Understanding turbulence, which is characterized by growing chaos at multiple scales

Mathematics proves turbulence's chaos creates super diffusion

Turbulent flow is responsible for the rapid scattering of dandelion seeds, volcanic ash, and untied balloons. Its swirling behavior accelerates particle scattering faster than other mixing methods, as particles acquire energy from the interactions of eddies.

Turbulence has been called the most important unsolved problem in classical physics

Despite being the most common type of fluid flow in our world, scientists have struggled to model turbulent flow accurately. Though behaving unpredictably, understanding inertia and viscosity can help determine whether turbulence will occur.

View the transition from laminar to turbulent flow

Using a dye released in the water, streamlines, which are parallel to one another and consistent at low flow velocities, become visible. As the water moves more quickly, viscosity cannot suppress the velocity change, and streamlines become chaotic, creating turbulence.

When experiencing turbulence, fluid elements undergo stretching and folding

Simulations show patches of fluid particles, such as splashes of milk, bend under turbulent flow, creating curvature that grows linearly then exponentially. This accelerated deformation enhances folding and mixing faster than other methods, such as stirring or beating.

Laminar flow moves in smooth, parallel layers, while turbulent flow is chaotic

In laminar flow, particles that make up a fluid move in consistent paths that do not cross each other. Contrastingly, differences across the speed of these particles cause them to mix, creating turbulence when viscosity cannot suppress the differences.

Learn how natural systems exhibit characteristics of chaos theory

In biology, some mathematical models of ecosystem populations and heart irregularities show strong sensitivity to initial conditions, which scientists can simulate to determine quantitative tipping points at which these systems become unstable. Within the social sciences, crowd behavior and the virality of social media posts have shown how human behavior fits within the framework of chaos theory.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

View the Lorenz attractor, a graphical solution to chaotic equations that resembles a butterfly

The discovery of chaos theory came from Edward Lorenz's computer model of the atmosphere, which used three equations to quantify atmospheric circulation. However, the chaotic evolution of this system creates wandering figure-8-like shapes—some resembling butterfly wings—as it repeatedly attempts to settle on one of two values along unique trajectories.

The universe only evolves toward increasing disorder, providing a direction to time

Within physics, the second law of thermodynamics states that entropy always increases, as seen by a concentrated drop of dye slowly diffusing throughout a cup of water, increasing disorder. Because such processes do not unfold in reverse, entropy may be what provides time with a single direction, unlike space.

Turbulence is crucial to the formation of stars in molecular clouds

Within simulations of these clouds, gravity, jets, supernovae, and galactic motion-induced stirring have been shown to develop turbulence that creates shocks. These turbulent shocks move quickly in low-density regions and slow in high-density areas, forming lumps of matter with sufficient gravitational force to collapse and initiate fusion, birthing a star.

A mathematical and visual analysis distinguishing chaos from randomness

Random systems lack any underlying pattern or causal relationships, while chaos is mathematically deterministic because the behavior follows established laws of nature. In 3D plots, chaotic systems produce outputs that approximate a mathematical function, while random points appear as statistical noise.

Turbulence is needed to make airplanes more stable and golf balls fly farther

Vortex generators—small fins placed along airplane wings—create small eddies that prevent airflow separation, maintaining lift and preventing stalls. Golf balls have dimples that create a turbulent boundary layer on their surface, minimizing drag forces.

Pilots are familiar with multiple types of turbulence, each with varying severity

Each type is defined based on what disrupts airflow in the atmosphere, including thunderstorms, mountains, and wakes produced by aircraft that previously took off. Pilots classify turbulence as light, moderate, severe, or extreme based on how it affects aircraft movement.

An explanation distinguishing the butterfly effect from causality, necessity, and sufficiency

In pop culture, the analogy has conveyed the impression that the flapping of a butterfly's wings has a cascading effect that directly produces a tornado somewhere else on Earth. However, butterfly-wing flapping alone is insufficient to cause tornadoes, as the complexity of atmospheric systems requires many more conditions to produce them, any of which can be the tipping point to initiate tornadogenesis.

Swimming in schools helps some fish conserve energy in turbulent flows

Scientists studying groups of giant danios swimming in turbulent waters found that the fish used up to 79% less energy than they did when swimming individually in the same conditions. The same fish were found to use the same amount of energy in turbulent and calm water when in schools.

Researchers identify a hidden instability pattern in simple ocean wave models

Stokes waves—a solution to the mathematics of water waves—were once assumed to be stable. Italian mathematicians have proven disturbances cause these waves to collapse and such collapses follow an infinite repeating pattern. To complete the proof, the team offered a $100 donation to solicit online help.

In a tornado outbreak, a single severe weather system can spawn multiple twisters

By maintaining the ingredients for tornadoes—differences in wind speed and direction across altitudes, moisture, and rising air—for long periods of time as it moves across a region, a severe thunderstorm can continuously produce tornadoes by lifting multiple columns of horizontally rotating air.

