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Quantum mechanics gives new insights into the Gibbs paradox

Entropy has been a subject of debate among physicists ever since it was formulated in classical thermodynamics some 150 years ago. One such debate centres on the so-called Gibbs paradox, in which the entropy of a system seems to depend on how much an observer knows about it. Astounding and confounding the physics community when it was first put forward by the American physicist Josiah Willard Gibbs in 1875, the paradox has since found numerous resolutions, albeit mainly in the classical setting with ideal gases.

Researchers at the University of Oxford and the University of Nottingham, UK, have now shed light on what the Gibbs paradox may look like in the quantum realm. By leveraging quantum effects, they show that more work can be extracted from a system than would be possible classically. Their result lays the theoretical groundwork for an experimental demonstration in the future, and could have applications in the burgeoning effort to manipulate large quantum systems.

The classical Gibbs paradox

The classical Gibbs paradox takes the form of a thought experiment involving a box with a partition that separates two bodies of gas. When the partition is removed, the two gas bodies mix spontaneously. To an informed observer who can distinguish the two gas bodies, the system’s entropy increases. On the other hand, for an ignorant observer who cannot discern any differences between the two gas bodies, there is no visible mixing and the entropy remains unchanged.

This difference of opinion has a physical significance since work can be extracted through the mixing process when the entropy increases. That suggests that the system’s entropy should be an objective quantity – something that does not reconcile with the existence of the different outcomes for the two observers. Gibbs, however, noted that the extraction of work depends on the experimental apparatus of the observer. Hence, the informed observer can extract work, whereas the ignorant observer has to contend with their inability to do so. This makes each observer’s reality consistent with the entropy change they witness.

Quantum effects

In the new work, the Oxford-Nottingham team considered how quantum effects such as superposition would affect the thought experiment. As in the classical case, the informed observer witnesses an entropy increase. For the ignorant observer, however, there is a marked difference after transitioning to the quantum realm. Although they are still unable to distinguish the two gases, they, too, can now witness an entropy increase. At the macroscopic limit, this entropy increase can even become as large as that which the informed observer perceives, providing the maximal discrepancy to the classical case.

Though the result might seem surprising at first, the researchers behind it say that it is a stark reminder that the classical limit is not always the same as the macroscopic one. “The classical limit is not just about large particle numbers, but also about limited degrees of control,” Benjamin Yadin, Benjamin Morris and Gerardo Adesso explain in an e-mail to Physics World. By giving the ignorant observer complex control over microscopic quantum degrees of freedom, they add, that observer becomes able to derive quantum effects at the macroscopic scale.

While some consider quantum mechanics to be a resolution to the classical Gibbs paradox, Yadin, Morris and Adesso note that their result indicates otherwise. “Our work shows that quantum effects can add an additional layer of seemingly paradoxical behaviour,” they say. They emphasise that their result is impossible in classical physics, as it relies on the symmetry requirements of bosons and fermions – a property not found in classical mechanics.

The researchers are now working on a proposal for demonstrating this effect experimentally. They explain that doing so requires a degree of quantum control, which may be possible in optical lattices and Bose-Einstein condensates. In the long term, they believe it could be possible to use this theory to build an effective quantum heat engine, one that could operate in regimes where a classical heat engine would fail.

“The question of how quantum features of identical particles may be harnessed for thermodynamical advantages is currently gaining a lot of interest – and we would like to see our work inspire other novel ideas in this area,” Yadin, Morris and Adesso conclude.

The research is reported in Nature Communications.

Spoilt for choice: APS March meeting explores the wide range of careers available to physicists

Before I chose to study physics, I remember hearing more than once that ”you can do anything with a physics degree”. As encouraging as that statement sounds, it is also vague. Although I already knew that most people who study physics don’t become professional academics, the overriding picture I had of a physicist was of someone working in a lab at a university or research institute. Where did all those missing physicists end up?

I now have a renewed interest in this question, having recently taken on the role of reviews and careers editor at Physics World, where we aim to spread the word about the possible careers you can pursue with a physics background. Apart from regular careers articles online and in the print magazine, we also publish annual career guides for the Institute of Physics and the American Physical Society (APS). That’s why I was keen to attend the APS March meeting 2021, which demonstrated some of the many directions that a degree in physics can take you in.

