turbulence

In 1934 Jean Leray proved that the Navier–Stokes equations always have solutions "in a generalized sense". Whether a solution stays smooth or can break down into a singularity he could not tell, and nobody could for ninety years. In 2000 the Clay Institute made the question one of its seven Millennium Prize problems.

A vacuum cleaner sucks in dust even if there is more of it near the nozzle. The same happens in a tokamak: plasma particles are drawn toward the center, even though their density is higher at the edge. This phenomenon is called particle pinch, and it contradicts the usual rule that everything tends to move from dense regions to sparse ones.

Water in a tank spins at nearly four revolutions per second, and, as if by magic, a column the size of a dinner table emerges. The vortex lives for dozens of rotations, even though everything around it churns and trembles. Where does such stability come from? The secret is that the vortex is not isolated.

The churning cauldron of turbulence burns energy in two distinct ways. Vortices, like whirlpools in a maelstrom, twist the fluid and rub layers against each other. Shock waves, like a sudden clap, abruptly compress the gas and turn motion into heat.

In a Paris laboratory, light was made to flow around an obstacle the way water flows around a rock in a stream. But this water is special: it feels no friction.

Water confined between two cylinders flows in smooth layers when the inner one rotates. But once the speed crosses a certain threshold, the layers crumple into toroidal rolls, like a stack of bagels. Physicists call these Taylor vortices: the flow loses stability and a regular pattern emerges.

Water confined between two cylinders flows in smooth layers when the inner one rotates. But once the speed crosses a certain threshold, the layers crumple into toroidal rolls, like a stack of bagels. Physicists call these Taylor vortices: the flow loses stability and a regular pattern emerges.

A raindrop slides on the wind and hits the ocean not straight down but at an angle. At that moment, its energy splits into two channels: one pushes the water forward along the flight path, the other presses it downward into the depths. Which channel proves stronger determines what happens at the surface: a quiet submergence, a fan of spray to one side, or a crown that shatters in all directions.

When a fluid flows around an obstacle, it spawns vortices and shock waves. Describing their behavior means solving a nonlinear equation in which the flow velocity depends on itself. Classical supercomputers spend days on this, while quantum computers have barely been used: their native language is linear operations, but fluids are inherently nonlinear.

A car with a single suspension setting for all wheels — smooth on asphalt, but bumpy on dirt roads. That's roughly how modern computer models of fluids and gases work: all disturbances, from large whirlpools to fine ripples, are calmed with one common "brake." Stochastic modeling of flows has long been seeking a more refined tool.

A shock wave is like a steep wall of water rolling down a calm river. In physics, such waves arise when matter is compressed faster than the signal about that compression can spread sideways. In ordinary water or air, things are more or less clear.

After the Big Bang, according to inflationary cosmology, the Universe underwent rapid expansion and a series of phase transitions.

In calm water, the route is clear. But in turbulent flows, a robot needs a different strategy. Typical approaches demand an accurate map of currents, but in reality, you can't get one. Nature does it differently: fish feel pressure and vortices right against their bodies.

To swing a playground swing, push it in rhythm. That's how you use resonance — amplifying oscillations when the beat matches. A similar mechanism twists hydroturbine shafts when they receive electrical jolts from AI data centers. Modern AI servers consume energy unevenly: millions of processors suddenly kick into action, then go quiet.

In a world locked in a crystal lattice and cooled nearly to absolute zero, matter knows how to hide its deepest secrets. A quantum spin liquid is a state where electron spins never freeze, even at zero temperature, remaining in an eternally flickering superposition.

An ocean current hundreds of kilometers wide lives its own life, fed by energy from tiny eddies. Something similar happens in the atmosphere: small swirls pass their power on to huge air currents. This process, the inverse energy cascade, has been known for a long time.

Water is not just a wet substance. On a picosecond scale, it resembles a dance floor where molecules continuously break and form bonds with each other. Usually, this dance is described by one main movement — collective relaxation, as if the whole crowd simultaneously slows down after the music stops.

Fast radio bursts (FRB) — mysterious beacons of the Universe, emitting in milliseconds energy comparable to the Sun’s radiation over centuries.

In the intricate dance of active turbulence, where invisible engines spawn chaos, a soft droplet takes on the role of a detective. Its shape is not merely an outline but a sensitive cipher: it reads the hidden signals of its environment.

In the new model, each active particle has an internal rhythm: it spins either left or right. Chirality is key: some twirl clockwise, others counterclockwise. But when such a particle bumps into an obstacle or a neighbor, it flips its spin, like a figure skater who, after touching the board, explodes into a reverse pirouette.