Explore a simulation of ideal gas behavior, which can be explained by kinetic molecular theory

The theory describes particles as moving in random directions, with a distribution of velocities determined by the gas's temperature. The particles collide elastically like billiard balls, are negligibly small, and do not exert forces on one another. The gas laws can be derived from these principles using statistics or observed via this interactive.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

The Reynolds number is the ratio of viscous and inertial forces in fluids

It can approximate fluid behavior in simple systems by non-dimensionalizing—removing the units within—the Navier-Stokes equations. A value close to zero indicates that the fluid will exhibit laminar flow, while a large number suggests that turbulence will occur.

The ultraviolet catastrophe is the infinite energy prediction of classical physics

When scientists first tried calculating the radiation emitted by a heated object, their assumption was that energy was equally distributed across wavelengths and produced infinite energy at low wavelengths. This contradicted observations, which showed near-zero energy intensity at those values.

Emergent quantum phenomena can produce nonfundamental quasiparticles

While physicists have discovered new particles by colliding known ones at high speeds, placing known particles in extreme environments or configurations can allow quantum mechanics to produce bizarre behaviors, making them seem like new types of matter.

Explore a simplified breakdown of the Einstein field equations

Often depicted as one formula, Einstein's equation represents a suite of 16 nonlinear partial differential equations, which can be simplified to six unique ones, that relate the geometry of spacetime to the presence of mass and energy.

Is ice slippery because of amorphization—a chaos of molecules caused by sliding?

Traditional explanations cite three factors that make ice slippery: pressure, friction and so-called premelting. A fourth has been proposed in recent years: amorphization, that sliding along some surfaces creates molecular disorder, causing liquid-like behavior.

Within topology, time can be modeled as restarting after reaching its 'edge'

A manifold is any space that appears flat when zoomed in close enough, even if it is globally curved. Some of these structures can be curved to connect back on themselves, much like bending a line into a circle. This property can be mathematically established in a four-dimensional manifold by allowing time to loop back on itself.

Dirty lightning is a thunderstorm created from friction between rising and falling flows of ash and smoke during volcanic eruptions.

Wind energy 101

Learn more about the wind industry, from how a wind turbine works, to the new and exciting research in the field of wind energy.

Stars appear to twinkle because turbulence in the motion of molecules in Earth's atmosphere causes light to bend and wiggle rapidly on its way to the surface—a phenomenon called scintillation.

How fusion—which releases energy when two lighter atoms combine to form a heavier atom—differs from fission

Hurricanes, which rely on air consistently spinning in the same direction, cannot cross the equator because air curves in opposite directions north and south of it.

All rainbows are 'raincircles' caused by water droplets separating white sunlight into a spectrum of colors, but Earth's surface blocks the bottom half of the circle from our line of sight.

The boiling temperature of water decreases with increasing elevation because the molecules need less energy to overcome the lower atmospheric pressure associated with thinner air.

Pure water does not conduct electricity because this flow of energy requires the movement of charged particles, and water is a neutral molecule.

Some renewable energy sources may weaken the resiliency of electric grids by removing outage buffers provided by coal- and natural gas-fired plants, which provide the system with more time to find a new power source if a plant goes down.

Explore our favorite visualization of the immense scale of space, from an astronaut to the size of the observable universe

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

Ebola infects and disables immune cells, triggering a cascade of events that leads to small blood clots throughout the body, weakening blood vessels and interrupting blood flow to key organs.

Waves off the coast of Nazaré, Portugal, can reach over 100 feet and are caused by the area's deep underwater canyon geography

Watch how algorithms can be designed to train themselves and self-improve without human input, to the point where the optimized code is too complex for programmers to understand.

The word 'jazz' evolved from 'jasm,' 19th-century American slang for 'energy'

To reduce wrinkles in clothing, research recommends gentle wash cycles with more water and tumble drying with smaller loads and longer times.

Gerrymandering works through two techniques: cracking opposing voters across districts to dilute their power, and packing them into a few to waste their votes in lopsided majorities.

Fear or disgust related to clusters of holes and cracks, called trypophobia, may stem from evolutionary processes to help us avoid pathogens.

The rivalry between Alexander Hamilton and Thomas Jefferson centered on federalism—the question of how much power the federal government should hold relative to the states.

While the first exchange-traded fund (a 'basket' of different assets that can be bought and sold on a stock exchange) in the US only launched in 1993, the global ETF market has grown to more than $10T in the short time since.

SpongeBob exemplifies Aristotle's philosophy for living well because he understands that happiness doesn't come from external factors like money, recognition, or power.

The Russia-Ukraine conflict is the largest ground war in Europe since World War II in terms of casualties, forces mobilized, and displacement of civilians.

Planarian flatworms are small, aquatic worms with exceptional regenerative capabilities. When cut, the worms can regenerate multiple bodies in a matter of weeks.

The Brothers Grimm were lawyers before they were storytellers, but became interested in fairy tales as they began investigating how rules and customs had been passed down through cultures.