity datum was determined from the changes in phase shift averaged over a set of N"50 successive wave packets. For this experiment, the period of wave packet emission was decreased to T "0.128 ms, allowing a rate of measurement of P 156.2 Hz if all velocity data were validated. Actually, about 30% of the data were rejected and the record contains about 14,000 validated velocity data. For further
Fig. 8. Velocity record measured by ADV in a mixing tank containing #uid mud of concentration C"50 g l\.
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Fig. 9. Distribution of a velocity record (plotted in Fig. 8) measured in a mixing tank containing #uid mud. A Gaussian distribution (*) is superimposed.
analysis, the missing values in the record were replaced with the last preceding validated velocity datum. The propeller generated both a mean rotating #ow and turbulence. For this record, the mean velocity in the direction of propagation of ultrasonic waves is ;M "1.25 cm s\ and the rms turbulent velocity is u "2.15 cm s\. The histogram of velocity variations for the record considered in Fig. 8. is shown in Fig. 9. The distribution is Gaussian, as shown by the Gaussian curve superimposed on the data. This is a "rst indication that the statistical properties of the turbulence are captured in the velocity records measured by the ADV. As random white noise also displays a Gaussian distribution of events, a time frequency spectral analysis of velocity records was made in order to estimate the proportion of the signal corresponding to turbulent #ow and that associated with noise. The power spectrum of turbulent #uctuations is presented in Fig. 10. Energy density decays as frequency increases. The threshold level reached at frequencies higher than 70 Hz indicates the level of noise contained in the record. In hydrodynamic turbulent #ows, the energy density decays for increasing frequency, a phenomenon that is associated with a transfer of energy from low frequencies (large eddies) to high frequencies (small eddies). In Fig. 10, the energy spectrum decay versus frequency follows approximately a power law of the form E( f )+f \ , which is the decay law predicted by Kolmogorov's theory for a homogeneous isotropic turbulent #ow. Although these observations do not prove that the turbulence measurements are quantitatively accurate, they provide consistent indications that ADV measurements capture the hydrodynamic properties of turbulence and, in particular, that aliasing due to an insu$cient rate of data validation is unlikely to occur.
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Fig. 10. Power spectrum of turbulent #ow velocity measured by the ADV in a mixing tank containing #uid mud. Suspended sediment concentration is C"100 g l\.
The integral length scale l of turbulence was not measured, and, therefore, only a range of variations of the Taylor microscale j "l(u l/l)\ can be inferred. The 2 Taylor microscale varies in the range 0.7}7 mm for a rms turbulence velocity in the range 1}10 cm s\ and an integral length scale in the range 1}10 cm (l" 5 10\ cm s\ for this estimate). The Taylor scale of turbulence is seen to be larger or, in some cases, may be of the order of the size of the measurement volume. The measurement volume of the ADV appears to be su$ciently small for the turbulence measurements carried out during the present investigation.
6. Conclusions The present paper does not intend to present a new acoustic back-scatter system, but rather to investigate whether such a system can measure unsteady and turbulent velocities in concentrated #uid mud mixtures, and to determine the appropriate settings of the apparatus. For the purpose of making measurements in the laboratory, but also potentially in the "eld, di!erent natural muds were employed. An ADV does not require calibration and is a non-intrusive measurement device. It is therefore an attractive technology for measuring velocities in the laboratory and in the "eld. Speci"c questions arise concerning the use of an ADV in the presence of cohesive sediments. Acoustic wave absorption is enhanced in concentrated mud suspensions, but it does not hinder the reception of back-scattered echoes, even for concentrations as high as 100 g l\, and when the distance of measurement from the probe is as far as 50 mm. On the other hand, the considerable absorption of acoustic waves in their
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interactions with particles appears to eliminate echoes resulting from multiple scattering in the back-scattered signal received by the transducer. A simple experiment was carried out, that shows that echoes resulting from multiple scattering make a negligible contribution to the signal received by the transducer in the time window considered for signal analysis. The accuracy of velocity measurements by an ADV has been demonstrated, without prior determination of particle and #oc sizes, in an unsteady laminar #ow, for sediment concentrations in the range 20}160 g l\. Data rate validations were found to be in the range 20}75 for a rate of measurement of 78.1 Hz. While this is not a high rate of data acquisition, it is su$cient for many applications, especially in concentrated Benthic suspensions where velocities are not high. Turbulence measurements were carried out in a mixing tank containing a #uid mud mixture. By setting the period of pulse repetition to ¹ "0.128 ms we improved the rate of data acquisition P up to 110 data s\. The ADV measurement volume (0.5}1.5 mm) was smaller than the Taylor microscale of turbulence and the usual statistical behaviour of hydrodynamic turbulence was recovered by the ADV measurements made in the mixing tank. ADV appears to be an appropriate tool for measuring low Reynolds turbulence. Although this was not tested in the course of this study, using an ADV system for measuring velocities in #uid mud mixtures in the "eld is not a priori subject to any particular restriction, as far as the principle of operation is concerned. The principle of operation of our system is a standard one. Commercial pulse to pulse ADV systems should work as well, and sometimes may provide measurements of several velocity components. Using ADV is especially attractive because the measurement volume is small and it does not require calibration. For the present settings of our ADV system, the maximum velocity that can be measured is 12 cm s\. It is certainly desirable to increase the range of measurements in order to use our ADV system in the "eld. Eq. (2) indicates the signi"cant settings of the apparatus. The period of pulse emission ¹ cannot be reduced much as it "xes the location of measurement, which has to be P su$ciently far from the probe. To increase the velocity range it would be necessary to increase the acoustic frequency f or to decrease the number n of echoes analysed for determining a velocity datum. The settings of the apparatus were f "5 MHz and n"10 in our study. The velocity range can presumably be increased, but checks should be made to determine how far the accuracy of measurements is reduced if the number n of data used for velocity determination is decreased. The ability of ADV for measurements in the "eld has to be evaluated.
