Background
Turbulence is the irregular motion of fluid—a liquid or a gas—characterized by the presence of eddies, or spirals, in a wide range of sizes.
Unlike laminar flow, where all parts of the fluid move together smoothly and consistently, turbulent flow is an example of chaos, where paths taken by individual fluid particles—called streamlines—combine, separate, and mix unpredictably (see visualization).
Turbulence is commonly associated with jolty aircraft movement, resulting from deviations in expected wind currents (watch explainer).
Despite being an everyday experience, turbulent flow has been impossible to predict mathematically, limiting our ability to accurately simulate fluid phenomena, including blood flow, pollution dispersion, and climate change (1440 Topics: Climatology).
What Causes Turbulence
Whether laminar or turbulent flow occurs depends on the result of two competing fluid properties: inertia and viscosity.
Inertia—as described in Newton’s laws of motion—is an object’s ability to maintain its existing motion. Fluid particles naturally continue with the velocity provided by an external force.
Viscosity measures resistance to flow and is colloquially described as a fluid’s “thickness.” Honey spills more slowly than water, so honey is more viscous.
Viscosity comes from friction between streamlines in a fluid. Like cars stuck near one another as traffic slowly moves, this friction prevents neighboring fluid particles from achieving significant differences in velocity (friction, explained).
However, it is common for particles in a fluid to undergo inconsistent velocity changes when interacting with their surroundings. For example, a boulder can slow the movement of river water that collides with it, while water moving far from the boulder is unaffected.
High viscosity suppresses these velocity differences, keeping streamlines together. Low viscosity will be overwhelmed by inertial forces, causing streamlines to push into one another and turn—just as a person in a hurry turns when squeezing between others moving more slowly in a crowd (watch visualization).
Properties of Turbulence
Turning streamlines produce large-scale eddies, which carry a fluid’s kinetic energy into patterns that resemble whirlpools. As eddies collide, they break into smaller, less energetic ones and undergo turbulent mixing—the fastest way to mix substances.
After multiple collisions and splits, the eddies become slow enough to be stamped out by a fluid’s viscosity, dissipating any remaining energy as heat. This gradual energy transfer from large to small scales is called the energy cascade.
Every system has a unique layout of eddies and how the cascade progresses—where turbulence begins and evolves. Replicating the results of any turbulent flow experiment is impossible because it requires identical velocity differences across every fluid particle.
For this reason, turbulence is considered mathematically chaotic—turbulent flow follows well-understood rules, but minor changes to initial conditions produce drastically different outcomes (watch explainer).
Modeling Turbulence
Tracking every fluid particle’s properties across time and size scales makes numerical solutions of the Navier-Stokes equations—physical laws that describe fluid motion—impossible to calculate, even on supercomputers. As of 2021, the largest particle simulator in the world models 60 trillion particles, but a single cloud can have quintillions of times as many.
The equations have also not yet been proven to work in three dimensions for all initial conditions and scales (watch explainer). In 2000, the Clay Mathematics Institute announced a $1M reward to anyone who could do so.
Instead, scientists model turbulence with modified versions of the equations (e.g., resolving patches of fluid representing the average of many particles rather than each one). In addition, wind tunnels and water channels can be used to investigate the effects of turbulence.
Accurately modeling turbulent flow would do more than improve aviation safety. Scientists and engineers could improve any technology involving fluids and energy, including the accuracy of weather and ocean mixing models, the fuel efficiency of vehicles, and the energy generation of wind turbines.
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