Bernoulli's principle

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.

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 particle sits in an energy pit like a pea in a dimple. To get out, it needs to go over the barrier, and usually this is rare: the higher the barrier, the longer the wait. The Arrhenius law says the waiting time grows exponentially, meaning doubling the barrier height increases the time by hundreds of times.

A raindrop falls on glass and flattens into a pancake. Add a bit of polymer to the water, and it becomes elastic, like jelly. You'd think such a jelly would spread differently.

The brain self-cleans its waste: cerebrospinal fluid flows through narrow channels surrounding arteries. The channel walls are soft and ripple with each pulse, and the tissue is porous like a sponge. Every heartbeat turns arteries into tiny pumps, driving fluid through the pores.

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 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.

An ordinary magnet always carries two poles — north and south. Split it in half, and each piece immediately grows its own pair. But deep in particle theory lives a strange notion: the monopole — a particle carrying just one magnetic charge, a lone pole without a partner.

When you squeeze ketchup out of a bottle, you're battling its stubbornness: it sits still at first, then suddenly shoots out in a blob. That's typical non-Newtonian behavior — resistance to flow changes with how hard you push. But the authors of a new study found a way to almost completely eliminate that resistance.

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.

An air bubble escapes from a thin needle at the bottom of a glass and shoots upward. In clean water, it behaves like a spring: it flattens, then stretches, exchanging energy between motion and shape. Add a drop of soap to the water, and the bubble immediately calms down, becomes an almost perfect sphere, and rises smoothly without trembling.

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.

Near black holes and neutron stars, plasma churns like water in a boiling kettle. But this 'kettle' has no walls — only magnetic fields that twist and tear. At the tears, thin sheets form where magnetic field lines reconnect, giving particles a kick like a surfer catching a wave.

The Mpemba effect is surprising: hot water sometimes freezes faster than cold. Scientists built a simple model: a bead in a thick, honey-like medium, on a landscape with two dips and a wall at the edge. The bead moves viscously, unable to hop over the central bump.

Lymphatic vessels are one-way streets. Through them, fluid flows only forward thanks to tiny flap valves. These valves open in just one direction, creating asymmetry, directionality, without which the flow would stop. In the lab, scientists modeled a vessel and sent compression waves along it, like a parade of gentle nudges.

Splitting water into hydrogen and oxygen with electricity is an age-old dream of clean fuel. But tiny gas bubbles stand in the way: they cling to the electrodes like foam on the side of a soda glass, interfering with the current's work. Each bubble is a tiny plug, blocking part of the surface where the reaction should occur.

In quantum batteries, charging can be accelerated by shuffling the steps in time, like a deck of cards. Instead of a smooth energy climb, you get abrupt efficiency explosions, like microscopic supernovae inside atoms.

In a wind tunnel, air accelerates to enormous speeds and breaks into a chaos of eddies. To see how this chaos dies on the smallest scales, scientists took a sensor thinner than a human hair and placed it in the flow. Inside the tunnel, they created a shear layer — a region where fast air rubs against slow air, spawning vortices.

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.

A branching network, like a river delta or a tree crown, is built on the principle of economy. The classic law, derived back in 1926, stated that the cube of the parent vessel's diameter equals the sum of the cubes of the daughter diameters. This rule worked beautifully for ideal tubes, but real arteries stubbornly gave a different exponent — around 2.7 instead of 3. The authors of the new study found the reason.

A pot of water heated from below is a simple example of turbulence. Hot fluid rises, cold fluid sinks, and the flow spontaneously breaks into rotating cells that look like horizontal rolls. In a new study, physicists took a wide rectangular container (ten times longer than its height) and tracked how many such rolls appear.

In a narrow vertical tube, alcohol flows upward, surrounded by water, and carbon dioxide bubbles are born inside it. As soon as they appear, they rush toward the axis of the flow, as if an invisible hand gathers them into a neat chain.

A drop falls into a glass, and a tiny jet, a thin fountain, shoots up from the surface for an instant. Something similar happens with a bubble stuck to the wall of a tube when you yank the tube downward. Water around the bubble rushes in, and a jet fires from its top. The speed of this jet depends on the bubble's shape — how much it bulges, like an umbrella dome.

Rain doesn't fall just any old way. If you take records from nearly fifty thousand rain gauges scattered across the globe and compare how much water falls on a rainy day in different parts of the planet, you'll spot a surprising pattern.

The ocean is like a layered cake: warm, light water on top, cold, heavy water below. Between the layers, at the interface, invisible waves roam. They don't lift crests like a storm; instead, they slowly rock the entire water column, as if someone were shaking a giant aquarium from within.

The law discovered by Wolfgang Pauli forbids identical particles from occupying the same spot. Hence, in cold matter, a Fermi sea is born: particles, like water, fill energy levels from bottom to top. The shape of the sea's surface — including 'islands' of emptiness — dictates the properties of the whole system.

The Paglia River behaves like a pendulum that resists being pushed. If a sudden influx of water pours in, the river does not keep gaining strength but quickly swings back to its usual level. This behavior is called antipersistence, and it was found in a twenty-two-year record of half-hourly discharge measurements near the Italian town of Orvieto.