One session I attended focused on early-career physicists, and kicked off with a talk from Maika Takita, who studied physics at Barnard College, New York, before doing a PhD in the department of electrical engineering at Princeton University. Now a quantum computing researcher at IBM Quantum in New York, she spoke about her work on superconducting qubits – a career she never imagined she would have – and described how her academic background led her into industry.

Kenneth Gotlieb, who studied physics at Harvard University and completed a PhD in applied physics at the University of California, Berkeley, also spoke about making the transition from academic to industry research. He is now a senior scientist at Triple Ring Technologies, which has branches in California and Massachusetts, and described some of the medical devices he works on, from X-ray machines mounted on robots for taking X-rays of horses to non-invasive oxygen monitoring systems for use in surgery.

The speakers compared industry research with academic research, mentioning the importance of data analysis and creative problem solving within a team in both environments. A key difference was the strong focus in industry on clients’ needs and a willingness to change your line of work depending on their wishes.

Other talks in the session showed how a background in physics can be used more indirectly. Yue Zhang, a machine learning engineer who works on recommendation algorithms at Facebook, spoke about how she uses mathematical tools that she became familiar with during her PhD in applied physics at Rice University. I was fascinated to learn that vectors, which are used in physics to describe a distance, can be used in machine learning to represent similarities between items in a numerical way, and thus be used in recommendation algorithms.

Similarly, Calvin Patel, a stock analyst at Morgan Stanley, emphasized the value of mathematical skills, which he developed during his PhD in physics at the University of California Irvine, for careers in finance. He described the function of finance as the evaluation of the profitability of ideas, and explained the importance of statistics and probability in the field.

Physics is also essential to tackling some of the most pressing problems we face today, which was highlighted by a session on ”Seeing the energy future”. Among several talks was one by Denise Gray, president of LG Energy Solution, Michigan. Having worked on electric vehicles for over a decade, she outlined the remarkably quick progress that has been made in the area, with the distance they can travel on a single charge soaring from a little over 100 km to nearly 500 km. She attributes this to the collaboration between researchers who saw the potential in the technology and to funders who have supported their work. She also spoke about the promising future of the technology and the challenges currently being addressed, such as increasing the speed at which the vehicle batteries charge.

These are just a handful of the many careers at the APS March meeting. Indeed, it’s hard, impossible even, to summarize what physicists end up doing, because there are so many branches and niches in which physics is useful. In a world where science and technology are so advanced and ubiquitous in daily life, the answer to where physicists end up is easy: they’re everywhere.

Physics World is always on the lookout for people to talk about their careers in our magazine and online. If you’re interested in spreading the word about your field, get in touch at pwld@ioppublishing.org

World’s smallest origami bird, why hummingbirds hum, physics meeting ‘ain’t got that swing’

 

Spring has arrived here in Bristol and the birds are going bonkers in our garden, especially the amorous wood pigeons. So this edition of the Red Folder is dedicated to our feathered friends.

Cornell University is famous for its ornithology lab, but now physicists at the US university have also gone to birds and created what they describe as the “world’s smallest origami bird”. Measuring about 60 microns across, the folding bird is actuated by an extremely thin layered material that bends when a voltage is applied to it. It was created by Qingkun Li, Itai Cohen, Paul McEuen and colleagues – who explain how and why they have created the tiny folding bird in the above video.

Hummingbirds are not quite as small as the Cornell origami bird, but their tiny size and habit of feeding on nectar from flowers means that they have a unique way of flying. Indeed, hummingbird refers to the humming sound that the birds’ wings make as they flap furiously to hover in front of flowers.

Now researchers at Eindhoven University of Technology and the spin-out company Sorama, both in the Netherlands, and Stanford University in the US have used a myriad array of sensing equipment to work out how the hum is generated. They found the hum is made by changes in the pressure differences between regions above and below the wings as the birds flap to create their upward hovering force. The team have developed a model to describe hum generation and say that it could be used to design quieter fans. You can read more in a paper in the journal eLife.

