When experiencing turbulence, fluid elements undergo stretching and folding

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.

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

As energy is lost in fluids undergoing turbulent, non-linear flow, particles will collectively form eddies, or whirlpools, of various sizes that mix together. The energy cascade of larger eddies becoming smaller ones before dissipating completely varies based on the initial conditions of the fluid, a characteristic feature of chaotic systems.

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.

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.

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.

Horsehead-shaped features seen on the sun and the clouds of Earth and Jupiter are examples of Kelvin-Helmholtz instabilities, where a faster-moving fluid rolls atop a slower-moving fluid.

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.

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.

Atmospheric processes amplify the strength of storms by coalescing clouds

Research has shown that turbulent mixing of air at the edges of clouds and other small-scale thermal activity beneath them help clouds group together, intensifying short bursts of rainfall, especially in tropical regions. Simulations reveal this produces more powerful storms than predicted by older models, though they may occur less frequently.

The turbulence experienced in airplanes results from unexpected changes in airflow

Pilots rely on forecasts, onboard tools, and air traffic control to avoid regions of severe turbulence during flight. Turbulence is generally weaker for those sitting in the front of the main cabin and for morning flights that follow cooler nighttime temperatures.

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.

The Navier-Stokes equations are fundamentally accurate but unsolved in 3D

The equations model fluids and have been shown to have solutions for all systems in two dimensions. Averaging and approximations let the equations be used in climate models, aerodynamics, and medicine, though their use in some systems produces nonsensical answers.

The Navier-Stokes equations include the fluid version of Newton's second law

The first equation is the fluid version of the conservation of mass, which prevents incompressible fluids from gaining or losing matter. The second equation replaces acceleration and inertia, which is resistance to acceleration, with fluid pressure and viscosity.

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.

Explore a visualization of curved spacetime under general relativity

While depictions involving bends in elastic fabrics are common to illustrate gravity, they are circular representations that rely on gravity in the real world to depict gravity in the model. The river model instead shows how bends in spacetime convert speed through time into speed through space, producing acceleration.

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.

Wave tanks can be used to create and study the impacts of tsunamis by building tension in an underwater object before allowing it to slip and rapidly displace water.

Tornado formation relies on wind shear to create a tube of rotating air

Once a horizontal vortex is created by air circulating between winds of different directions and speeds, an updraft, such as those seen in powerful thunderstorms, tilts the vortex vertically. The updraft then strengthens the vortex, which becomes a tornado upon touching the ground.

Climate change is increasing the frequency and intensity of severe turbulence

Severe turbulence over the North Atlantic has increased by 55% over the past 40 years, driven by strengthened jet streams and storm systems. Ongoing increases in global temperatures, which fuel these changes, may triple severe turbulence incidents in the coming decades.

Explaining the Leidenfrost effect, where water can hover and move against gravity

Water droplets can glide across surfaces whose temperatures are well above water's boiling point. This heat instantly vaporizes the bottom of the droplet, creating a layer of steam that the rest of the droplet rides and bounces upon. This can be seen when sprinkling water on skillets to determine if the surface is hot enough to cook on.

During World War II, fighter plane turbulence was used to make ice cream.

Running a ribbon around the edge of a blade creates curls because it stretches its outer side beyond the yield—the limit at which a material can be deformed but still return to its original shape once the force is removed.

Hurricane conditions are created in a University of Miami wind-wave tank

The SUrge-STructure-Atmosphere INteraction Wind Wave Laboratory contains a 38,000-gallon wave pool connected to a wind tunnel that can generate air currents of up to 155 mph. SUSTAIN allows scientists to study how the atmosphere interacts with the ocean in extreme weather.

Simulations suggest ice's slipperiness comes from rearranging molecules

Past models have proposed that slipperiness arises from a thin layer of liquid water formed at the ice's surface by frictional melting. However, new research suggests that electromagnetic forces between interacting surfaces push water molecules out of an ordered, crystalline structure and into a shapeless, soft, slippery layer. This process occurs solely through contact, independent of pressure or friction.

View a collection of sound animations, which depict how a source of sound waves pushes against particles to carry energy away without matter being displaced.

Viscosity is a fluid's resistance to flow, which varies with temperature

Liquids become less viscous as temperature increases, while gases become more viscous and therefore flow more slowly. The increased gas collisions at higher temperatures contribute to greater friction between streamlines, increasing viscosity.

Some tectonic plates move faster than their underlying convection currents

Like a chain slipping off a ledge, as tectonic plates sink, their weight can pull the rest of the trailing plate forward, accelerating their movement. Plates can also break apart and fall, creating a suction effect that drives movement, resembling leaves following a passing car.

