Geophysical Research Letters

Singing-sand avalanches without dunes

Authors


Abstract

[1] Singing-sand dunes have attracted curiosity for centuries and are now the subject of controversy. We address here two aspects of this controversy: first the possible link between the frequency heard and the shear rate (for a gravity avalanche on a dune slip-face, scaling as inline image, with d the ‘mean’ grain diameter), and second, the assumed necessity of a layered dune structure under the avalanche that acts as a resonator. Field recordings of singing dunes over the world reveal that they can present very different spectral characteristics: a dune with polydisperse grains produces a very broad and noisy spectrum, while a dune with sorted grains produces a well-defined frequency. Performing laboratory avalanches on a hard plate with singing-dune sand shows that there is no need for a dune below the sand avalanche to produce the singing sound, anda fortiorineither for the dune's layered structure nor for its particular sound transmission. By sieving the polydisperse grains, the same well-defined frequency is obtained to that of the dune with sorted grains, with the same diameter-frequency relation. The various frequencies heard in the field avalanches match the shear rates not calculated from the average size, but from the various peaks of the grain size distributions.

1. Introduction

[2] The ability of some dunes in sand deserts to emit sustained, loud sound has fascinated travelers and philosophers, as far back as O. de Pordenone during the Middle-Ages (quoted byCurzon [1923]), or in the 7th century manuscripts of Xuanzang [Beal, 1884] and of course Polo [1938]. It has aroused interest among European explorers of the 19th century, such as Hoffman [1830], and Darwin [1839], who pointed that the sound comes from the avalanching of the sand. Scientific observations are recorded from 1880 with works of Bolton and Julien [1884] as well as of Carus-Wilson [1891]. Important theoretical advances were made by Poynting and Thomson [Poynting and Thomson, 1904; Poynting, 1908]. They explained the phenomenon with the simple idea that a granular media submitted to a constant shear should expand and compact periodically (via the dilatancy explained by Reynolds [1885]), with a frequency equal to the shear rate. However this theory fails to explain the synchronization of the movement of the grains, necessary for the sound production. During the 20th century, several authors [Lewis et al., 1936; Lindsay et al., 1976] have described some conditions for sound emission : the sound is produced when the sand is sheared, and when it is ‘clean’, ‘fresh’, and dry. Haff [1986] pointed that the sound emission comes from particular properties of the sand and its environmental conditions. Douady et al. [2006] described these conditions as threshold effects. To insist on the sand properties, we call it ‘singing sand’. The sound emission on the dunes is rather described in the literature as ‘booming dunes’.

[3] Despite all these advances, none of these authors achieved a full understanding of the phenomenon.

[4] Today the mystery is still not solved and two opposing theories exist. One is developed by Vriend et al. [2007], and the other by Andreotti [2004] Andreotti et al. [2008]. Vriend et al. showed experimentally that a dune has a layered structure with a different sound propagation speed in each layer, creating waveguides. They also recorded the different frequencies emitted by steady avalanches on the same dune. They showed that a dune that sings in summer could also remain silent in winter. Abandoning Poynting and Thomson's point of view and the threshold effects, they deduced from their observations that the sound frequency was not imposed by the shear rate, but comes from a resonance of the layered structure excited by the gravitational energy of the avalanching grains. From the height of the first layer, they calculated the first resonance frequency that they identified with the sound frequency. However this approach cannot explain the various frequencies obtained on the dune by other means [Hunt and Vriend, 2010]. The frequency can be higher when a little amount of sand is pushed with the hand [Lewis, 1936; Douady et al., 2006], or lower when a bigger amount is pushed with the feet (http://www.youtube.com/watch?v=4yFaMsUawi4). This contradiction was pointed out by Andreotti et al. [2008], who proposed two successive points of view. They did not dispute the presence of a waveguide in a layered dune - though they disagreed on the complexity of the wave propagation in the granular media. They established that the shear rate in the surface avalanche [Quartier et al., 2000], is equal to the observed sound frequency [Andreotti, 2004]. They proposed a first model [Bonneau et al., 2007, 2008] where the oscillation comes from the shearing of granular media and where the synchronization is due to the long-range waves propagating in the underneath wave-guide. They recently presented another model [Andreotti, 2012; Andreotti and Bonneau, 2009] where the sound is produced through the amplification of propagating elastic waves by a frictional sliding interface (the avalanche). This recent model provides a better agreement with field observations as the variation of the sound amplitude, as well as the sensitivity with friction. However it loses the relation with the shear rate, and it remains based on a wave propagation in the flowing layer.