Acknowledgements This work was carried out as part of the COSINUS Program, which is funded by the European Commission (contract MAS3-CT97-0082). SogreH ah IngeH nierie is thanked for providing natural mud samples from the Gironde estuary. K. Dyer and A. Manning are thanked for providing natural mud samples from the Tamar estuary. K. Dyer is "nally thanked for having drawn our attention to the paper by Lhermitte (1983).
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References Baker, E.T., Lavelle, W.J., 1984. The e!ect of particle size on the light attenuation coe$cient of natural suspensions. Journal of Geophysical Research 89 (C5), 8197}8203. Berlamont, J., 1989. Pumping #uid mud } theoretical and experimental considerations. In: Mehta, A.J., Hayter, E.J. (Eds.), High Concentration Cohesive Sediment Transport. Journal of Coastal Research (Special issue No. 5), 195}205. de Croutte, E., Gallissaires, J.M., Hamm, L., 1996. Flume measurements of mud processes over a #at bottom under steady and unsteady currents. SogreH ah IngeH nierie Report No. R3, December. de Wit, P., Kranenburg, C., 1996. On the e!ects of a lique"ed mud bed on wave and #ow characteristics. Journal of Hydraulic Research 34 (1), 3}18. Feates, N.G., Hall, J.R., Mitchener, H.J., Roberts, W., 1999. COSINUS "eld experiment, Tamar Estuary, measurement of properties of suspended sediment #ocs and bed properties. Report No. TR 82, HR Wallingford, March. Fukuda, K., Lick, W., 1980. The entrainment of cohesive sediments in freshwater. Journal of Geophysical Research 85 (C5), 2813}2824. Land, J.M., Kirby, R., Massey, J.B., 1997. Developments in the combined use of acoustic doppler current pro"lers and pro"ling siltmeters for suspended solids monitoring. In: Burt, N., Parker, R., Watts, J. (Eds.), Cohesive Sediments. Wiley, New York, pp. 187}196. Lhermitte, R., 1983. Doppler sonar observation of tidal #ow. Journal of Geophysical Research 88 (C1), 725}742. Mehta, A.J., 1989. On estuarine cohesive sediment suspension behavior. Journal of Geophysical Research 94 (C10), 14 303}14 314. Odd, N.V.M., Bentley, M.A., Waters, C.B., 1993. Observations and analysis of the movement of #uid mud in an estuary. In: Mehta, A.J. (Ed.), Nearshore and Estuarine Cohesive Sediment Transport, Coastal and Estuarine Studies, Vol. 42. AGU, Washington, DC, pp. 430}446. Richards, S.D., Heathershaw, A.D., Thorne, P.D., 1996. The e!ect of suspended particulate matter on sound attenuation in seawater. Journal of the Acoustical Society of America 100 (3), 1447}1450. Sakakiyama, T., Bijker, E.W., 1989. Mass transport velocity in mud layer due to progressive waves. Journal of Waterway, Port, Coastal and Ocean Engineering 115 (5), 614}633. Shen, C., Lemmin, U., 1997. A two-dimensional acoustic sediment #ux pro"ler. Measurement Science Technology 8, 880}884. Soulsby, R.L., 1980. Selecting record length and digitization rate for near bed turbulence measurements. Journal of Physical Oceanography 10, 208}219. Sternberg, R.W., Kineke, G.C., Johnson, R., 1991. An instrument system for pro"ling suspended sediment, #uid, and #ow conditions in shallow marine environments. Continental Shelf Research 11 (2), 109}122. Thorne, P.D., Hardcastle, P.J., Dolby, J.W., 1998. Investigation into the application of cross-correlation analysis on acoustic backscattered signals from suspended sediments to measure nearbed current pro"les. Continental Shelf Research 18, 695}714. Trowbridge, J.H., Kineke, G.C., 1994. Structure and dynamics of #uid muds on the Amazon continental shelf. Journal of Geophysical Research 99 (C1), 865}874. van der Ham, R., 1999, Turbulent exchange of "ne sediment in tidal #ow. Ph.D. Thesis, TUDelft.
