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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

An overview of Earth's atmospheric cells and how they distribute Earth's uneven heating

The Hadley, Ferrel, and Polar cells are circulation patterns that act like gears, moving warmer air from the equator to the poles. The rising and falling of air currents within these patterns creates semi-persistent regions of low and high pressure, which contribute to the formation of regional climates, such as tropical zones.

Trade winds blow from east to west due to the Coriolis Effect

Warm air rises near the equator while cooler air sinks near the poles, creating circulation patterns that curve due to Earth's rotation. At the equator, doldrums—calm regions of no wind—build warm, moist air, creating storms.

All hurricanes have a central eye where no extreme weather phenomena take place

When standing in the eye of a hurricane, you're likely to experience sunny, cloudless skies surrounded by a wall of intense winds and thunderstorms. The physics behind this formation is the same as what causes water to spiral around a hollow cone as it goes down a drain.

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.

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.

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.

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.

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 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.

Convection flows in Earth’s mantle drive the movement of tectonic plates

These processes transfer heat from Earth’s core to the surface via rising magma plumes, while cooler, denser rock falls into the mantle at rates similar to human fingernail growth. These rates are determined by combining seismic data with computer simulations to model Earth’s interior.

How its uneven rotation produces the sun's 11-year cycle and flips its magnetic poles

While charged material rises and falls in the sun's convection zone, which induces magnetic fields, different latitudes rotate at different rates, making these fields increasingly turbulent. This builds to a critical point—the solar maximum—where magnetic field-driven events, such as solar flares, become more common before the field collapses and flips, restarting the cycle.

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.

The centrifugal force is associated with the feeling of being pushed outward when moving in a circle, but it is a fictitious force arising from objects' tendency to move in straight lines.

Earth's magnetic field can trap high-energy charged particles produced by the sun and distant cosmic events in doughnut-shaped rings called Van Allen belts.

The history of helioseismology, which studies seismic waves traveling within the sun

Following World War II, scientists began studying the sun's influence on radio waves, the most popular form of mass communication at the time. NASA missions to study the sun's interior have since helped develop explanations for various phenomena in its atmosphere and protect digital infrastructure.

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.

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.

Just as the moon deforms the Earth to create tides, Jupiter deforms its moon, Io, generating the thermal energy in Io's interior that powers the more than 400 volcanoes on its surface.

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.

The life of Edward Lorenz, who originally used a seagull in his 'butterfly effect' metaphor

By accidentally finding that rounding one variable to its third decimal place and re-running a weather simulation produced a drastically different two-month forecast, the American mathematician established the field of chaos theory. His paper—"Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?"—introduced the well-known metaphor for the behavior of chaotic systems. (Some readers may experience a paywall.)

Differential rotation and density waves create the arms of spiral galaxies

Stars and gas near the galaxy's center complete an orbit in less time than objects farther out. Pressure waves cause material to bunch, lagging behind stars and gas that orbit closer to the center and forming the arms.

Instabilities in the polar jet stream can bring cold Arctic air southward

The polar jet stream marks the boundary between mid-latitude air and the much colder polar air, which are normally contained by the polar vortex—a ring of strong winds that circles the Arctic around 16 to 50 kilometers (10 to 30 miles) above the Earth's surface. Climate change may be responsible for "blocking patterns" that distort the jet stream, allowing polar air to leak into lower latitudes.

Heat slowly moves through Earth's mantle like softened wax

Energy trapped during Earth's formation and released via the radioactivity of elements is carried by convection currents towards the surface, while cooler, denser material sinks. The planet's core is almost as hot as the sun's surface.