[5] In a previous publication [Dagois-Bohy, 2010] we presented a laboratory experiment of a singing-sand avalanche in a large channel, and by looking at the phase of the signal of two accelerometers floating at the surface, we showed that no propagating wave could be associated to the sound emission.

[6] In this letter, we focus on the link between this experiment and field observations. We will first report on several field recordings that agree with the observations of both Vriend et al. and Andreotti et al., then we will present the laboratory experiment with the same characteristics, and reveal the effects of polydispersity on the sound heard. Finally, in the light of these experiments, we will interpret the polyphonic field records and show that the frequencies heard depend undoubtedly on the various grain sizes and therefore on the various shear rates in the flow.

2. Field Recordings

[7] The field experiments reported here were made mainly during two trips, the first in November 2007 to Morocco and the second in December 2008 to Oman. In Morocco, we studied the compound megabarchanes of Foum Agoutir, near Tarfaya (Omega 1, 28.036 N, −12.159 E). There we recorded the sound on a video camera with several microphones. The sound in Tarfaya has a frequency of 105 ± 5 Hz whatever the location of the avalanche on the slip face, as well as on other smaller slip faces at the windward side of this compound dune. Avalanches recorded were natural or human-triggered and sustained, following the method described byAndreotti et al. [2008]. This sand is very well sorted with a mean grain diameter of 160 ± 10 μm, and the mean shear rate of avalanches fits the frequency measured quite well (see Figure 1 and auxiliary material), as observed earlier by Douady et al. [2006] and Andreotti [2004]. The mean shear rate is given at the surface of the slip face by the formula inline image with d the mean diameter of the grains [Quartier et al., 2000]. Other trips were made at this location during all the seasons, however no perceptible difference in the singing was observed - even when the slip face was partly reversed from winter storms [Elbelrhiti and Douady, 2011].

Figure 1.

Wavelet spectrogram of a singing avalanche at the ‘Omega1’ megabarchan dune near Tarfaya, Morocco. In the right inset the spectrum (i.e. the spectrogram averaged over time) shows a fundamental frequency of 100 ± 5 Hz, and the n = 2 harmonic at 195 ± 10 Hz. The width of the frequency peak comes mainly from time fluctuations visible in the spectrogram. The left inset shows the size distribution of the grains of the dune, with a clear peak at 150 μm. In the spectrogram, the last signal at low frequency (< 70 Hz) is a noise produced by the wind.

[8] In Oman, we visited two singing dunes, one in Al-Wagan near the U.A.E. border (23.714 N, 55.636 E) and the other one in Al-Askharah at the south east of Oman (21.887 N, 59.559 E). The first one is a big star dune of 40 m high, but its ability to sing was very weak, and only 3 persons forcing at the same time a huge avalanche were able to make it sing (in dry winter time). The frequency measured was 80 ± 5 Hz with the mean grain diameter equal to 185 ± 60 μm. The frequency measured does not equal the shear rate calculated from the mean grain size. The dune in Al-Askharah, a double barchan 30 m high, sings very well (even in early morning, in December) but it is impossible to identify a single frequency : depending on the experiment the spectrogram is different and does not usually display a single frequency (seeFigure 2). The mean frequency does not match the shear rate using the mean grain size equal to 230 ± 80 μm: the recordings in Oman show that a simple analysis in terms of average frequency and grain diameter may not be relevant. Other field trips were made to various locations, including the South-West Rocky Mountains in early September 2009, China in July 2004 and Chile in December 2003. Recordings were made during singing avalanches of approximately 1 minute, and samples were collected from the middle of the singing slip faces of those dunes (seeTable 1, Figure 5, and the auxiliary material).

Figure 2.

Wavelet spectrogram of a singing avalanche at the Al-Askhara double-barchan dune, Oman. The averaged spectrum in the right inset shows several peaks with a maximum at 120 Hz, the distribution is very broad and the spectrogram shows that this peak is not well-defined. The grain distribution (left inset) is also very broad.

Table 1. Name, GPS Coordinates, Peak Frequencies and Sizes for Recordings Used in Figure 5 (right)a
NameGPS CoordinatesFrequency Peaks (Hz)Grain Size Average (μm)Grain Size Peaks (μm)
  • a

    The frequency error is the width of the peak (the deviation over several recordings is usually lower). The grain size error is the width of the fitted gaussian for the average, and the gap between two sieves for the peak values.