An acoustic Doppler velocimeter (ADV) for the characterisation of turbulence in concentrated #uid mud Nicolas Gratiot*, Mathieu Mory, Daniel Auche`re Laboratoire des Ecoulements Ge& ophysiques et Industriels (Lab. de l'UJF, de l'INPG et du CNRS), Domaine Universitaire, BP 53, 38041 Grenoble Ce& dex 9, France Received 12 May 1999; received in revised form 22 December 1999; accepted 5 January 2000
Abstract The paper describes a velocimeter, based on the back-scattering of ultrasonic waves by particles, designed for measuring instantaneous turbulent velocities in a concentrated #uid mud mixture. The acoustic Doppler velocimeter (ADV) needs no calibration and is therefore a potentially useful tool for measuring velocities in the laboratory or in the "eld. We investigate its reliability for measurements in concentrated cohesive sediment suspensions, where the particle size is usually unknown due to the occurrence of #occulation, and where there is considerable acoustic wave absorption. Measurements in a resonant standing wave demonstrate the ability of the apparatus to measure unsteady velocities. The data validation rate ranges between 20 and 80 Hz for a cohesive sediment concentration in the range 20}140 g l\. Experiments were performed with two di!erent natural mud mixtures. It is observed that using an ADV does not require prior determination of particle and #oc properties. It is furthermore demonstrated that the amplitude of the back-scattered signal received by the transceiver results mainly from a single re#ection on particles, whereas echoes experiencing multiple re#ections are strongly damped. The use of an ADV for measuring turbulence properties is "nally assessed for low Reynolds turbulence, which occurs in Concentrated Benthic Suspension layers. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Acoustic; Velocimeter; Fluid mud; Turbulence
* Corresponding author. Tel.: #33-47-68-25-068; fax: #33-47-68-25-001. Present address: Ecole Nationale en GeH nie des Technologies Industrielles, UniversiteH de Pau et des Pays de l'Adour, rue Jules Ferry, 64000 PAU, France. E-mail address: [email protected] (N. Gratiot). 0278-4343/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 2 7 8 - 4 3 4 3 ( 0 0 ) 0 0 0 3 7 - 6
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1. Introduction During the few last decades, investigations in estuarine and coastal areas have shown the occurrence of near-bed layers in which concentrations of up to 200 g l\ can be measured. These #uid mud layers, also called concentrated benthic suspensions (CBS), are separated by a sharp interface (lutocline) from the upper water layer where the sediment suspension is dilute (Mehta, 1989). Several studies (Odd et al., 1993) have pointed out the importance of CBS for cohesive sediment transport. However, only a few surveys provide "eld observations of the CBS layer including suspended sediment concentration and velocity measurements (Trowbridge and Kineke, 1994). The di$culty in obtaining velocity measurements within the CBS layer stems from its thickness, which usually does not exceed a few centimetres, and the high concentration (20}200 g l\). Various methods have been considered for measuring #ow velocity in natural sediment suspensions. Using a hot "lm probe led to failure resulting from particle impingement on the sensor (Fukuda and Lick, 1980). Laser Doppler anemometry does not operate in #uid mud because the incident laser beams are rapidly attenuated and the light di!used by the particles is spread when the sediment concentration exceeds a few hundred milligrams per litre (Baker and Lavelle, 1984). Micropropeller current meters are often used in "eld surveys, but they only provide an estimate of the mean current. Turbulent velocity measurements have been made using radioactive tracers (Berlamont, 1989), dyed material (Sakakiyama and Bijker, 1989), and electromagnetic current meters (Sternberg et al., 1991; de Witt and Kranenburg, 1996). The electromagnetic current meter has proved to be a useful tool in shallow water environments and in "eld deployments, but one of its limitations is due to its spatial resolution (van der Ham, 1999; Soulsby, 1980). Ultrasonic probes are an attractive technology for measuring unsteady velocities as they are non-intrusive remote sensing systems. Various systems have been developed, some of which allow the three velocity components to be measured simultaneously at a single point while others provide instantaneous measurements of velocity pro"les. Their application in assessing sediment #uxes in marine environments is di$cult because ultrasonic waves are absorbed in sediment-laden #ows. Instantaneous sediment #ux pro"les were nevertheless successfully measured in the laboratory with quartz-like particles having concentrations as high as 28 g l\ (Shen and Lemmin, 1997). In the "eld, despite the heterogeneity of the natural material, acoustic backscattering has been used to measure the mean velocity in a tidal #ow (Lhermitte, 1983) and in an estuarine environment (Thorne et al., 1998). Most systems have been used up to now in sand-like sediment-laden #ows. This article considers the case of natural cohesive sediments having high concentration values (in the range 20}160 g l\). This investigation was conducted in the course of a laboratory study of the occurrence and properties of CBS layers, for which it was desirable to measure turbulent unsteady velocities. The aim of the study presented in this paper was to examine the ability of an ADV system to measure instantaneous velocities in concentrated #uid mud. A standard ADV system was used, the principle of operation of which is based on analysis of the back-scattered phase change
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observed from pulse to pulse. Because this apparatus was built in our laboratory, the settings could be conveniently modi"ed. Several di$culties have to be considered when applying ultrasonic methods in #uid mud. First of all, acoustic waves are subject to absorption and multiple scattering. Secondly, particle sizes may change as a result of #occulation in cohesive sediment suspensions. They are usually not known precisely. An attempt was made to determine whether an ADV can operate without prior determination of #oc size and whether the quality of operation depends on the composition of the mud. Because the apparatus is not new in itself, the operating principle is only brie#y described in Section 2. The focus in Section 3 is then on the reliability of this apparatus for measurements in cohesive sediment suspensions. Unsteady velocity measurements were performed in a standing wave #ow. They are presented in Section 4. The precision of measurement, rate of data acquisition, and quality of measurement as a function of sediment concentration were determined. Measurements in turbulent #ows were "nally carried out. The statistical properties of the turbulence measurements are presented in Section 5.