The saxophonist Charlie Parker was famously known as Bird and is much revered in music circles for his development of bebop in the 1940s. With a fast tempo and complex chord changes, this form of jazz continues to have an important influence on musicians today.

The riddle of swing

Bebop often incorporates highly syncopated rhythms, which I am sure delight the German physicist Theo Geisel who uses mathematics to study musical rhythms. At this week’s virtual March Meeting of the American Physical Society, Geisel gave a talk on “Psychophysics of musical rhythms and the riddle of swing”.

Geisel and colleagues at the Max Planck Institute for Dynamics and Self-Organization have shown that “certain systematic microtiming deviations between musicians do enhance and are relevant for the swing feel in jazz”.

Unfortunately, the recording of Geisel’s talk seems to have been expunged from the video of the meeting session, E14 Physics of Social Interactions III. However, you can read more about this fascinating topic in this open access paper: “Microtiming deviations and swing feel in jazz”.

Spacecraft in a ‘warp bubble’ could travel faster than light, claims physicist

Albert Einstein’s special theory of relativity famously dictates that no known object can travel faster than the speed of light in vacuum, which is 299,792 km/s. This speed limit makes it unlikely that humans will ever be able to send spacecraft to explore beyond our local area of the Milky Way.

However, new research by Erik Lentz at the University of Göttingen suggests a way beyond this limit. The catch is that his scheme requires vast amounts of energy and it may not be able to propel a spacecraft.

Lentz proposes that conventional energy sources could be capable of arranging the structure of space–time in the form of a soliton – a robust singular wave. This soliton would act like a “warp bubble’”, contracting space in front of it and expanding space behind. Unlike objects within space–time, space–time itself can bend, expand or warp at any speed. Therefore, a spacecraft contained in a hyperfast bubble could arrive at its destination faster than light would in normal space without breaking any physical laws, even Einstein’s cosmic speed limit.

Negative energy

The idea of creating warp bubbles is not new, it was first proposed in 1994 by the Mexican physicist Miguel Alcubierre who dubbed them “warp drives” in homage to the sci-fi series Star Trek. However, until Lentz’s research it was thought that the only way to produce a warp drive was by generating vast amounts of negative energy – perhaps by using some sort of undiscovered exotic matter or by the manipulation of dark energy. To get around this problem, Lentz constructed an unexplored geometric structure of space–time to derive a new family of solutions to Einstein’s general relativity equations called positive-energy solitons.

Though Lentz’s solitons appear to conform to Einstein’s general theory of relativity and remove the need to create negative energy, space agencies will not be building warp drives any time soon, if ever. Part of the reason is that Lentz’s positive-energy warp drive requires a huge amount of energy. A 100 m radius spacecraft would require the energy equivalent to “hundreds of times of the mass of the planet Jupiter”, according to Lentz. He adds that to be practical, this requirement would have to be reduced by about 30 orders of magnitude to be on par with the output of a modern nuclear fission reactor.  Lentz is currently exploring existing energy-saving schemes to see if the energy required can be reduced to a practical level.

Any warp drive would also need to overcome several other serious issues. Alcubierre, who regards Lentz’s work as a “significant development”, cites the “horizon problem” as one of the most pernicious. “A warp bubble travelling faster than light cannot be created from inside the bubble, as the leading edge of the bubble would be beyond the reach of a spaceship sitting at its centre,” he explains. “The problem is that you need energy to deform space all the way to the very edge of the bubble, and the ship simply can’t put it there.”

Spacecraft doubts

Lentz describes his calculations in Classical and Quantum Gravity, where other recent research on the topic is outlined in an accepted manuscript from Advanced Propulsion Laboratory researchers Alexey Bobrick and Gianni Martire. The duo describes a general model for a warp drive incorporating all existing positive-energy and negative-energy warp drive schemes, except Lentz’s which they say “likely forms a new class of warp drive space–times”.

However, they argue that a Lentz-type warp drive is like any other type of warp drive in the sense that, at its core, it is a shell of regular material and therefore subject to Einstein’s cosmic speed limit, concluding that “there is no known way of accelerating a warp drive beyond the speed of light”.

Though he recognizes these huge hurdles to building a warp drive, Lentz feels they are not insurmountable. “This work has moved the problem of faster-than-light travel one step away from theoretical research in fundamental physics and closer to engineering,” he says.

