Acoustic absorption in seas and rivers by suspended particulate matter

TG Leighton (Principal Investigator), NR Brown, SD Richards

Solid particles in suspension can be found in many marine, river and coastal regions. They first rise from some bed (sea, river, or estuary) as the result of turbulence, tidal action, waves etc. and then tends to settle back towards it under gravity (Figure 1). In still water there would therefore be a concentration gradient of such matter, it becoming less concentrated as one moves away from the sea bed, a tendency which is reduced by turbulence etc. The importance of such 'sediment in transport' has been recognized for thousands of years: its deposition during the annual flooding of the Nile determined the fertility of the land, a dominant feature in the religion, culture and politics of Egypt from 4500 BC until the last century. Today the presence of suspended sediment reduces the ability of active sonar systems to detect mines and torpedoes. Conversely, the acoustic scattering and absorption it produces can be used to monitor this environmentally important feature.

Figure 1. True-color satellite images (from the Moderate Resolution Imaging Spectroradiometer MODIS carried by NASA) of sediment carried by rivers into the sea. (a) As a result of by the confluence of the Tigris and Euphrates Rivers (at center), the sediment-laden waters of the Persian Gulf (November 1, 2001) appear light brown where they enter the northern end of the Persian Gulf and then gradually dissipate into turquoise swirls as they drift southward (Image courtesy Jacques Descloitres, MODIS Land Rapid Response Team at NASA GSFC). (b) The Mississippi River carries roughly 550 million metric tonnes of sediment into the Gulf of Mexico each year. Here (March 5, 2001 at 10:55 AM local time) the murky brown water of the Mississippi mixes with the dark blue water of the Gulf two days after a rainstorm. The river brings enough sediment from its 3,250,000 square km (1,250,000 square mi) basin to extend the coast of Louisiana 91 m (300 ft) each year. (Image courtesy Liam Gumley, Space Science and Engineering Center, University of Wisconsin-Madison and the MODIS science team). Source: NASA, reproduced with the permission of the Lunar and Planetary Institute. (c) Scanning electron microscope image of a typical fine-grained marine sediment (see also Richards, S.D., Leighton, T.G. and *Brown, N.R. Visco-inertial absorption in dilute suspensions of irregular particles, Proc. R. Soc. Lond. A, 459(2038), 2003, 2153-2167).

Because typical particle diameters 2a are in the range 0.1-100 microns, such suspensions scatter most strongly at VHF. Up to ka~1 (which for c=1500 m s^-1 occurs at frequency f of 2.4 MHz for a=100 microns; and at higher frequencies for the smaller particles), Rayleigh scattering occurs: The scattered power increases as both particle size and frequency increase (eventually taking an oscillatory form in the geometric regime where ka>~1). The surface plotted in figure 2 is still undergoing this Rayleigh-regime growth as it passes through the rear right corner (i.e. large-radius, high-frequency limits) of the figure. Within this Rayleigh regime, at a fixed frequency the cross-sectional 'target' area πa²  'seen' by the ultrasonic beam increases quadratically with radius.

However figure 2 plots, not just the scatter, but the attenuation. There is a second contributing factor to this, namely the acoustic absorption. This occurs because the density of the solid is different from that of the water. As a result, when an acoustic wave propagates through the water (the particle velocity reversing every half-cycle), the motion of the latter is not in phase with that of the particles. There is net flow around the particle, and viscous losses occur in a viscous shear boundary layer which extends around each particle to a 'skin depth' (of O[1 micron] in water at 500 kHz). The contribution of these losses to attenuation exhibits a local maximum for fixed frequency (see the bold line in Figure 2). This is because very small particles move almost in phase with the fluid, whilst very large particles hardly move at all. Hence both activities are almost loss-less. Maximum absorption losses occur when the particle radius is a comparable size with the skin depth for shear waves, resulting in a maximum phase difference between the motion of the water and that of the particle.

To use either scatter, absorption, or both to measure suspended sediments at sea requires development, testing and calibration of those instruments in the laboratory. Because of this, measurement of backscatter from suspended sediment has been far simpler than use of absorption, because the backscattered signal is so much easier to detect in controlled laboratory systems than the absorption loss. Whilst the latter can be significant in the ocean, where propagation lengths of km or more are used, the finite size of laboratories makes it difficult to generate controlled, sizeable absorption losses. This difficulty increases as the acoustic frequency decreases, because the absorption is greater at higher frequencies. Below we detail the experimental system designed to measure such small losses, which has been used to verify models which predict absorption through suspended sediments. This has allowed predictions of sonar performance close to the mouths of large rivers, and feasibility studies of how absorption might be used to monitor mass flux by large rivers. Crucially the technique would allow the measurement to be made right across the length of the river, averaging over 100 m or more, to monitor the entire mass flux. Further details on these topics can be found by clicking here.

Measurement at low ultrasonic frequencies of absorption due to suspended particulate matter

Photograph of the experimental system showing, from left to right in the bag, the light scattering sensor (LSS), transmitting and receiving hydrophones, and the stirrer. The diameter of the bag is 235 mm.

The water volume is 16 litres.

The reverberation time is the time it takes the sound pressure level of a diffuse sound field to fall by 60 dB after the source is turned off. This is a function of the boundary absorption (which includes the absorption of the hydrophones) and the absorption in the propagating medium. Using room acoustics expressions for reverberation, the difference in attenuation between the two solutions, which is the viscous absorption due to the particles, can be obtained from the reverberation times of the clear water (Tw), which has a speed of sound, c, and the water containing particles (Ts) thus:

Assuming that:

• the speed of sound of the suspension stays constant as particles are added;
• the volume remains constant; and
• the addition of the particles does not affect the absorption of the boundaries.