2. Principle of operation of the ADV The ADV system is based on a Doppler Sonar concept described previously by Lhermitte (1983). The latter showed that such an apparatus is appropriate for measuring mean vertical pro"les of the longitudinal velocity in a tidal channel. Our application case is very di!erent as the aim here is to measure velocities in highly concentrated #uid mud, with su$cient spatial and temporal resolutions to measure turbulence. The ADV operating principle di!ers from more classical ADV systems which deduce the velocity from measurements of the Doppler frequency shift 2u v/c of the re#ected signal, u being the pulsation of the emitted pulse. Even if a long transmitter pulse is analysed, this method is not applicable for low velocities because determining the Doppler frequency using Fourier analysis is not very accurate. Analysing the back-scattered echoes in terms of changes in the time shift ¹ "2vt/c of pulse-to( pulse back-scattered signals, as done by our apparatus and described by Lhermitte (1983), provides a much better resolution of velocity. As the volume of measurement is not in"nitely small, the received signal is a combination of echoes back-scattered by a randomly distributed set of particles. The pulse-to-pulse Doppler system requires several successive echoes to remain coherent. This condition is satis"ed if the volume of measurement and the period of repetition ¹ between two successive pulses are P su$ciently small to consider that the motion is approximately of solid body type inside the measurement volume. Furthermore the velocity must be constant over a period that covers a su$cient number of successive echoes. The speci"cations of the ADV, as shown in Fig. 1, were determined with regard to the previous conditions. In order to reduce the volume of measurement, the beam is convergent, focusing the sound wave in a focal zone F where the beam cross-section X is almost constant. Its value is of the order of 1.5 mm, corresponding to the transverse distance where the wave energy is !6 dB the value of the wave energy on the axis of
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Fig. 1. Transducer speci"cations: (a) Multigate pro"ling system; (b) Shape of the emitted pulse; (c) Size of measurement volume.
the beam. Measurements are made in this section of length F "8.8 cm in front of the X beam probe. The depth of the volume of measurement is dependent on the frequency f and the number of periods n of the emitted pulse. The value is presently of the 2 order of 0.5 mm as f "5 MHz and n +3. This speci"cation gives a volume of 2 measurement of nearly 1 mm. It may be noticed that the volume of measurement is smaller than those of classical electromagnetic current meters (a few cm) usually used to measure velocity in estuaries. An option of our system, by gating the back-scattered signal in "ve successive time windows, enables the velocities to be determined at "ve distances along the beam. The minimum value for the periodicity ¹ of wave packet emissions is determined P by considering the position of measurement, because a back-scattered echo has to be received before sending the next pulse. During this study, pulse emission periods of ¹ "0.128 ms and ¹ "0.256 ms were used. The corresponding maximum distances P P of measurement from the probe are c¹ /2+10 cm and c¹ /2+20 cm. There is also P P a maximum distance of measurement from the probe on account of the ultrasonic wave absorption properties of the sediment mixture (see Section 3). The time shift increase between two successive back-scattered echoes of two wave packets emitted at a time interval ¹ is P 2v ¹ (i#1)!¹ (i)" ¹ . ( ( c P
(1)
Time shift values are digitised for successive wave packets and stored in a "le. As an example, a 29 ms record of the changes in time shift of the back-scattered echoes for 226 successive wave packets is shown in Fig. 2. It displays a saw tooth behaviour as
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Fig. 2. Typical record of changes in time shift versus time. The software validates the calculated velocity if the correlation between a minimum of n"10 data and a "tted straight line is su$cient.
the phase of the back-scattered echo is between 0 and T . While the velocity can be deduced from Eq. (1), the velocity averaged over a time interval of duration N¹ is P instead determined numerically by "tting a straight line to a minimum of n successive time shift data (N"50 and n"10 for the example in Fig. 2), in order to reduce the variability in measurements. Fitting a straight line to at least n successive time shift data requires that ¹ (i#n)!¹ (i) should be less than T . This condition "xes the ( ( upper bound of the measurement velocity range, v((¹ /n¹ ) (c/2)+12 cm s\, (2) P as derived from Eq. (1) for n"10 and T "0.128 ms. The estimated velocity is P validated as being in su$ciently good correlation, as obtained for instance for the data contained in the "rst two saw teeth in Fig. 3. The third saw tooth displays more scatter; the estimated data cannot be validated when N¹ is too large as compared to P the typical time scale of variation of the velocity. If we consider the vertical deviation e of datas to the straight line, the velocity is validated as long as the standard deviation p is lower than 0.06T (see Fig. 3). C 3. Limitations for using an ADV in concentrated 6uid mud mixtures Speci"c questions arise in relation to the use of an ADV in cohesive sediment mixtures. In the "eld, the size of cohesive sediment #ocs can change drastically within the #uid mud because of the steep velocity gradients and because of the changes in concentration. Acoustic systems have already been used in cohesive sediment suspensions (Land et al., 1997). The e$ciency of back-scattering is linked to the nature of the sediments. The intensity and propagation of an acoustic wave packet is a!ected by
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Fig. 3. Output voltage of the back-scattered echo received at time t after emission of a wave packet. d "ct/2 is the position of the back-scattering if only a single re#ection occurs. Grey line: no sediment in the Q domain 0(d (5 cm. Dark line: #uid mud mixture in the domain 0(d (5 cm; 4a) C"70 g l\, 4b) Q Q C"194 g l\.The zero-mean voltage has been o!set to improve readability.