After addressing energy requirements, Lentz plans to “devise a means of creating and accelerating (and dissipating and decelerating) the positive-energy solitons from their constituent matter sources”, then confirm the existence of small and slow solitons in a laboratory, and finally address the horizon problem. “This will be important to passing the speed of light with a fully autonomous soliton,” he says.

Nanoparticle-based vaccine offers new approach to COVID-19 immunity

As the international effort to vaccinate the population against COVID-19 gathers pace, the demand for vaccine doses that can be used in all countries and climates is enormous. Researchers from Cleveland Clinic and Chungbuk National University have described a new vaccine candidate that triggers an immune response using antigens attached to nanoparticles, potentially bypassing the need for cold storage during delivery. They report their findings in mBio.

All vaccines approved to date cause an immune response against the same part of the SARS-CoV-2 virus: the receptor binding domain (RBD) of the spike protein. However, they employ different mechanisms to bring this about – from using inactivated viruses to cause RBD production to delivering genetic instructions directly into cells. This new candidate provides an alternative approach – using inert nanoparticles to carry the RBD and display it to the immune system.

Direct delivery

Delivering the RBD protein directly, rather than causing the cell to produce it, seems an appealing option for vaccination. However, the body’s immune defences won’t respond to such a small molecule. Attaching multiple RBD units to a larger nanoparticle overcomes this challenge and makes them visible to the immune system. The nanoparticles used in this study are built from ferritin – a naturally produced protein existing in most organisms that can self-assemble into a useful nanoparticle structure.

The researchers tested the vaccine candidate in ferrets – which are susceptible to the same respiratory infections as humans. They saw that after three injections with this vaccine, the vaccinated ferrets had high levels of antibodies against SARS-CoV-2 in their bloodstreams. Ferrets treated with the vaccine and then exposed to the virus did not experience symptoms and cleared the virus from their system far quicker than unvaccinated ferrets.

The researchers were even able to show how vaccinated ferrets avoided lung damage caused by the infection. They note that combining intramuscular injection with introducing the vaccine through the nose – where SARS-CoV-2 commonly enters the body – produced an even stronger protective effect.

A hot topic

One of the biggest challenges in vaccinating the world’s population is getting the vaccine efficiently to every place it is needed. The vaccines in current use all need consistent cold storage, and in some cases ultracold storage, to remain effective. By being built from a nanoparticle structure that is naturally very thermostable, this new candidate may not need such conditions.

“This protein is an attractive biomaterial for vaccine and drug delivery for many reasons, including that it does not require strict temperature control,” says study author Jae Jung.

“This would dramatically ease shipping and storage constraints, which are challenges we’re currently experiencing in national distribution efforts. It would also be beneficial for distribution to developing countries,” adds co-first author Dokyun Kim. The authors note that this stability needs to be more rigorously verified, but were it to remain true, this could be one tool to help reduce global inequities in vaccine availability.

Any vaccine candidate still has many stages to progress through before it is approved for widespread use in humans, but the data so far for this approach are promising. If the vaccine comes to fruition, it will add a different type of weapon to the already diverse arsenal available to combat the continuing COVID-19 pandemic.

Hydroplaning of tyres is imaged using tiny fluorescent particles

Detailed images showing how water drains through tyre grooves during hydroplaning have been obtained by Serge Simoëns and colleagues at France’s University of Lyon. Their technique could provide crucial guidance to engineers trying to design tyres that are better suited to driving in wet conditions.

When a tyre rolls over a wet or flooded road, a build-up of water pressure at the front of the tyre can generate a lifting force. Known as hydroplaning, the effect can cause tyres to lose all contact with the road if this lift becomes greater than the weight of the car. To minimize its influence, tyre treads must drain as much water as possible from front to the back, without significantly reducing road adhesion. Since the fluid dynamics involved in hydroplaning are highly complex, tread designs must be informed by detailed information about these flows.

Particle imaging velocimetry (PIV) is a widely used technique for measuring flow velocities in 2D. It involves seeding fluid with fluorescent tracer particles that must be small enough to accurately reflect the dynamics of the fluid surrounding them. Then, a 2D slice of the fluid is illuminated by a laser sheet, causing the particles to glow and create a direct image of the flow.

