7 August 2012

Musical dunes: what makes sand dunes sing?

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Exploring an ancient mystery of physics that continues to confound modern science.
Singing dunes

The Caltech team investigating a booming dune. The team’s field surveys with ground penetrating radar and seismic refraction confirm the existence of the waveguide for booming dunes. Subsurface soil sampling shows that a firm layer exists at a depth of approximately two metres with a higher water strata and chemically altered sand. Credit: Melany Hunt / Caltech

IN THE REMOTE EUREKA VALLEY in eastern California, atop a special type of sand dune, a group of scientists are preparing to fling themselves down the slip face on their backsides. This isn’t a prank, and the scientists aren’t suffering the effects of the searing desert Sun. They are conducting an experiment to unlock the secrets of a physical phenomenon that has long puzzled physicists and laymen alike: why do some sand dunes sing?

“We generally go out during the heat of the summer,” says Melany Hunt, professor of mechanical engineering at the California Institute of Technology (Caltech) in Pasadena, California. “We usually plan the trip to leave when it’s still dark, drive three-and-a-half hours to the desert and work for about four to five hours.”

Conditions are tough and the climb to the top of these large dunes lugging heavy listening equipment can be gruelling, although “we try and bring along some youthful students to help carry the equipment,” adds Hunt. Skidding down the dune induces a rare sound that inspires them to continue. It’s a sound that has not only perplexed physicists, but led to a decade-long schism between top scientists that’s been played out in international physics journals and continues to this day.

SINGING, OR BOOMING, dunes were first documented over 1,200 years ago in the ancient Chinese Tun Huang Lu manuscript. During the centuries since, they have aroused the curiosity of explorers, scientists and even emperors – from Marco Polo and Afghan Emperor Baber to Charles Darwin. Yet, despite much investigation, the phenomenon remains a mystery, with scientists unable to agree on an explanation for the strange booming.

Much of the scientific fascination surrounding booming dunes stems from the fact that their properties are so hard to pin down. Booming doesn’t occur on all desert dunes. And on those that do boom, the phenomenon doesn’t occur throughout the entire year or everywhere across the dune. The frequency can vary too – from roughly 65 to 120 Hertz – while the volume can reach 110 decibels. Booming is not related to the type of dune or its location. And while it’s mostly at a pitch akin to the drone of a low-flying aeroplane, its timbre ranges from a rough brass-like clamour of Oman’s dunes, on the Arabian Peninsula, to the pure vocal sound of Morocco’s.

Scientists agree that the noise only arises from a dune’s upper slip face (the leeward side), never from the shallow, windward face. What’s more, booming only happens when conditions are hot and dry and when the sand grains are clean, round and polished. Despite these clues, the most fundamental question remains: what does make the dunes sing?

The Caltech team uses an array of techniques, such as seismic refraction and ground penetrating radar, to analyse the booming sounds they create as they skid down the dunes on their rumps. By stopping and starting as they slide, they can create a tremolo effect, modulating the amplitude of the sounds’ wavelengths to make the volume rise and fall. With practice and by using their whole bodies, the scientists can even play the dune like a musical instrument. But by noon the heat is too much for most desert animals, let alone scientists, and the Caltech team heads back to analyse the day’s findings in the cool of the lab.

ONE OF THE FIRST credible explanations for booming dunes came from the work of an army officer based in North Africa during World War II, Ralph Bagnold: the founder and first commander of the British Army’s Long Range Desert Group. Bagnold heard the dunes’ songs while on operations, was inspired to study them and developed a simple mathematical model to describe the phenomenon. The frequency of the sound, he proposed, was proportional to the speed of the avalanche of sand grains down the dune and inversely proportional to the size of the grains. While some scientists today believe Bagnold’s model is more or less correct, it has never been fully embraced because calculations using it result in a frequency far higher than what has been recorded in the field.

Many more measurements were made and theories developed through the second half of the 20th century. Then, in 2004 and 2006, two Parisian scientists, Bruno Andreotti and Stéphane Douady, released two different but equally convincing theories.

Andreotti and Douady were colleagues at the École Normale Supérieure Paris in 2001. That year they went to Morocco to study crescent-shaped dunes, known as barchans, and accidentally set off avalanches that triggered the characteristic booming sound. This got them both hooked and, over a period of three or four years, they studied booming dunes together in great detail. Soon, however, their theories for the mechanism controlling booming began to diverge.

In 2004, Andreotti published a paper in the journal Physical Review Letters explaining the phenomenon through his various field measurements. Two years later, Douady and collaborators published the results of their lab experiments in the same journal. These largely backed up the ideas presented in Andreotti’s paper, but there were subtle differences. Despite the similarities of their theories, the disagreement ended their working relationship, with Andreotti ultimately moving to the Université Paris Diderot to set up a new research group.