absorption, scattering by suspended particles, or by the presence of gas bubbles. Furthermore, it can change drastically, depending on the size and shape of the particles (Richards et al., 1996). For the purpose of experimental studies with natural mud mixtures, where the #oc properties are not known, we checked whether accurate velocity measurements required prior knowledge of #oc properties. Absorption and multiple re#ections of acoustic waves are two processes that have to be considered for using ultrasonic methods within #uid mud mixtures. On the one hand, the increase in ultrasonic wave absorption with increasing mud concentration implies a reduction in the magnitude of the back-scattered signals. This process sets a bound to the maximum distance of velocity measurement but it does not appear by itself to preclude using an ADV in a concentrated #uid mud mixture. On the other
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hand, it is very important to quantify the contribution of the echoes received after multiple re#ections in the magnitude of the back-scattered signal, since the ADV operating principle assumes a single re#ection for each echo analysed. Experiments were conducted in a small tank to assess the occurrence of single or multiple re#ections and to quantify absorption. The tank contained two chambers (A and B, respectively) separated by a thin "lm of plastic. Chamber A was "lled with #uid mud mixture while chamber B contained clear water. The probe was plunged into A and emitted a single pulse in the direction of B. Back-scattered acoustic echoes were recorded versus time. Fig. 3 presents the variation versus time in the magnitude of echoes produced in #uid mud mixtures at two di!erent concentrations (70 and 194 g l\). To interpret the diagrams, d "ct/2 is used instead of time; it is the distance Q from the probe where the echo received at time t was back-scattered if a single re#ection occurred. The acoustic propagation celerity is assumed to be constant and uniform in A and B (c"1500 m s\). We will show later that this condition is validated. As the probe is acting both as emitter and receiver, the emission of acoustic wave packets considerably disturbs the piezoelectric sensor; measurements are not available for a short time after emission, which corresponds to a distance of approximately 5 mm. When the two chambers contain clear water, back-scattering is insigni"cant in the domains 5 mm(x(48 mm and x'52 mm (parts A and B of the tank, respectively), as the absence of scatterers hinders re#ection. An echo of small amplitude is, however, observed at a distance of 50 mm. This is the re#ection of the acoustic pulse on the thin plastic "lm separating the two chambers. When sediments are contained in section A, we can quantify the relative importance of multiple re#ection echoes in the amplitude of the received signal by comparing the magnitude of echoes for x'50 mm and x(50 mm (dark plots) in Fig. 3. If a signi"cant proportion of the echoes is related to multiple re#ection events, the magnitude of the signal should be comparable on both sides of x"50 mm. Actually, the magnitude of echoes for x'50 mm is as low as it is when measured in clear water (gray lines in Fig. 3), where no sediment is present. The graphs in Fig. 3 do not indicate that multiple re#ections are not occurring, but that there is considerable absorption of acoustic waves when multiple re#ections do occur. The magnitude of echoes resulting from multiple re#ections is as low as the magnitude of echoes in clear water, and the magnitude of echoes resulting from a single re#ection predominates in the back-scattered signal. For a low sediment concentration (Fig. 3(a)), the received output voltage of echoes is high and has an almost constant amplitude for x(50 mm. In that case, the absorption is small and the magnitude of the acoustic pulse is not a!ected by sediment loading. The distance for which the amplitude of the signal drops corresponds to the distance of the plastic "lm. It is exactly the distance of the echo when the two chambers contain clear water. This indicates that the acoustic propagation celerity is constant. For a higher sediment concentration (Fig. 3(b)) the magnitude of the echoes decreases rapidly in front of the probe. For the highest concentration considered (194 g l\), echoes are no longer detected at more than 35 mm from the probe. To identify the e!ects of mud properties on ADV measurements, experiments were performed using two di!erent natural muds, extracted from the Gironde estuary (France) and from the Tamar estuary (UK). The mineralogical compositions of
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D in lm Grain size distribution (% by weight)
sand (63}100 lm) mud ((63 lm)
Gironde 12
Tamar 15.0
3 97
7.8 92.2
Gironde mud and Tamar mud were determined by de Croutte et al. (1996) and Feates et al. (1999), respectively. They are given in Table 1. Gironde mud contains about 30% of quartz. As quartz is known to be a good ultrasonic re#ecting surface, the presence of a signi"cant quantity of quartz suggests there should be a good ADV response. While Gironde mud was chemically treated with potassium permanganate and passed through a 100 lm sieve, Tamar mud was neither treated nor sieved. The ADV system was used in di!erent mixtures with sediment concentrations in the range 20}160 g l\. The mud properties (in particular for Tamar mud) in the tank were representative of those occurring in the "eld. For the high concentrations considered, it is to be expected that "ne sediments and #ocs are both present in the measurement volume.
4. Unsteady velocity measurements in a concentrated 6uid-mud mixture The accuracy of measurements was determined for 10 di!erent mixtures with sediment concentrations of up to 160 g l\. Velocity measurements were carried out in a resonant standing wave within a tank of "nite length (Fig. 4). Furthermore, in this unsteady #ow, it is possible to quantify the ability of the ADV to make unsteady #ow measurements, by determining the data measurement rate. In the linear regime, a simple theory relates free surface motions to the velocity "eld in the water layer. The accuracy of the ADV was estimated by comparing velocity measurements to the theoretical estimates of velocity variations deduced from measurements of free surface motions, as no other technique was available for comparing velocity measurements among themselves. Fig. 4 shows a sketch of the experimental set-up, consisting of a small #ume of length ¸"25.0 cm and width 9.0 cm. The water depth was set to h"5.0 cm. Gravity waves were generated mechanically by oscillating a vertical plate located in the middle of the #ume with the period of oscillation of resonant standing waves
¹"2
p¸ , g tanh(ph/¸)
(3)
where g denotes the acceleration due to gravity. The plate was removed when surface waves were established and their amplitude appeared to be qualitatively constant. After approximately 10 s, secondary modes were dissipated and the resonant wave mode was then predominant. The oscillation amplitude decreased slowly due to
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Fig. 4. Resonant gravity wave facility. Free surface oscillations are measured using an ultrasonic wave gauge. The ADV is immersed in a separate chamber.