Fluorescent test track

In their study, Cabut’s team used PIV to image a thin film of water on a test track, as a car drove through it at several different speeds. Their images were captured from below, through a transparent window embedded in the road. To overcome the optical constraints of the setup, the researchers combined their fluorescence images with measurements of laser sheet refraction at the interface between the window and the flowing water.

Inside the grooves, Cabut and colleagues observed white elongated filaments, which hinted at a gaseous phase – possibly cavities or air bubbles – within the liquid water. In the largest grooves, these columns showed some local periodic distortions. The team suggests that the nature of this phase could be linked to properties of a tread including groove widths, spacings between adjacent grooves, and the locations of the transverse grooves connecting them. The team also observed swirling vortices in some of the grooves. These could have arisen from flows around the sharp edges of the tyre’s ribs, and their number may be related to the ratios between the heights and widths of the grooves.

For now, it is not yet possible for Cabut’s team to determine exactly how these vortices and bubble columns came about, and further studies will be needed to pin down their formation mechanisms. However, their innovative new setup will likely be a key first step in these efforts. With a greater knowledge of the flow velocities involved in hydroplaning, engineers could design tread patterns that are better suited to minimizing the effect, while maintaining overall tyre performance.

The research is described in Physics of Fluids.

Artist draws on her physics background for inspiration, improving proton therapy for better cancer care

This episode of the Physics World Weekly podcast features the artist Geraldine Cox, who draws on her background in physics to create pieces inspired by the patterns of nature. Cox talks about her ongoing collaboration with physicists at Imperial College London and also about her work with World of Atoms, a UK-based organization that uses art, experiment, poetry and dance to teach children about atoms.

Also featured this week is the University of Liverpool accelerator physicist Carsten Welsch. He talks about his role as coordinator of Optimization of Medical Accelerators, which is a European training network, and he explains how the network is working to improve cancer care by optimizing proton therapy technologies.

 

Ultracold atoms permit direct observation of quasiparticle dynamics

Theories of how quasiparticles form have been around for more than 80 years, but direct observations of the process have remained elusive due to experimental challenges. A team of researchers at the Center for Complex Quantum Systems, Aarhus University, Denmark has recently overcome these obstacles by studying quasiparticle formation and dynamics in ultracold atoms.

The Soviet physicist Lev Landau developed a theory of quasiparticles – emergent phenomena that arise from a complex interaction between many real particles – in the 1930s. This theory, which is still routinely used in practical applications ranging from superconductivity to transport processes in electronic devices, considers the motion of an electron through a solid and describes how the electron (the quantum impurity) triggers the formation of a quasiparticle within the solid.

An ultracold analogue

Due to the high densities and fast timescales of this system, however, experiments cannot directly probe such quasiparticle behaviour in solids. The Aarhus team instead studied an analogue system: a quasiparticle called a polaron in a Bose-Einstein condensate (BEC). This dilute gas of ultracold atoms offers a pristine, controlled environment in which to study the quantum dynamics of many-body phenomena.

Photo of optical elements used in the experiment, bathed in purple light from a laser
Simulation centre: The region of the Aarhus experiment where atoms are initially trapped and cooled. (Courtesy: Lars Kruse/AU foto)

“Quasiparticles are exceedingly interesting to study since they may be composed by numerous particles and their excitations,” explains lead author Magnus Skou, a PhD student at Aarhus. “The Bose polaron is an excellent example of such a challenging quasiparticle that nonetheless holds great potential for helping us to understand exotic technologies like organic semiconductors and superconductors. This inspired us to investigate the polaron in an ultracold cloud of atoms and, in particular, to see if we could observe its gradual formation.”

Witnessing the formation of a Bose polaron

The team created the impurity not with an electron, but by manipulating the quantum state of only a few atoms in the BEC. Through theoretical modelling of the system, the authors identified three different dynamical regimes to describe the state of the impurity. By tuning the interaction strength of the atoms in the condensate and evolving the experiment for different lengths of time, the group experimentally probed each of these regimes. Their experiments, which Skou and fellow co-author Kristian Nielsen describe in a video posted to Twitter, showed how the impurity gradually evolved to form the polaron.