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

How jet streams, which reside in the troposphere, shape and confine pockets of atmospheric air

These fast-flowing ribbons of air are hundreds of kilometers wide and typically travel from west to east due to Earth's rotation, with the polar front and subtropical jets serving as major drivers of global circulation. Warmer air near the equator pushes the polar front jets toward the poles, which can buckle and deform them as they contain frigid polar vortex systems.

The origin of chaos theory, colloquially known as the 'butterfly effect'

The theory explains that systems following well-understood physical laws can still produce unpredictable outcomes due to small variations in their initial conditions. Originally identified in weather data, elements of chaos have been observed in stock market fluctuations, cardiac arrhythmias, and the evolution of online social movements.

What makes food crispy, and how science can be used to maximize this property

The fracturing texture experienced when biting into vegetable tempura, fried chicken, pastry crusts, and other foods comes from having a dehydrated, porous surface. When frying food in hot oil, trapped water vaporizes and escapes, creating tunnels and pores in the food as it dehydrates. Breading, particularly with the large, irregular shapes of panko, and leaveners can help create more air spaces.

Explore the effects of tornadoes of different scales

In this simulation, users can adjust the tornado's diameter and rotation speed to see its impact as it passes through a series of trees and a one-story home.

Scientists are experimenting with ways to probe the multiverse theory

Researchers are simulating vacuum bubbles—the theorized starting points of universes—using quantum computers, digital models, and exotic lab setups to study how they form, expand, and possibly collide. One experiment aims to "blow" artificial universe-like bubbles inside ultra-cold quantum gases, potentially capturing real-time glimpses of cosmic birth processes in a lab.

AI tools that generate images, audio, video, and 3D models rely on diffusion models, which begin with random data, such as visual noise, and gradually refine it into the requested media.

Protein content and multiple fermentations create beer foam stability

Single-fermentation beers rely on protein viscosity for foam, with lipid transfer proteins transforming into stabilizing structures during fermentation. Scientists believe foam research may result in safer lubricants for electric vehicles.

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.

Quantum field theory reveals that particles are ripples in universal fields

Instead of being made of indivisible particles, all visible matter in the universe is built from underlying quantum fields—smooth, invisible entities that behave like waves. The theory suggests these fields are fundamental, and particles are disturbances that move through them.

How chefs suspend liquid in edible pearls resembling caviar to introduce a new texture to fluids

Through spherification, drops of a solution of sodium alginate and a flavored liquid are placed in a calcium lactate solution, which forms a chemical skin around them. This is because calcium replaces the sodium in the alginate chains, forming a gel around each drop's liquid interior.

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.

'Viscoelasticity' allows muscles to be elongated briefly after stretching

The protective tissues around skeletal muscles consist of elastic proteins like collagen. Stretching them expands their length while retaining strength, ideal for athletes.

A collection of molecular gastronomy techniques, from flavored air to turning oils into powder

Soy lecithin can be blended with flavored mixtures, such as herbs and Parmesan, to produce edible bubbles, which can be frozen into a solid foam. Maltodextrin can be combined with liquid fats in a food processor to create light, flavorful powders.

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

The solar system's planets orbit in the same direction in a nearly flat disc because the particles that made up the gas cloud from which the system formed had an initial, overall plane of rotation.

Airplanes generate enough lift to fly by accelerating air faster over their moving wings, which makes the pressure above the wings lower than the pressure below.

Beyond a certain pressure and temperature, matter can become a supercritical fluid—an exotic state of matter that simultaneously exhibits properties of gases and liquids.

Various types of tornadoes are distinguished by their shape, size, and location

Waterspouts form over water as long, thin columns of mist and air, while elephant trunks are tornadoes that elongate vertically as they become tilted during their formation, resembling the mammal's appendage. Wedge tornadoes are among the most powerful, often spanning a mile or more in width.

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.

The ingredients that make up severe weather

A seven-minute video illustrating how a storm is made. These factors—moisture, instability, lift, and shear—are explained through a series of data sets and creative, descriptive diagrams.

How to create salad dressings with oil and water solutions that don't separate into layers

Such dressings, even when whisked together, often break within a few minutes, resulting in bites that are either harsh or oily. Small amounts of emulsifiers, such as mustard or mayonnaise, can stabilize and suspend oil droplets in water for longer periods because they possess both hydrophilic (water-loving) and hydrophobic (water-repelling) ends.

The 'butterfly effect' is the informal name for chaos theory

In mathematics, chaos theory involves complex systems that are highly sensitive to their initial conditions. Originally discovered when analyzing weather data, slight variations in the data input into such systems create drastically different results, despite following known physical laws.