Fig. 5. Time-dependent changes in free surface displacements for a resonant standing wave: (䉭) experimental data, (*) model function given by Eq. (4).
bottom and side-wall friction. The time record of the free surface displacements measured using an ultrasonic wave gauge at a "xed location in the #ume is shown in Fig. 5. The time-dependent changes in free surface motions were in good agreement with a function of the form g(x, t)"a e\?R cos(px/¸) cos(ut) (4) (u"2p/¹), which is superimposed on the data. This indicates that the wave energy is entirely contained in the resonant standing wave mode. Exponential decay accounts for viscous dissipation. While the wave frequency was determined theoretically, the initial amplitude a and the wave decay rate a were estimated from the free surface displacement record for each condition investigated. The transducer was placed in a section of the tank separated by a Plexiglas wall from the part of the tank where the gravity wave #ow was generated (see Fig. 4). The
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section where the transducer was located was "lled with tap water, to ensure the propagation of acoustic waves through the Plexiglas wall between the probe and the position of measurement. Any #ow disturbance due to the ADV probe was therefore eliminated. Just before generating the gravity wave, the #uid mud mixture was fully mixed by hand. Obviously, the sediment settles slowly when mechanical mixing is stopped. The interface separating #uid mud and clear water was clearly visible in our experiments. The slow downward displacement of the interface provided an estimate of the settling velocity w . The latter quantity was found to be less than 1 mm s\ A (generally 0.3 mm s\). We therefore estimate that the concentration at the position of velocity measurement did not drop below the mean concentration before t'h /w +40s (h is the water depth above the measurement volume; the position of N A N measurement was located 1 cm above the bottom). The velocity was measured during the time interval 20 s(t(30 s after the gravity wave was generated. The wave height remained of su$cient magnitude during this time interval. The variation in mud concentration with time, if it occurred, must have increased as a consequence of settling. The averaged mud concentration was measured from bottle samples taken from the initial #uid mud mixture. For the free surface displacements given by Eq. (4) the variation in the horizontal velocity component predicted by the linear potential theory is a gk cosh k(z#h) u(x, z, t)"! e\?R sin(kx) sin(ut), u cosh kh
(5)
where h is the mean depth of the water layer inside the tank, z is the vertical co-ordinate (here at the position of measurement) and z"!h is on the bottom. Solution (5) veri"es u(0, t)"u(¸, t)"0 on the boundaries of the tank. Free surface and velocity measurements were not actually performed simultaneously in order to avoid any disturbance of the #ow by the wave gauges immersed in the tank. Considering Eq. (5), a function of the form u (x, z, t)"u e\?R sin(ut#h), (6) was superimposed on the experimental data after adjusting the initial amplitude u and phase h, while the wave height decay rate a was determined from the wave gauge records. Fig. 6 shows the time records of the velocity measured for three sediment concentrations (43, 50 and 100 g l\) of Gironde or Tamar mud. The best agreement between the experimental data and Eq. (6) is observed for the lowest concentrations, i.e. C"43 and C"50 g l\. For the higher concentration C"100 g l\, a few signi"cant errors arise when the velocity is maximum, but wave motion and wave decay are satisfactorily accounted for in the experimental data records. We believe that the variations at maximum velocity are measurement errors rather than turbulence production, because they are mainly observed for the higher concentration. Turbulence resulting from internal wave breaking is less likely to occur for the higher concentration. Each record displays short time intervals containing no data; these correspond to periods during which the software did not validate the velocity measurements. The data
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Fig. 6. Horizontal velocity measurement in a resonant standing wave #ow. Gironde mud is used for the plots in (a) and (b). Tamar mud is used for the plot in (c). (a) C"100 g l\, (b) C"50 g l\, (c) C"43 g l\. (䉫, ;, *): ADV measurements, (*) model.
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Fig. 7. Isoline of the rate of validation of velocity measurements (data per second) versus suspended sediment concentration C and versus distance of measurement from the sensor d . Q
records display slight asymmetries, which are not understood. The wave model used for comparison is linear and does not include secondary-mode oscillations. Although the observed asymmetry is not signi"cant, it is surprising that the asymmetry in Figs. 6(a) and (b) is opposite in direction to that in (c). No di!erence was observed in the accuracy of the measurements and in the rate of measurement between the Gironde and Tamar mud mixtures. Fig. 7 quanti"es the variations in measurement validation rate. The isoline plots were interpolated from a set of 60 cases for di!erent distances of measurement d from the probe and for di!erent concentrations of Tamar #uid mud Q mixtures. The maximum validation data rate is 78.1 Hz as ¹ "0.256 ms (N"50). As P expected, the rate of data validation increases for decreasing concentration and decreasing distance of measurement from the probe. It is therefore established that the ADV system can measure unsteady velocities in #uid mud mixtures with concentrations of up to 140 g l\ with a data validation rate better than 20 data s\.