Al Askharah21.887 N, 59.559 E66 ± 5, 87 ± 7, 101 ± 5, 115 ± 10230 ± 80218 ± 6, 155 ± 5, 118 ± 6
Al Wagan23.714 N, 55.636 E80 ± 5185 ± 60218 ± 10
Baidan Jirin39.556 N, 102.355 E56 ± 7, 81 ± 10186 ± 40190 ± 40
Cerro Bramador−27.319 N, −70.418 E70 ± 7, 76 ± 5300 ± 20225 ± 25, 290 ± 10
  88 ± 6 118 ± 6
Dumont dunes35.676 N, −116.223 E84 ± 7174 ± 50190 ± 10
Dunhuang40.082 N, 94.684 E75 ± 10184 ± 70237 ± 13
Eureka dunes37.101 N, −117.674 E93 ± 15165 ± 50190 ± 10
Mar de dunas−27.238 N, −70.553 E96 ± 5168 ± 40190 ± 10
Foum Agoutir (Omega1)28.036 N, −12.159 E100 ± 5155 ± 15155 ± 10
Sand Mountain39.308 N,−118.399 E85 ± 10, 70 ± 5243 ± 40237 ± 13

3. Laboratory Experiment

[9] We brought back to Paris 50 kgs of sand from the compound megabarchan dune in Morocco and 150 kgs from the Al-Askharah double-barchan dune. Each time, the sand samples were taken from the middle of the main slip face of the dune where significant singing had been recorded. The samples brought were used in a large channel (2.1 m × 0.41 m × 0.26 m) with a hard bottom (3 cm thick) in an avalanche experiment. To avoid sliding at the bottom of the channel, it was covered with cloth. The avalanche was prepared as follows (seeFigure 3): the channel was inclined at the avalanche angle and two layers separated by a gate were prepared. The down stream layer was prepared between 1 and 2 cm high, and the upper layer was prepared with a supplementary height varying from 4 to 10 cm. The gate was then removed, initiating a spontaneous avalanche flow. Two accelerometers on floating rafts measured the vertical vibration of the flowing surface. Flow surface speed was measured by filming and subsequent analysis. A scale measured the output flow rate. Finally, a laser position detector measured the flow height. The flow is complex and transient, as on the field. We suppose that during the main flow period it has a sheared region with a constant shear rate equal to inline image. This assumption is based on dimensional analysis as well as on experimental results [Quartier et al., 2000; Bonamy and Mills, 2003; Orpe and Khakhar, 2007; Schaefer et al., 2010]. For several experiments using samples from the Morocco Omega1 sands, Figure 3 shows the variation with time of the frequency of the signal of the second accelerometer and microphone. There were approximately 3 seconds during the experiment where the sand is singing as in the field, and the experiment is reproducible. Since the total height of sand (flowing plus static part) during the avalanche does not exceed 3 cm, the waveguide cutoff frequency should be greater than 900 Hz according to the first Andreotti et al. model [Bonneau et al., 2007, 2008]. In addition, the channel plate made of reinforced hard chipboard has a sound speed of several orders of magnitude larger than in the sand, and so is the associated cutoff.

Figure 3.

(left) Scheme of laboratory avalanches. First the wedge was settled, then the door was placed to fill the upper part of the channel with sand. The experiment began when the door was opened, starting the avalanche. (right) Measurements with the sand from Omega1 dune for H0 = 4 to 10 cm and d0 = 1 cm: Accelerometer signal (bottom inset), height (top inset) and fundamental frequency of 12 experiments, calculated here by autocorrelation of the microphone(blue) and accelerometer (red) signals. The time origin was set with the avalanche front, but the sand started to sing as soon as the gate was opened. At this moment, the angle, the shear rate and the frequency were higher until the flow reached a stationary-like regime when height ceased to increase. For all avalanches, the sound died after 4s (points below 50 Hz are detection errors from noise). The minimum of the average frequency (black line, averaged over all experiments) corresponds to the frequency heard in the field.

[10] Thus the 105 Hz frequency heard during the avalanche (90 Hz for the Oman sand) cannot be the result of propagating Rayleigh acoustic waves, as it was pointed earlier using phase measurements [Dagois-Bohy, 2010]. This contradicts also the model of the frictional sliding interface, for which the frequency in the field (infinite depth) and in the experiment (shallow depth) should be significantly different. This is not what is observed.

