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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Unlike quantum mechanics, classical physics suggests free will does not exist

Models based on Newton's laws of motion suggest all actions are predetermined and must follow specific trajectories and outcomes, such that everything that will ever occur in the future has already been set in motion by past causes. However, quantum mechanics challenges determinism because it is based on probability, where no outcome is certain.

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.

As of 2025, the Standard Model has at least five unresolved problems

Among the issues with the most successful theory of the universe at subatomic scales is its inability to explain the extreme imbalance observed between visible matter and antimatter, since both should be roughly equal. The Standard Model also omits gravity and cannot account for the observed rate of cosmic expansion.

Science is rarely a linear progression of understanding

Particularly at the frontiers, investigations conducted based on established knowledge can provide unexpected results. This opens the door to revising existing models, inspiring new lines of research, and ultimately leading to better future comprehension. For instance, experiments on the speed of light and the expansion of the universe yielded then-confusing data that led to revolutionary insights.

Even in a perfect vacuum, empty space is full of quantum activity

Scientists have tried to create “nothing” by removing all matter, energy, and heat from a container, but the uncertainty principle and relativity prevent such conditions within any period of time. This means the universe is full of quantum foam, which can produce forces from nothingness.

Their 1901 Wind Tunnel system revolutionized the study of aeronautics

Only the second to be built in the US, the wind tunnel allowed the brothers to study how air moves around more than 200 different wing shapes. This data helped them refine a key math equation, long held as the standard, that had been based only on one wing shape.

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.

Physicists detect the sound of heat in superfluids, theorized since 1938

Referred to as "second sound," the flow of heat in a superfluid resembles a sound wave bouncing back and forth. The heat-mapping techniques used to make the detection may improve the study of neutron stars and superconductors.

Watch a simulated flight through Jupiter's Great Red Spot

Since its discovery over 350 years ago, the anticyclonic storm—with a high-pressure center and flows opposite to the low-pressure system underneath it—has fascinated astronomers due to its size, which is larger than Earth's, and its prominent features, including winds that surpass 250 miles per hour.

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.

Tachyons are theoretical particles that travel through space faster than light

The equations of special relativity require these objects to possess imaginary mass, and they would travel faster the more energy is taken away from them. The existence of tachyons would necessitate an unknown form of matter and lead to paradoxes involving information that can hypothetically travel backward in time.

Why dizziness is still a mystery

Dizzy spells can completely upend the lives of those suddenly struggling to find their footing. Despite this severe impact, the different flavors of dizziness and their sources continue to elude medical understanding. This article follows a health...

How salt, sunlight, and wind drive ocean currents

The Atlantic Meridional Overturning Circulation plays a critical role in regulating earth's climate, but is threatened by climate change. Explore the effects of temperature, density, and salinity on ocean currents in this 13-minute PBS video.

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.

Most of the observable universe's volume consists of voids and supervoids—enormous regions of space with little to no galaxies, stars, or light.

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.

The deadliest aspect of volcanic eruptions is often not lava, but pyroclastic flows—avalanches of ash, gas, and rock that can move more than half the speed of sound.

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

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

The Mona Lisa's celebrity status and repeated restorations have obscured what made the painting so revolutionary for its time

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.

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

The US dollar is the most widely circulated currency in the world, and is involved in nearly 90% of global transactions

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

Discover the catastrophic consequences of a failure of the US electrical grid—something that is more likely than many Americans think.

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

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

Larger animals like giraffes, elephants, and blue whales have developed a unique defense against cancer, a phenomenon known as Peto's Paradox

How the most famous Ebola book, The Hot Zone, which sold 3.5 million copies and was translated into 30 languages, got aspects of the disease so wrong.

Double world record holder Hunter Ewen helped conquer his fear of balloons, called globophobia, by training to win Guinness World Record titles for balloon inflation.

Researchers believe the brain consolidates memories, processes emotions, and plans for the future during dream states

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.

The first robot in literature may have been a 'mechanical man' in 1907's 'Ozma of Oz,' a book in L Frank Baum's 'Wizard of Oz' series.

Objects can be 3D printed with light by projecting 2D computerized tomography (CT) scans onto rotating cylinders of resin, which solidify upon exposure.

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.

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