5. Measurements of turbulent velocity in a concentrated 6uid mud mixture The determination of turbulent velocities in #uid mud layers is a necessary step for assessing the vertical transfer of sediments between the muddy bed and the dilute suspension in estuarine environments. The investigations described in Section 4 demonstrated the ability of an ADV to make accurate measurements of unsteady velocities in concentrated #uid mud mixtures. The rate of validation, in the range 20}75 data s\, is not high, but it may be su$cient for turbulence measurements in concentrated Benthic suspensions in the "eld, where the velocity is quite low. A limitation on using an ADV for turbulence measurements in concentrated #uid mud
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mixtures is the size of the measurement volume. For our system, this is typically 0.5 mm in the direction of propagation of ultrasonic waves and 1.5 mm in the perpendicular direction (see Section 2). The ADV operates on the principle that solid-body motion is achieved inside the measurement volume. The size of the measurement volume must therefore be smaller than the smallest scale of turbulence. In order to investigate the ability of the ADV to measure turbulence properties, turbulence velocity variations were recorded in a simple sediment mixing experiment and some of the statistical properties of the turbulence were determined. The sediment was mixed in a square tank, 0.3 m wide and 0.2 m deep, by a rapidly rotating propeller. The propeller was set to a su$ciently rapid speed to maintain all the sediment in suspension. Velocity measurements were made in #uid mud mixtures of various concentrations (20, 50, 80 and 100 g l\). Before the velocity was measured, the water and sediment were mixed for about 10 min and visual observations were made through the transparent bottom of the tank to ensure that no sediment remained deposited there. Fig. 8. presents a time history record measured by the ADV, covering a period of 128 s. Each velocity datum was determined from the changes in phase shift averaged over a set of N"50 successive wave packets. For this experiment, the period of wave packet emission was decreased to T "0.128 ms, allowing a rate of measurement of P 156.2 Hz if all velocity data were validated. Actually, about 30% of the data were rejected and the record contains about 14,000 validated velocity data. For further
Fig. 8. Velocity record measured by ADV in a mixing tank containing #uid mud of concentration C"50 g l\.
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Fig. 9. Distribution of a velocity record (plotted in Fig. 8) measured in a mixing tank containing #uid mud. A Gaussian distribution (*) is superimposed.
analysis, the missing values in the record were replaced with the last preceding validated velocity datum. The propeller generated both a mean rotating #ow and turbulence. For this record, the mean velocity in the direction of propagation of ultrasonic waves is ;M "1.25 cm s\ and the rms turbulent velocity is u "2.15 cm s\. The histogram of velocity variations for the record considered in Fig. 8. is shown in Fig. 9. The distribution is Gaussian, as shown by the Gaussian curve superimposed on the data. This is a "rst indication that the statistical properties of the turbulence are captured in the velocity records measured by the ADV. As random white noise also displays a Gaussian distribution of events, a time frequency spectral analysis of velocity records was made in order to estimate the proportion of the signal corresponding to turbulent #ow and that associated with noise. The power spectrum of turbulent #uctuations is presented in Fig. 10. Energy density decays as frequency increases. The threshold level reached at frequencies higher than 70 Hz indicates the level of noise contained in the record. In hydrodynamic turbulent #ows, the energy density decays for increasing frequency, a phenomenon that is associated with a transfer of energy from low frequencies (large eddies) to high frequencies (small eddies). In Fig. 10, the energy spectrum decay versus frequency follows approximately a power law of the form E( f )+f \ , which is the decay law predicted by Kolmogorov's theory for a homogeneous isotropic turbulent #ow. Although these observations do not prove that the turbulence measurements are quantitatively accurate, they provide consistent indications that ADV measurements capture the hydrodynamic properties of turbulence and, in particular, that aliasing due to an insu$cient rate of data validation is unlikely to occur.
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Fig. 10. Power spectrum of turbulent #ow velocity measured by the ADV in a mixing tank containing #uid mud. Suspended sediment concentration is C"100 g l\.
The integral length scale l of turbulence was not measured, and, therefore, only a range of variations of the Taylor microscale j "l(u l/l)\ can be inferred. The 2 Taylor microscale varies in the range 0.7}7 mm for a rms turbulence velocity in the range 1}10 cm s\ and an integral length scale in the range 1}10 cm (l" 5 10\ cm s\ for this estimate). The Taylor scale of turbulence is seen to be larger or, in some cases, may be of the order of the size of the measurement volume. The measurement volume of the ADV appears to be su$ciently small for the turbulence measurements carried out during the present investigation.
6. Conclusions The present paper does not intend to present a new acoustic back-scatter system, but rather to investigate whether such a system can measure unsteady and turbulent velocities in concentrated #uid mud mixtures, and to determine the appropriate settings of the apparatus. For the purpose of making measurements in the laboratory, but also potentially in the "eld, di!erent natural muds were employed. An ADV does not require calibration and is a non-intrusive measurement device. It is therefore an attractive technology for measuring velocities in the laboratory and in the "eld. Speci"c questions arise concerning the use of an ADV in the presence of cohesive sediments. Acoustic wave absorption is enhanced in concentrated mud suspensions, but it does not hinder the reception of back-scattered echoes, even for concentrations as high as 100 g l\, and when the distance of measurement from the probe is as far as 50 mm. On the other hand, the considerable absorption of acoustic waves in their
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interactions with particles appears to eliminate echoes resulting from multiple scattering in the back-scattered signal received by the transducer. A simple experiment was carried out, that shows that echoes resulting from multiple scattering make a negligible contribution to the signal received by the transducer in the time window considered for signal analysis. The accuracy of velocity measurements by an ADV has been demonstrated, without prior determination of particle and #oc sizes, in an unsteady laminar #ow, for sediment concentrations in the range 20}160 g l\. Data rate validations were found to be in the range 20}75 for a rate of measurement of 78.1 Hz. While this is not a high rate of data acquisition, it is su$cient for many applications, especially in concentrated Benthic suspensions where velocities are not high. Turbulence measurements were carried out in a mixing tank containing a #uid mud mixture. By setting the period of pulse repetition to ¹ "0.128 ms we improved the rate of data acquisition P up to 110 data s\. The ADV measurement volume (0.5}1.5 mm) was smaller than the Taylor microscale of turbulence and the usual statistical behaviour of hydrodynamic turbulence was recovered by the ADV measurements made in the mixing tank. ADV appears to be an appropriate tool for measuring low Reynolds turbulence. Although this was not tested in the course of this study, using an ADV system for measuring velocities in #uid mud mixtures in the "eld is not a priori subject to any particular restriction, as far as the principle of operation is concerned. The principle of operation of our system is a standard one. Commercial pulse to pulse ADV systems should work as well, and sometimes may provide measurements of several velocity components. Using ADV is especially attractive because the measurement volume is small and it does not require calibration. For the present settings of our ADV system, the maximum velocity that can be measured is 12 cm s\. It is certainly desirable to increase the range of measurements in order to use our ADV system in the "eld. Eq. (2) indicates the signi"cant settings of the apparatus. The period of pulse emission ¹ cannot be reduced much as it "xes the location of measurement, which has to be P su$ciently far from the probe. To increase the velocity range it would be necessary to increase the acoustic frequency f or to decrease the number n of echoes analysed for determining a velocity datum. The settings of the apparatus were f "5 MHz and n"10 in our study. The velocity range can presumably be increased, but checks should be made to determine how far the accuracy of measurements is reduced if the number n of data used for velocity determination is decreased. The ability of ADV for measurements in the "eld has to be evaluated.
