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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Friction is the force that resists the sliding of surfaces along one another

Friction always acts to resist movement and is determined by how rough the surfaces are and how hard they are pressed together. In the case of fluids, friction arises from the relative motion between adjacent fluid layers, which act like sliding surfaces.

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.

Lightning is the sudden flow of electricity in the atmosphere as two oppositely charged regions seek to become balanced via the movement of electrons.

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 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.

Lava flow viscosity plays a significant role in the type of volcano formed

Thin, runny flows spread quickly before cooling, producing expansive layers that build over time into wide shield volcanoes. The ejection and fast hardening of thicker lava flows and pyroclastic material create steep slopes and the characteristic cone shape of composite volcanoes.

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.

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

Light appears to slow down as it travels through different materials

As electromagnetic waves interact with particles in a transparent medium, particles vibrate and generate their own electromagnetic waves. The interference of the original and generated waves, which are slightly delayed, results in ensemble light with an effective slower speed but unchanged color.

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.

Differences in pressure and temperature between atmospheric gases create wind

Because Earth's surface is not uniformly heated by the sun at all times, pockets of warmer and cooler air will form and interact. Warmer pockets of less dense air will rise, leaving gaps for cooler, denser air to move in. Wind is this movement of air from high-pressure to low-pressure areas.

While landslides are associated with the downward flow of unstable terrain, the term encompasses a variety of geological processes, which are distinguished by how the material moves and what materials are involved.

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.

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.

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.

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.

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.

Hurricanes spin due to differences in air and ground speed as they move across Earth

The movement of an object across latitudes causes it to take a curved trajectory because its speed no longer matches that of the ground beneath it. This phenomenon, called the Coriolis effect, explains why hurricanes spin counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.

Lightning forms when streams of rising and falling charged particles connect

In cloud-to-ground lightning, a buildup of negative charge at the bottom of clouds repels electrons on Earth's surface, leaving behind positively charged particles. When descending negatively charged air—the stepped leader—meets rising positively charged particles—the upward streamer—brightening runs up the connection, producing intense flashes known as return strokes.

Wind is the movement of air caused by the sun's uneven heating of Earth

The tilt, curvature, and variations in Earth's surface composition across the globe cause different regions to receive different amounts of solar radiation. As the Earth spins and tries to achieve thermal equilibrium, air masses move and interact, creating wind.

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.

Money laundering is a three-step process: placement, layering, and integration

"Placement" occurs when dirty money is introduced into the financial system. Then "layering" happens when the money is moved around to disguise where it actually came from. Finally, the money is placed in other assets or investments in a step called integration.

How skeletal and smooth muscles differ

Skeletal and smooth muscles are two of the three muscle types found throughout the body. The former is attached to bones via tendons, enables limb movement, and is consciously controlled. The latter is found lining blood vessels and hollow organs (e.g., the intestines, stomach, and esophagus) and is managed by the autonomic nervous system, which means it's outside conscious control.

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.

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.

Vincent Van Gogh's 'The Starry Night' accurately depicts turbulent flow

Analysis of the swirling patterns in the painting found an alignment with the mathematics used to describe turbulence, despite Van Gogh's unfamiliarity with the science. The depiction may indicate he possessed an uncanny ability to capture nature's details.

Astronomical models suggest dark matter must be 'cold,' or slow-moving

Theories for what constitutes dark matter have ranged from slow, planet-sized objects to light subatomic particles that travel at high speeds. However, fast-moving candidates would quickly spread across the universe, preventing the gradual gathering of visible matter into the galaxies and galaxy clusters seen today through gravity.

Once cooled to temperatures just above 2 Kelvin, helium atoms exhibit a quantum property that removes internal friction, allowing the fluid to climb up walls.

View the most turbulent flight routes and airports around the world

Using data from NOAA and the UK Met Office, these maps identify South America as the geographic region with the highest average turbulence. The most turbulent flights in North America are all found in the western United States.

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.

The arrow of time—the concept that time only moves in the forward direction—is thought to result from the universe progressing toward greater disorder, or entropy.

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.

Traffic flow can be improved through research into card shuffling

Card-shuffling mathematics has been applied to solving problems in biology to estimate the evolutionary distance between organisms and in computer science to determine the optimal distribution of files and folders in databases.

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.

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.

According to the special theory of relativity, because the passage of time depends on how quickly objects move through space, people will not agree on the order of events they observe if they are moving at different speeds.

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.

View the various types of lightning

The most common form of lightning involves channels of electricity between oppositely charged regions within a cloud or between two clouds to reestablish electrostatic equilibrium. While cloud-to-ground lightning is understood best, research is ongoing to fully model the mechanisms behind rarer forms of lightning, such as transient luminous events.

Particle interactions follow rules related to specific quantum properties

Like a business whose purchased inventory matches sold inventory, physicists identified specific patterns across decades of particle accelerator data, which became new conservation laws for elementary particles. These laws help identify which particle decays are expected or forbidden.