Skou predicts that their experiments offer promising pathways to better understand the interactions between quasiparticles. “Now that we have a better understanding of polarons,” he says, “it will be interesting to study how they interact with each other. These intricate interactions were recently predicted to enable the formation of a completely new quasiparticle known as a bipolaron. This quasiparticle has not yet been observed in an ultracold atomic gas, but we now believe that our experiment may allow for it to finally be seen.”

The research is described in Nature Physics.

Glashow resonance is spotted in a neutrino detector at long last

Physicists working on the IceCube Neutrino Observatory in Antarctica say they have made the first observation of the Glashow resonance – a process first predicted more than 60 years ago. If confirmed, the observation would provide further confirmation of the Standard Model of particle physics and help astrophysicists understand how astrophysical neutrinos are produced.

In 1959 the theoretical physicist and future Nobel laureate Sheldon Glashow worked out that an electron and an antineutrino could interact via the weak interaction to produce a W boson. Subsequent calculations indicated that this coupling – known as the Glashow resonance – should occur at antineutrino energies of around 6.3 PeV (6.3 × 1015 V). This is well beyond the energies achievable in current or planned particle accelerators, but natural astrophysical phenomena are expected to produce such neutrinos, which could then create a W boson by colliding with an electron here on Earth

IceCube is well placed to detect such an event because it comprises 86 strings of detectors suspended in holes bored into the Antarctic ice cap. When a neutrino occasionally interacts with the ice, tiny flashes of light are seen by the detectors. However, most interactions are equally probable for neutrinos and antineutrinos, and many neutrino detectors cannot tell which triggered the interaction.

Parity conservation

The need to conserve parity demands that the Glashow resonance be different. “At 6.3 PeV, this peak is only possible if you have an antineutrino interacting with an electron or, in an alternative symmetric world, a neutrino interacting with an antielectron,” explains Lu Lu of the University of Wisconsin-Madison, a senior member of the IceCube team. As a result, measuring the proportion of Glashow resonance events relative to the total number of neutrinos detected from an astronomical event could constrain the ratio of neutrinos to antineutrinos. This in turn could suggest how the neutrinos were produced.

Although astrophysical events are expected to produce neutrinos with very high energies, the number of neutrinos drops off following a power law in energy. Catching neutrinos requires a large detector in any case, so catching very high energy neutrinos requires an immense one. IceCube therefore uses a cubic kilometre of ice at the South Pole as its detection medium.

To search for Glashow resonance collisions in IceCube, the team analysed data taken by the detector between May 2012 and May 2017 using a machine learning algorithm. One event that occurred on 8 December 2016 stood out. The researchers estimate the detectable energy from the event to be 6.05 PeV, which – when losses through undetectable channels are factored in – is consistent with an antineutrino energy of about 6.3 PeV.

Highest energy deposition

The signature from the “early pulses”, caused by particles that outrun the light waves in the ice, helped the researchers rule out other possible explanations, such as a cosmic ray muon, and conclude that the event was indeed caused by an astrophysical neutrino. “This is definitely the highest energy deposition event IceCube has ever recorded from a neutrino,” says Lu. Based on the extremely low background levels expected at this energy, the researchers concluded it was at least 99% likely to be a Glashow event.

The researchers are now planning an even bigger detector, called IceCube Gen-2. As well as detecting neutrinos predicted to have even higher energies, the researchers hope this would allow them to detect a statistically significant number of Glashow events, confirming the findings and allowing the phenomenon to be used in astronomy.

Lu is particularly excited by the potential to understand how particles are accelerated by astrophysical processes. “For cosmic rays, it’s too difficult because they deflect everywhere,” she says. “High-energy photons interact with the cosmic microwave background; if you don’t have gravitational waves, the only other messenger is the neutrino, and the neutrino-to-antineutrino ratio brings a completely new axis to this game.”

