In the chaos of turbulence, scientists chase glimpses of hidden order Premium

Moving fluids like air and water contain mysterious, chaotic patterns of motion called turbulence. Nonlinear equations and sensitive initial conditions make it hard to predict, but experiments and simulations using the Navier-Stokes equations have revealed pockets of order. Scientists are being led by these glimmers of hope and aspire to one day have a self-consistent theory of turbulence.

We frequently come in contact with moving fluids like air and water, probably without realising that these mundane daily occurrences are in fact encounters with one of nature’s more profound mysteries.

Consider the smoke rising from an incense stick. For a short distance, the plume of smoke remains well-ordered with a definite, if also twisting, shape. Then the plume suddenly breaks up, contorting and swirling into multiple eddies, or whorls. This irregular, seemingly random fluid motion is turbulence.

The disordered patterns of turbulent motion rapidly mix the agarbatti’s aroma with the air, allowing you to enjoy the fragrance from across a large room just a few seconds after it is lit. Such turbulent mixing also kickstarts our mornings, when we stir milk and sugar into our tea and coffee: without turbulence, you’d have to wait for about a month to enjoy a uniformly sweetened cup. You also create turbulence with every breath you exhale: the air gushing out of your nostrils forms short-lived and complex flow patterns that become visible on a frigid winter day.

Chaotic fluctuations, sudden bursts of motion, hard-to-predict variations – these features are typical of turbulent flows. Yet they also contain persistent swirling patterns called vortices. In water streams and cloudy skies, vortices have inspired artists and imprinted themselves upon our collective visual consciousness through the work of Leonardo da Vinci and Vincent van Gogh. That turbulence has ordered patterns is a testament to its origin in the laws of mechanics: turbulent whorls don’t turn on a whim, after all, but are governed by deterministic, well-understood physical forces.

The two key physical effects that determine the state of a fluid’s motion are inertia – the tendency of a fluid to keep moving – and viscous friction, which tends to bring all motion to a halt. The strength of inertia increases with the speed of motion, the mass of the fluid, and the distances over which the flow occurs. The strength of friction is determined by the fluid’s viscosity, which is higher for honey, moderate for water, and lower for air.

When viscous effects dominate, a flow is well-ordered and predictable, and disturbances quickly dampen out. There is little mixing and the fluid tends to move as if it were composed of distinct layers, which is why it’s called laminar flow. But when inertia dominates, the flow is highly unstable. Without much friction, small disturbances don’t die out but instead grow and spread. This is what happens to a rising plume of incense smoke: tiny fluctuations in the air are amplified within the plume, causing it to become turbulent.

The balance between fluid inertia and viscosity (and other forces due to pressure differences and gravity) are precisely described by the Navier-Stokes equations, which extend Newton’s law for a rigid body (like a billiard ball) to a fluid. These equations, now about 200 years old, describe both laminar and turbulent flow. They’re compact enough to fit on a postcard and don’t look formidable – yet they are. Today, we can use powerful supercomputers to solve them to an extent to determine how some turbulent flows might behave, but even this hasn’t allowed us to crack all their mysteries.