A ball sits in a pit. It won't roll out on its own: it needs a push. But in the quantum world, a particle can leak through a barrier without extra energy. This trick is called tunneling.

Two-dimensional worlds never cease to amaze: here even crystal melting is not a symmetry breaking but a vortex drama discovered by Kosterlitz and Thouless. At the heart of this theater are topological сингулярности, whose energy and энтропия bargain for order. This language is common to сверхтекучести и сверхпроводимости.

Air flowing over a wing or turbine blade behaves like a string: it starts smooth and layered: that's the laminar regime. But as speed increases or external ripples appear, the string breaks into chaotic vibration — turbulence. Predicting the exact moment of breakdown is crucial: it affects drag, heating, and noise.

A stone falls into a pond, and ripples spread evenly in all directions. But some media behave as if the wave knows which way to turn, like water that only swirls clockwise. This asymmetry comes from odd viscosity and odd elasticity — properties of media with broken mirror symmetry.

A lump of sugar drops into hot tea, a spoon stirs a few times, and the sugar disappears. But how exactly does it spread through the churning liquid? Physicists have peered into this process with unprecedented detail: they simulated turbulence on a grid of 8192³ points. If you were to split every millimeter of the cup into a hundred cells, you'd get a similar resolution.

A supersolid is matter that is both crystalline and fluid. It is created from atoms cooled almost to absolute zero. In new work, physicists obtained such a substance as a triangular lattice of droplets. Each droplet oscillates in its own rhythm.

The paradox of the young solar wind has long puzzled heliophysicists. Measurements showed that near the Sun, proton beams aren’t smeared out but sharply compressed, as if someone had neatly hammered them into the shape of a hammerhead.

There's a leak in the garden hose. You patch the hole with duct tape, but the water presses harder and harder, and sooner or later the patch gives way. A growing clot in a blood vessel behaves much the same way. When the vessel wall is damaged, tiny blood platelets rush to the scene.

A clap of the hands compresses the air, and it flies outward — the simplest shock. In space, exploding stars play the role of hands: their shock waves sharply compress gas and trigger chaotic mixing — turbulence.

Mountain river water doesn't flow smoothly: it churns, swirls into eddies, and suddenly accelerates. This chaotic motion is called turbulence. But even within it, there are hidden rhythms — rare and intense bursts that briefly alter the entire flow pattern.

A cylinder slams into the air at enormous speed, and a shock wave is born around it — a sharp boundary where the air is instantly compressed and heated. Ernst Mach was the first to photograph these jumps, and since then we've thought of them as thin, almost invisible walls.

A drop of thick shampoo falls into water and freezes into a strange rope. A liquid that both flows and springs back is called viscoelastic. In it, tiny particles under ultrasound behave quite differently than in water. Viscoelasticity is a material's ability to both spread like honey and return to shape like rubber.

A pot of water has just been stirred: the whirlpools and eddies gradually calm down, and the liquid becomes smooth. A similar process, but in the quantum world, occurs in superfluid helium or in a cloud of ultracold atoms.

A stone falls into a pond, and ripples spread across the water. But if the stone is very small and the water is not quite ordinary, the ripples pass right through it, as if it weren't there.

River water often swirls into funnels. But in semiconductors, the foundation of microchips, electrons at low temperatures and high purity also turn into a fluid. If you create a circular cavity, vortices appear, just like in a river backwater.

Water going down the drain swirls into a vortex. An everyday sight in the kitchen. But this very vortex turned out to be able to reproduce two effects that physicists usually associate with black holes and the rotation of planets. The first effect is the shift of a wave as it goes around an obstacle.

A ball rolls up a hill, but it doesn't have enough energy, so it rolls back down. That's classical mechanics for you. But in the quantum world, a tiny particle can sometimes pass right through the hill, as if the barrier weren't there. This trick, tunneling, is business as usual for a light atom like hydrogen.

A chemical reaction resembles passing through a turnstile: a crowd creates chaos and gets stuck, while an orderly line moves. In the quantum world, however, when the jostling subsides, the barrier can become ghostly — a particle passes through it as if the turnstile has vanished.

Water churns behind a rock in a river, air swirls behind an airplane wing: it seems like completely random motion. But the authors of the study found a rigid kitchen recipe in this chaos. They decomposed the fluid's rotation (angular momentum) into two independent parts.

In a pot of boiling water, steam bubbles rise and pop. In the quantum world of a superfluid, bubbles behave differently: they can collide and give birth to vortices — tiny swirling flows, like whirlpools in a river. Scientists modeled such a liquid using a holographic approach.