Kelvin-Helmholtz instability

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.

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.

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 star circles a rotating black hole like a figure skater at the center of a rink. While it is far away and can be treated as a point, the dance remains predictable: the orbit follows clear laws, like music that is easy to glide to. But as it approaches, gravity begins to act unevenly.

Plasma is not just hot gas; it's an entire orchestra of charged particles, each group playing its own part. Heavy ions (atoms that have lost electrons) set the slow rhythm, while light electrons dart around ten thousand times faster.

At the center of many galaxies lurks an invisible cloud — a halo of dark matter. If this matter is cold and light enough, it behaves like a superfluid: it flows without friction, and any rotation in it twists into tiny quantum vortices — threads the size of an atomic nucleus.

Inside planets and stars, in rotating oceans of plasma, turbulent flows, Coriolis forces, and magnetic tension collide. The central question is how the energy of this chaos crystallizes into a stable magnetic framework that can last billions of years.

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.

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.

Imagine a spinning top the size of a city, weighing more than the Sun and making hundreds of revolutions per second. That's a neutron star — the remnant of an exploded star. Occasionally, its rotation suddenly speeds up, as if something inside has switched. Astronomers call these jumps glitches and suspect that invisible vortices in the star's superfluid interior are to blame.

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.

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.

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.

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.

A crystal that promised to conduct electricity without loss at room temperature turned out to be like a house of cards: touch it and it falls apart. Two compounds (one with silver, one with gold) were considered superconductor candidates, but tests showed that neither can withstand even ordinary conditions. In the silver variant, the lattice simply collapses.

The young star HL Tau is surrounded by a disk of gas and dust — the cradle of future planets. Inside this disk, the gas is not static: it orbits the star, but it also trembles and churns, like water in a raging river. Astronomers have now directly measured the strength of this churning for the first time.

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.

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.

In a protoplanetary disk, a cloud of gas and dust around a young star, dust grains don't just fly in circles. They are carried by the gas flow, like sand by the wind, and in turn alter that flow. Layers emerge, sliding past each other, and at their boundaries an instability arises — waves and vortices.

A piece of dough, when pulled from the sides, doesn't stretch evenly: in one spot it thins and tears. Living tissue behaves similarly, but instead of a tear, shear bands appear — narrow zones where cells begin to slide past each other, like cards in a deck when cut.

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 calm river suddenly starts churning in the middle of a flat stretch: that's the puzzle the authors of a new study set out to solve. They took a thin layer of charged gas with a very weak magnetic field and tracked on a computer what would happen to it. At first, everything flows smoothly, like water from a tap.

A young planet in a gas disk is like a swimmer trying to swim against the current: friction with the gas slows it down, and it spirals toward the star. For small rocky planets, this fall can take less time than they need to grow. But the disk also has countercurrents — vortices that can push the planet outward. Scientists built a computer model of a disk around a young star.

The diffusion equation, a mathematical tool describing how particles spread out in space, has long painted a paradoxical picture: a disturbance, like ripples on Water, instantly engulfs the entire universe. This challenged the theory of relativity, which holds that nothing can move faster than light.

A total solar eclipse offers rare minutes when the Moon blocks the Sun's bright disk, revealing its outer atmosphere — the corona. In white light, the corona extends tens of solar radii, and images show fine structures: vortex rings, waves like ripples on water, and huge plasma ejections.

Inside giant planets like Jupiter and Saturn, heat doesn't always rise freely. Heavy elements, which are more abundant in some layers than others, prevent hot fluid from floating up. This creates semiconvection — a type of mixing where heat and composition spread at different rates.

A supersolid is ice that flows. Think of a pond with a frozen crust, but beneath it, a liquid depth without friction. Usually, creating that crust means changing the liquid's properties throughout its entire volume.