In order to compare theoretical measurements based on spherical particles, glass spheres were used. They have a very high sphericity and a smooth surface, as illustrated by the two micrographs (left). In reality, particles are neither spherical or smooth as shown below. The is no simple theory to calculate the drag, and, hence, the absorption, of such particles.

As the suspension must be stirred, reverberation measurements are made for both calm and stirred water in order to obtain a reference signal. The difference between the two is small and generally within the error expected for a non-spatially averaged reverberation measurement. As the suspension concentration increases so the reverberation time decreases. There is also a general decrease in reverberation time as frequency increases, indicative of an increase in the viscous absorption.

A light scattering sensor has been used to measure the concentration of the suspension as it settles after stirring. The concentration was sampled every second and then a running average made over fifty samples to smooth out the concentration variations throughout the volume and the turbulence from the stirring process. Agreement with the theory based on Stokes drag law is good. This provides some validation of the drag models used to calculate the acoustic losses due to viscous absorption.

These figures show the normalised viscous absorption due to the particles as a function of frequency for various concentrations of glass spheres. The solid line is the theoretical prediction. The agreement with the theory is good and generally within the error band governed by the 4% error on the reverberation time. As the concentration increases the difference between the reverberation time of the clear water and the water containing particles increases and so the error in the attenuation decreases. Again, the increase of attenuation with frequency is apparent.

CONCLUSIONS

• a simple reverberation technique can be used to measure the viscous absorption due to particles suspended in water.
• measurements on glass spheres show good agreement with theoretical predictions.
• a minimum attenuation of around 0.01 dB/m is necessary to achieve an acceptable error in the measurements.

For further reading, click on the author list to download a pdf of the relevant publications:

Richards, S.D., Leighton, T.G. and Brown, N.R. Visco-inertial absorption in dilute suspensions of irregular particles, Proc. R. Soc. Lond. A, 459(2038), 2003, 2153-2167).

Richards, S.D., Leighton, T.G. and Brown, N.R. Sound absorption by suspensions of nonspherical particles: Measurements compared with predictions using various particle sizing techniques, Journal of the Acoustical Society of America, 114(4), 2003, 1841-1850

Richards, S.D. and Leighton, T.G. High frequency sonar performance predictions for littoral operations?The effect of suspended sediments and microbubbles, Journal of Defence Science, 8(1), 2003, 1-7

Richards, S.D. and Leighton, T.G. Sonar performance in coastal environments: Suspended sediments and microbubbles, Acoustics Bulletin, 26(1), 2001, 10-17

Brown N.R., Leighton, T.G., *Richards, S.D. and *Heathershaw, A.D. Measurement of viscous sound absorption at 50-150 kHz in a model turbid environment, Journal of the Acoustical Society of America, 104(4), 1998, 2114-2120

Leighton, T.G., *Brown, N.R. and *Richards, S.D. Effect of acoustic absorption by hydrophone and cable on a reverberation technique for measuring sound absorption coefficient of particulate suspensions, ISVR Technical Report 299, Southampton, University of Southampton, 2002, 11pp

Brown, N.R., Leighton, T.G. and *Richards, S.D. Experimental procedures for measuring the viscous sound absorption of suspended particles via a reverberation technique, ISVR Technical Memorandum 916, Southampton, University of Southampton, 2003,

Richards, S.D. and Leighton, T.G. Acoustic sensor performance in coastal waters: solid suspensions and bubbles, in Acoustical Oceanography, Proceedings of the Institute of Acoustics, 23(2), 2001, 399-406

Brown, N.R., Leighton, T.G., *Richards S.D. and *Heathershaw, A.D. Boundary and volume losses in a diffuse acoustic field near the atmosphere/ocean boundary, Natural Physical Processes, , 1997, 123-132

Richards, S.D., White, P.R. and Leighton, T.G. Volume absorption and volume reverberation due to microbubbles and suspended particles in a ray-based sonar performance model, Proceedings of the Seventh European Conference on Underwater Acoustics, Delft, Holland, 5-8 July 2004, , 2004, 173-8

Brown, N.R., Leighton, T.G., *Richards, S.D. and *Heathershaw, A.D. Measurement at 50-150 kHz of absorption due to suspended particulate matter, Proceedings of the Joint meeting of the 16th International Congress on Acoustics and the 135th Meeting of the Acoustical Society of America, Seattle, , 1998, 1347-1348

Richards, S.D., Brown N.R. and Leighton T.G. Turbidity in future high frequency sonar performance models, Proceedings of the Joint meeting of the 16th International Congress on Acoustics and the 135th Meeting of the Acoustical Society of America, Seattle, , 1998, 1349-1350

Richards, S.D., Brown N.R. and Leighton, T.G. Characterization of propagation parameters for high frequency sonar in turbid coastal waters, Proceedings of the 4th European Conference on Underwater Acoustics, Rome, , 1998, 709-714

Richards, S.D., *Heathershaw, A.D., *Hewitt, R.N., Brown, N.R. and Leighton, T.G. The effect of suspended particles on the performance of minehunting sonars in turbid coastal water, Undersea Defence Technology Conference, , 1997, 171-174

Brown, N.R., Leighton, T.G., *Richards, S.D. and *Heathershaw, A.D. Sound absorption by suspended particulate matter, Proceedings of the NATO Conference on High Frequency Acoustics in Shallow Water, , 1997, 75-82

Richards, S.D., *Heathershaw, A.D., Brown, N.R. and Leighton, T.G. The effect of suspended particulate matter on the performance of high frequency sonars in turbid coastal waters, Proceedings of the NATO Conference on High Frequency Acoustics in Shallow Water, , 1997, 443-450

 

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(Page last updated by T. G. Leighton, 9 March 2005)