Neutrino physicist David Wark, the UK principal investigator of the Super-Kamiokande detector, is impressed. “People have been trying for 50 years to detect these high-energy astrophysical neutrinos, and so it is astounding that IceCube has finally done it. Just a few years ago they saw the first gold-plated astrophysical neutrinos and now one at a time they’re knocking off all the things we expect to see at these very high energies.” Uncertainties arising partly from the impossibility of calibrating collision energy without extrapolation make him want to see at least one more event to be sure, but he says that the odds of one single detection appearing to be exactly where theory predicts the Glashow resonance are “not large”.

The research is described in Nature.

Iceberg melting is driven by geometry, experiments reveal

New experiments with ice blocks have revealed that icebergs melt faster on their sides. The discovery paves the way for better models of melting that consider the varied shapes of icebergs. The research could also improve our understanding of the role of iceberg melting in climate change.

Icebergs are a major source of freshwater flowing into some parts of the oceans; the Greenland ice sheet alone releases about 550 Gt of icebergs per year. This affects water salinity, which in turn affects water circulation and the global climate. The production of icebergs by both the Greenland and Antarctic ice sheets has been increasing significantly because of climate change so understanding the melting rate of icebergs is crucial for predicting changes in the oceanic heat flux.

Icebergs come in various shapes and sizes, with the largest recorded iceberg spanning almost 300 km in length and 40 km in width. They melt due to solar radiation, subsurface interaction with seawater and breaking into smaller pieces. Models used to predict the melting of icebergs were initially developed in the 1970s to study the possibility of towing icebergs to arid regions to provide an economical source of freshwater. These early models ignored the shape of icebergs and assumed constant water movement – and both assumptions have been carried through subsequent research.

Irregular melting

Icebergs are classified by an “aspect ratio” – the ratio of their length to submerged depth. New research by scientists in Australia, New Zealand, the US, and France led by Eric Hester, a PhD student of Applied Mathematics at the University of Sydney, has shown that the melting rate strongly depends on an iceberg’s geometry.

In their small-scale experimental simulation, the team submerged large rectangular ice blocks containing blue dye into a tank with circulating salt water and left them to melt for 10 min. The ice blocks were then weighed and photographed to assess the melting of each side.

“We put dye in the ice to observe where the melting occurs. We observed that at the front, the ice started to slope and melted three times faster. The bottom started to melt preferentially in the middle,” Hester tells Physics World.

Varying water velocity

In calculating melting rates, the team held a depth of 3 cm and varied the water velocities. At the highest water flow of 3.5 cm/s, the melting of the sides was roughly twice as fast as the base. If an iceberg moves in an ocean, the front face could be melting up to three times faster than predicted by old models.

Considering the varying size and geometry of real icebergs, their aspect ratio can affect overall melting by changing the areas exposed to water, suggesting that wider icebergs melt slowly, whereas smaller icebergs could melt up to 50% faster because they have more surface area on their sides.

Following their experimental findings, the team compared their results against numerical simulations assessing the flow dynamics.

“We developed a mathematical model to simulate the flow of warm salt water around the melting iceberg,” explains Hester.

Considering different parameters, such as temperature, salinity, and pushing forces, the team observed the same melting behaviour as in the experiment; the front of the ice block was melting the fastest, with a middle part melting faster on the base.

Difficult to observe in the field

According to Ellyn Enderlin of the Geoscience Department at Boise State University, who was not involved in this study, “Iceberg melting is something that cannot really be observed in the field – at best we can use sonar to map iceberg geometries at discrete time steps and back-out melting from the change in geometry – so these experiments tell us a lot about spatial variations in iceberg melting and how both water shear and iceberg geometry influence iceberg melt rates”.

“The revised parameterizations that [Hester and colleagues] present could be implemented into numerical models that include iceberg melting as a freshwater flux, allowing us to more accurately account for this important source of freshwater and assess the influence of variations in iceberg melt fluxes on fjord water masses. Given the strong dependence of melt rates on iceberg geometry and the changes in iceberg geometry that often accompany rapid glacier change, it is important that the influence of geometry is accounted for in the model parameterizations,” says Enderlin.

Apart from predicting climate change impacts of melting icebergs, these results can be extended to modelling melting glaciers. In addition, improved ice melting models could be used to understand the dynamics of extraterrestrial ice sheets, such as those on Saturn’s moon Enceladus or Jupiter’s moon Europa.

The research is described in Physical Review Fluids.

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