hydrodynamics

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.

The orchestra starts playing, but each musician has their own tempo. If everyone plays at roughly the same speed, the music flows in a continuous stream. But if one group of instruments plays noticeably slower than the rest, the sound gathers into a dense clump that slowly moves forward.

Plasma is a gas in which electrons are stripped from atoms and roam freely. Sometimes, regions where electrons are almost absent spontaneously appear in such a gas; they are called holes. It is like a whirlpool forming in a stream, pulling everything around it in. But exactly how such a whirlpool is born has long remained a mystery.

A sphere rolls down a chute. What shape should the chute be to make the descent as quick as possible? Three centuries ago, the answer was the cycloid — a curve resembling the arc of an upside-down bridge. But submerge the chute in a thick liquid, and everything changes: the fluid slows the sphere, and the fastest path becomes something else.

Microwave plasma in a vortex is like a kitchen mixer that simultaneously heats and stirs the gas. In the reactor, the gas is swirled, and microwaves heat it to thousands of degrees, tearing carbon dioxide molecules apart. Scientists created a computer model of such a reactor to understand how pressure affects the process.

A cluster of glowing dots drifts through the darkness, now compressing into islands, now spreading out in waves. These are not fish or birds: this is a mathematical model of active matter, where each particle spends its own energy on movement, and also is born, dies, and competes with neighbors for space.

The universe right after the Big Bang was like a boiling cauldron: bubbles of a new state of matter were bursting and growing everywhere. These were first-order phase transitions — exactly like water boiling, only at temperatures reaching trillions of degrees.

The early universe was less like a calm pond and more like a boiling cauldron. Matter flowed, collided, and swirled against the backdrop of rapid spatial expansion. To understand how stars and galaxies emerged from this hot soup, physicists build digital simulations. This new work is the third part in a series on lattice-based cosmological modeling. The first two focused on fields; this one deals with fluids.

Soil is not a solid sponge but a labyrinth of pores of various sizes. After rain, water does not fill them all at once: first the narrowest ones, then the wider ones. Physicists built a theory of this process based on a simple image — a set of communicating vessels.

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.

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.

In the first moments of its life, the Universe resembled a boiling cauldron. As it cooled, phase transitions occurred — much like steam turning into water, but instead of molecules, the very state of space changed. In this cauldron, bubbles of the new phase were born, akin to bubbles in a pot coming to a boil.

When physicists drive electrons through an ultrapure gallium arsenide channel at helium temperatures, they expect to see a well-behaved, almost ideal fluid.

A regular object moves along a predictable path, like a ball. In the quantum world, a particle is smeared into a probability cloud. To find order in this fog, scientists have recast Schrödinger's equation in the language of flowing water.

Picture a pot of boiling soup, but every grain in it is not just a point but a tiny top spinning around its own axis. That's the world of spin-1 particles. For example, some short-lived mesons born in accelerator collisions.

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.

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.

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.

The shape of a riverbed precisely follows the equation describing the growth of a universe with negative curvature. In the lab, water flowing over sand spontaneously carves a cross-section that matches the solution for the Anti-de Sitter model. A river tends toward a shape that maximizes bottom friction.

Two grains of salt fall into a glass of water. They dissolve, and sodium and chloride ions spread throughout the volume. The schoolbook truth is simple: like charges repel, opposite charges attract. But recent experiments with tiny spheres in liquids have revealed a picture that breaks this rule.

In a pot of boiling soup, churning currents carry heat to the walls, and the soup cools. In a tokamak, a huge magnetic bottle for plasma, the same thing happens: turbulent eddies carry energy outward, hindering the ignition of a fusion reaction. But sometimes the plasma seems to find a way to calm itself.

In a crystal of water and caustic cesium, oxygen and cesium atoms sit in place like beads in a rigid lattice. Hydrogen atoms behave differently: they are like passengers constantly changing seats. In this layered material, each oxygen is linked to three neighbors via hydrogen bridges, forming a honeycomb-like pattern.

If you pour sand into a glass, it settles in a flat layer. But instead of sand, take the tiniest particles of gas: in a gravitational field they don't just fall: each particle races along its own trajectory, collides with neighbors, and all this commotion creates pressure.

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.

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.

A ship gliding through water constantly rubs against it, like a palm against a rough surface. This friction eats fuel and slows progress. One way to reduce it is to blow air under the hull: water stops sticking to the hull, and drag drops. But air is finicky: sometimes it helps, sometimes it hurts.

A drop of water on a table usually sits still. But make the table slightly softer on one edge and stiffer on the other, and the drop will crawl toward the stiffer side. This phenomenon is called durotaxis: the liquid itself chooses where to flow, without pumps or electricity. This trick works because the surface under the drop is not uniform.

The void can produce particles if a strong enough field is applied. Physicists call this the Dirac–Klein paradox. Previously, explaining it required the most complex calculations of quantum field theory. But we can make do with a visual image: a tightly stretched rubber band with a knot. The knot is a particle.

At the Large Hadron Collider, not only nuclei but also individual protons collide. Even in such small systems, collective behavior resembling the flow of a liquid is observed. But the proton is a quantum object; its state is described by a wave function, not by temperature and pressure.

A raindrop falls into a puddle, and the impact sends up a little fountain of fine spray. Each of those droplets is a new, secondary drop. How many there are, how big they are, and how long they live depend on a host of factors: the fall speed, the drop size, the properties of the water. Scientists set out to make sense of this chaos using computer simulations.

In a cloud, thousands of tiny water droplets hang in the air. For rain to fall, they need to grow: stick together into larger drops and become heavy enough to fall to the ground. But how exactly do droplets find each other in a huge cloud? Scientists created a computer model that tracks each droplet individually, as if each one had its own little sensor.

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 porous materials (soil, rocks, filters) fluids move through tiny, winding channels. When two immiscible fluids, such as water and air, are present simultaneously, their interface constantly shifts: air bubbles push water out of some pores and open paths through others.

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 water molecule, finding itself near a carbon ring, starts to vibrate, and immediately falls under the sway of an invisible conductor. The ring's electron cloud, like a maestro, dampens some vibrations while amplifying others.

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.

When a crowd of bacteria (mostly composed of carbon) gathers in a droplet of water, a synchronized round dance begins: millions of tiny ones glide along giant ellipses, like dancers on a ballroom floor. Without a conductor, complex patterns emerge from simple movements.

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.

The boundary between two liquids is like an invisible skin: it's there, but you can't touch it with your finger. Scientists have found a way to measure its elasticity without touching it. They made a tiny probe oscillate above the surface, and between the probe and the interface lay a thin film of liquid.

Water deep within the Earth is compressed more than a thousandfold compared to the surface. Even there, it continues to flow, but its internal structure changes. Researchers measured how water resists flow and compression as pressure rises from zero to 1.6 gigapascals — equivalent to placing a 16-ton weight on every square centimeter.