Their quarrel hinges on a small but important detail. Both researchers believe the sound is due to waves produced in the surface of the avalanche (see ‘How dunes sing’, p71), and that the mechanism that causes booming is an active amplification of these waves via friction. But the source of this amplification is where the two researchers disagree.

“It is the frequency [at which] you force grains to pass over each other that you can hear,” says Douady. He reasons that the sound must arise from a resonance within the sliding layer itself, whereby grains bump over each other at the same frequency and set up standing waves that, in turn, synchronise the grains. It’s this synchronisation that makes the sound of each small grain movement coherent and then audible, claims Douady.

Andreotti, however, believes that “although it is counterintuitive, seismic waves can be amplified when reflected on the interface separating the sand avalanche from the dune”. That is, collisions between grains excite waves outside the sliding layer and friction amplifies the waves. “As these waves are [also] reflected by the avalanche surface, the avalanche constitutes an amplifying waveguide which selectively amplifies certain frequencies.” According to Andreotti, these waves are guided up the sliding layer: “In some sense, the avalanche behaves like a granular laser; coherent wave energy is pumped to the mean, gravity-induced motion.”

One of the essential precepts of Douady’s theory is that the booming frequency is related to grain size, which essentially means the dune itself is not actually needed to create the sound. Indeed, Douady has conducted lab experiments where he moved sand at different speeds in a controlled way to produce sounds of different frequencies: “We [made our own] booming avalanches in the lab,” he says.

Using sand brought back from booming dunes in Morocco and Oman, Douady and his student, Simon Dagois-Bohy, made a reservoir of musical grains with a gate, below which sat a thin layer of sand. “We never had enough to even make a small dune, so we built an inclined channel,” he says. When they removed the gate, an avalanche flowed that produced startling results. “We obtained exactly the same type of booming sound, just slightly less powerful and less ‘musical’,” explains Douady.

He claims this proves that booming has nothing to do with the characteristics of the dune itself: “It shows the grains can ‘sing’ in the lab too, even if our opponents tend to say that this is not the same phenomenon as singing dunes.” He points out that the relationship between the motion and the frequency is the same, and that his lab’s ‘singing sand’ works only with the same ‘musical’ grains from dunes that boom. Douady and his collaborators believe that because the phenomenon is observed on a hard plate in the lab, a supportive layer of sand (a dune) isn’t necessary to create the booming sound.

In 2007, just a year after Douady’s first experimental results were published, Melany Hunt and her Caltech co-workers published their own theory in which they suggested an entirely different mechanism for booming. They claim their field measurements have shown that the booming sound depends on the characteristics of the whole dune: “The dune needs to have the right internal structure to create the booms, it’s not just the sand,” says Hunt.

The Caltech team’s theory has the avalanche and sliding surface layer provide energy to successive wave trains that are positively reinforced by reflection between two boundaries: the air and deep wet sand in the dune. The booming comes from body waves within these boundaries, and not surface waves as suggested by Andreotti and Douady, Hunt argues. “On the surface of the dune, the avalanching of sand generates a range of frequencies. However, the structure of the dune preferably transmits the booming frequency and its harmonics.”

This reasoning has reopened the booming dune argument, with both Andreotti and Douady attacking the Caltech theory while vehemently defending their own. “The explanation by the Caltech team is not self-consistent: they have themselves shown that seismic waves are propagating and are therefore not resonant. Moreover, although nobody else has ever observed this, they keep claiming that the sound can be heard several minutes after the last grain has stopped, which is physically impossible,” says Andreotti.

Douady also objects to the Caltech team’s theory: “In short, we disagree that a dune is necessary, that the frequency would be given by resonance in the dune, and that the frequency–grain size relationship does not hold.”

In response, Hunt argues that the research by her team describes why some dunes boom and other don’t. “The prior works by Andreotti and Douady do not offer an explanation for why most avalanching dunes do not boom,” she points out.

The debate went up a notch when, in 2008 in Geophysical Research Letters, Andreotti published a comment on the Caltech team’s paper to which the Caltech team immediately responded. Andreotti attacked some of the experimental methods Caltech had used in the field and argued that their results didn’t match their conclusions. In response, the Caltech team defended their research and cast doubt on some of Andreotti’s data.

Despite the squabbles, claims and counter-claims of the three groups, Hunt and her former PhD student

Nathalie Vriend (now at Britain’s University of Cambridge) published a review in 2010 in the Annual Review of Earth and Planetary Sciences, putting forward the case for their own theory. Andreotti has also recently published a review in Reports on Progress in Physics (January 2012), in which he too presents the conflicting explanations and argues for his own theory.

Normally, when such reviews are published it indicates the arguments are clinched, any controversies ironed out and the facts are more or less established. But booming dunes are unusual in this respect too. What is clear is that there is little hope of the debate coming to an end in the near future. The singing sands will retain their mystery for some time to come.

Benjamin Skuse is a British mathematician turned science writer and regular contributor to COSMOS.
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