vorticity

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.

An airplane wing, like a skier on a ski jump, remembers its acceleration. Change the angle of attack sharply, and the lift does not immediately reach its new value. It builds up gradually, as if the wing is not yet sure the maneuver is for real. This effect was discovered by engineer Herbert Wagner in 1925.

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.

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.

A vortex in a magnetic disk usually behaves like a large spinning top: to keep it from toppling, you need a spacious platform and a strong self-field that returns it to the center. But what if you shrink the platform to the size of a virus? Then the usual support disappears, and the vortex should fall apart.

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.

In a ring accelerator, a beam of electrons circles millions of times. If the electrons are twisted like strands in a rope, their vortex motion should persist. But along the way, random jolts from imperfect magnets can disturb them. Scientists have described how vortex motion changes under such perturbations.

When two heavy nuclei collide in an accelerator, a tiny fireball of quark-gluon plasma is born — a special state of matter where quarks and gluons are not confined inside particles. As it expands and cools, the emitted particles often come out "spinning"—their spins align along the beam direction.

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

A superfluid flows without friction, like water that never stops. But when you spin it, it doesn't just rotate: each tiny vortex remembers exactly how it was spun. This 'trace' is not a metaphor but a real geometric imprint, which physicists call the Berry phase (the phase acquired by a wave as it travels along a closed path).

In accelerators like the Large Hadron Collider, heavy nuclei collide at enormous speeds. For an instant, quark-gluon plasma (QGP) is born — a state of matter where quarks and gluons float freely, just like in the first microseconds after the birth of the universe. This plasma is not just hot.

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 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.

Spacetime flows like a river, and a black hole is a whirlpool. Particles in this flow are like waves with their own rhythm: alternating crests and troughs. It turns out the whirlpool shifts the wave's rhythm from a distance, without even sucking it in.

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.

Sound travels through a medium at a certain speed. If the medium moves faster, the sound gets swept along by the flow — like a wood chip pulled into a whirlpool. In superfluid helium — a frictionless liquid — rapid rotation spawns vortex funnels. Inside them, an acoustic black hole forms: a region from which sound cannot return.

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.

A magnetic field penetrates a superconductor not as a continuous flux but as thin filaments — vortices. Usually, they repel each other and arrange into a neat triangular lattice, like floats on water. But in CaSb₂, things went differently: vortices bunched into tight clusters, with almost empty space between them.

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.

According to the Standard Model, the vacuum is not emptiness but an ocean of virtual ghost particles. An ultra-strong electromagnetic field, like a storm, yanks electron-positron pairs into reality.

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.

Toss a handful of glitter into a river, and some flakes will drift straight while others spin in tiny eddies. Galaxies in the universe do something similar: they don't just recede due to cosmic expansion: they also swirl in giant currents, like wood chips caught in invisible whirlpools.

Deep inside Earth lies a solid iron core about the size of the Moon. It floats in liquid metal and sways slightly, like a pit in a peach when you shake the fruit. Such oscillations are called Slichter modes: the core shifts both along the planet's axis and perpendicular to it. Three forces act together to damp this motion.

In superfluid helium, a vortex is like a tornado in a bottle, but instead of water, it's a quantum liquid that flows without friction. Such a vortex doesn't dissipate on its own, so the question of where its energy goes has long remained open.

In the cold heart of a pure crystal, electrons flow like a viscous fluid — an idea predicted by Lev Landau. But the vortices of this fluid remained invisible, like a painting inferred from the noise of a crowd. Now scientists have created a nanostring: a semiconductor tuning fork with a circular cavity.

A powder avalanche isn't just a pile of snow sliding down a mountain. It's a cloud racing downhill at car speed. Inside, snow doesn't lie still: it flies: thousands of tiny particles are caught up in air vortices. Until now, no one had seen what actually happens to each snowflake in this chaos. Now scientists have the first footage.

A drop of ink falls into a glass of water, and ripples spread out from it. Water seems simple, but if you look inside, each molecule isn't just moving forward: it's also spinning like a tiny top. Physicists call this intrinsic rotation spin. Usually, it goes unnoticed: in calm water, the tops spin every which way, and their rotation doesn't affect the fluid's overall motion.

In ordinary water, ripples from a thrown stone spread in even concentric circles. But imagine a liquid whose molecules are like tiny screws with a right-handed thread. In such a medium, the surface acts like a one-way street: waves can only travel in a certain direction.

Liquid helium at ultra-low temperatures enters a state of superfluidity: it flows without friction, like a perfect lubricant.

A sudden gust hits a wing, and a huge vortex swirls above it. Such a vortex can abruptly change lift, making the plane's nose dip. Engineers have long sought ways to predict these vortices, but complexity gets in the way: fast airflow is full of small chaotic eddies.

A superfluid flows without friction, like water in a perfectly smooth pipe, but the moment it hits an obstacle, the picture changes. In a new study, researchers looked at how a superfluid stream flows around rectangular walls and pits with sharp corners.

In a container the size of a coin, light behaves like water: it gathers into a single quantum fluid. When energy is added, whirlpools, quantum vortices, spin up on their own. Each vortex is like a tiny whirlpool that cannot simply disappear. Physicists illuminated this fluid with a laser and took snapshots.

A superconductor is a material where electric current flows without loss, like water through a perfectly smooth pipe. But if vortices appear, the current starts to 'stumble' over these tiny whirlpools. In graphene twisted at a special angle, such vortices can be created and studied one by one.

In a superconductor, electric current flows without loss, like water through a perfectly smooth pipe. But if you place such a material in a magnetic field, vortices appear inside — tiny whirlpools where superconductivity is destroyed. As long as these whirlpools stay put, current flows freely.

A microscopic gel bead or a tiny oil droplet squeezes through a narrow channel whose walls rhythmically contract and relax. The particle flattens and then recovers its shape, and by how quickly it does so, you can infer its internal elasticity and viscosity.

Water swirls into a ring, and that ring flies through the bulk without breaking apart. Such vortex rings, from smoke rings to underwater currents, follow laws that are hard to capture on paper. Usually, the flow is divided into millions of cubic cells, and each one is tracked.

Water in a puddle after rain swirls differently than in a deep lake. A thin layer of fluid feels the bottom, and that changes the nature of its vortices. Scientists created such a layer in the lab: they poured in an electrolyte, ran a current and a magnetic field, and the fluid began to move.

Vortons are invisible cosmic hoops, closed loops of curved spacetime. Thinner than an atom but heavier than stars, these Big Bang relics spin like giant carousels, churning everything around them. Einstein's equations describe how particles dance near such a hoop: paths twist into spirals or dart chaotically.

In superfluid helium, a state where liquid flows without friction, quantized vortices spontaneously arise: microscopic funnels resembling whirlpools in ordinary Water, but governed by quantum mechanics.

A spinning black hole acts like a giant funnel, but instead of just sucking in everything around it, it twists space itself, like a swift river current. New calculations show that in this maelstrom, stable vortices can be born from ultralight particles — likely building blocks of dark matter.