[11] When the samples from Oman were used, multiple frequencies could be heard, as they were in the field (Figure 4, left). These frequencies were produced at the same time and same location in the avalanche, since they were recorded locally by the floating accelerometers (with no wave propagation). In this very polydisperse system, the shear rate (82 s−1) predicted with the mean diameter (230 μm) is on the border of the range of frequencies heard (90–150 Hz).

Figure 4.

Wavelet spectrograms of sound from laboratory avalanche using Al-Askharah sand. (left) Unsorted grains. Two main frequencies around 90 and 110 Hz are seen, as well as bursts of higher frequencies. (right) Sorted grains. Only the 90 Hz fundamental remains. Note also then = 2 harmonic at 180 Hz, absent when the grains are not sorted.

[12] When the Oman grains were sieved between 200 μm and 250 μm, the sound during the main part of the avalanche has a single frequency and harmonics. The fundamental of 90 ± 5 Hz match the frequency predicted with the peak at 218 μm in the grain distribution (within the error). After sieving the grains, the flow could have been closer to a constant shear and we recovered the relation between shear-rate and frequency emitted.

4. Back to the Field

[13] This last result suggests a new interpretation of the polyphonic field recordings. We know that the segregation process occurs during the shearing of granular media [Mobius et al., 2001; Savage and Lun, 1988]. In a polydisperse avalanche, the grains of the same size regroup quickly into layers. If a peak in the size distribution is important, it means that the width of the corresponding layer in the avalanche is larger, and we can suppose that this region has a constant shear rate of inline image, with d0 at the peak. When the distribution has more than one peak, this process can happen more than once.

[14] The grain distribution of the Al-Askharah dune (Figure 2, left inset) shows three peaks. The power spectra of different avalanche recordings at the surface of the dune are different but they seem to share at least 4 peaks in frequencies (Figure 5, left). The three highest values of those peaks correspond to the value of the shear rate calculated from the 3 peaks in the size distribution. The lowest frequency peak does not match a peak of grain size, however the corresponding value is still present in the distribution of the sand brought back and maybe more in the field. The fact that these various frequencies can be measured at the same time and place by the accelerometers, and that they match the local values of the shear rate in the flow, points toward a local self-synchronization, within each sublayer. In the right side ofFigure 5 are displayed the peak frequencies vs. the shear rates calculated with the maxima of the size distribution for different field avalanches, including those described in section 2- all the locations are displayed inTable 1. In this graph, the frequency peaks correlate with the shear rate calculated from the peaks in the size distribution - contrary to the mean frequency and mean grain size.

Figure 5.

(left) The 5 spectra obtained from 5 field avalanches on the Al-Askharah dune (seeFigure 2and supplemental material). The shear rate calculated with the peak sizes correspond to 3 over 4 of the frequency peaks present in the spectra. The size corresponding to the last frequency peak is also present in the dune. (right) Peak frequency of singing field avalanches vs shear rates calculated from peaks in the size distributions. The three points of Al-Askharah are explained in the text. The black triangle for Sand Mountains comes fromLindsay et al. [1976].

5. Conclusion

[15] Sound is produced by a synchronized motion of grains. We reproduced the singing avalanches in a controlled laboratory experiment with a total sand height much too small to allow acoustic waves to propagate in the granular media layer. This shows that a waveguide formed of layered grains is not needed to make the sand sing. We found that sand dunes containing multimodal grain size distribution can sing with multiple frequencies at the same place and time. After sieving those frequencies were isolated and corresponded to the shear rate calculated with the sorted grain size. This allowed us to correlate frequencies heard in the field with the shear rate calculated from the peaks in the grain size distribution - and not the average. To conclude, the synchronization occurs only within the flowing layers of similar grain sizes and does not require any external effect. Therefore it can come only from the particular contact interaction between these singing grains [Douady et al., 2006; Dagois-Bohy, 2010].

Acknowledgments

[16] The authors would like to thank the following people very much for their help during the field trips: A. Manning in Chile, China, and Rocky Mountains; A. Lianos-Campos in Chile; Mr. Zhou and Pr Qu in China; E. Chailloux and M. Théry in Morocco; and J. Kierkegaard, E. Reffet, and M. Receveur in Oman. Finally, thanks are due to H. Warner and M. Saghir for help in the manuscript preparation.

[17] The Editor thanks Pieter Vermeesch and an anonymous reviewer.