Acknowledgements This work was carried out as part of the COSINUS Program, which is funded by the European Commission (contract MAS3-CT97-0082). SogreH ah IngeH nierie is thanked for providing natural mud samples from the Gironde estuary. K. Dyer and A. Manning are thanked for providing natural mud samples from the Tamar estuary. K. Dyer is "nally thanked for having drawn our attention to the paper by Lhermitte (1983).
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References Baker, E.T., Lavelle, W.J., 1984. The e!ect of particle size on the light attenuation coe$cient of natural suspensions. Journal of Geophysical Research 89 (C5), 8197}8203. Berlamont, J., 1989. Pumping #uid mud } theoretical and experimental considerations. In: Mehta, A.J., Hayter, E.J. (Eds.), High Concentration Cohesive Sediment Transport. Journal of Coastal Research (Special issue No. 5), 195}205. de Croutte, E., Gallissaires, J.M., Hamm, L., 1996. Flume measurements of mud processes over a #at bottom under steady and unsteady currents. SogreH ah IngeH nierie Report No. R3, December. de Wit, P., Kranenburg, C., 1996. On the e!ects of a lique"ed mud bed on wave and #ow characteristics. Journal of Hydraulic Research 34 (1), 3}18. Feates, N.G., Hall, J.R., Mitchener, H.J., Roberts, W., 1999. COSINUS "eld experiment, Tamar Estuary, measurement of properties of suspended sediment #ocs and bed properties. Report No. TR 82, HR Wallingford, March. Fukuda, K., Lick, W., 1980. The entrainment of cohesive sediments in freshwater. Journal of Geophysical Research 85 (C5), 2813}2824. Land, J.M., Kirby, R., Massey, J.B., 1997. Developments in the combined use of acoustic doppler current pro"lers and pro"ling siltmeters for suspended solids monitoring. In: Burt, N., Parker, R., Watts, J. (Eds.), Cohesive Sediments. Wiley, New York, pp. 187}196. Lhermitte, R., 1983. Doppler sonar observation of tidal #ow. Journal of Geophysical Research 88 (C1), 725}742. Mehta, A.J., 1989. On estuarine cohesive sediment suspension behavior. Journal of Geophysical Research 94 (C10), 14 303}14 314. Odd, N.V.M., Bentley, M.A., Waters, C.B., 1993. Observations and analysis of the movement of #uid mud in an estuary. In: Mehta, A.J. (Ed.), Nearshore and Estuarine Cohesive Sediment Transport, Coastal and Estuarine Studies, Vol. 42. AGU, Washington, DC, pp. 430}446. Richards, S.D., Heathershaw, A.D., Thorne, P.D., 1996. The e!ect of suspended particulate matter on sound attenuation in seawater. Journal of the Acoustical Society of America 100 (3), 1447}1450. Sakakiyama, T., Bijker, E.W., 1989. Mass transport velocity in mud layer due to progressive waves. Journal of Waterway, Port, Coastal and Ocean Engineering 115 (5), 614}633. Shen, C., Lemmin, U., 1997. A two-dimensional acoustic sediment #ux pro"ler. Measurement Science Technology 8, 880}884. Soulsby, R.L., 1980. Selecting record length and digitization rate for near bed turbulence measurements. Journal of Physical Oceanography 10, 208}219. Sternberg, R.W., Kineke, G.C., Johnson, R., 1991. An instrument system for pro"ling suspended sediment, #uid, and #ow conditions in shallow marine environments. Continental Shelf Research 11 (2), 109}122. Thorne, P.D., Hardcastle, P.J., Dolby, J.W., 1998. Investigation into the application of cross-correlation analysis on acoustic backscattered signals from suspended sediments to measure nearbed current pro"les. Continental Shelf Research 18, 695}714. Trowbridge, J.H., Kineke, G.C., 1994. Structure and dynamics of #uid muds on the Amazon continental shelf. Journal of Geophysical Research 99 (C1), 865}874. van der Ham, R., 1999, Turbulent exchange of "ne sediment in tidal #ow. Ph.D. Thesis, TUDelft.