Today we understand turbulence well enough so that airplanes don't fall from the sky and liquid fuel igniting inside a rocket engine produces enough thrust to blast payloads into space.
We even exploit turbulence to make golf balls fly farther (ever noticed the dimples?) and stir milk thoroughly into a cup of tea.
Turbulence is the seemingly chaotic motion of gases and liquids (collectively known as fluids) under certain conditions, such as the smoke rising from a lit cigar or an oil film blown by the wind while floating on a puddle of water.
Water flow experiments through pipes, conducted by Osbourne Reynolds at the turn of the 20th century, gave rise to a basic understanding of the laminar (smooth flow) to turbulent transition through the Reynolds number. The governing partial differential equations for fluid flow, incorporating turbulence, were proposed even earlier by Navier (1827) and Stokes (1845). The Navier-Stokes equations assume fluids to be a flexible continuum (think "jelly") rather than a collection of molecules (think "salt grains"). Yet even with this simplification the Navier-Stokes equations remained stubbornly difficult to solve until the advent of computers and numerical analysis.
In recent times direct numerical simulation of the Navier-Stokes equations on the most powerful parallel computers has lifted the veil still further on turbulence. However, engineers have simulated turbulent flows since the beginning of the computer age to make safer, faster and more efficient machines (check out Formula 1 race cars for the ultimate aerodynamic devices). How so? By exploiting cunning models of the Navier-Stokes equations within the field commonly referred to as Computational Fluid Dynamics (CFD). The cunning involves recognizing that modeling the statistically significant turbulence (turbulence modeling) captures the majority of engineering flows relatively accurately. This makes such modeling possible on a laptop PC.
Yet for all our progress in simulating turbulent flows we are still limited to inaccurate five-day weather forecasts. The accuracy of our forecast models (though not perfect) is not the problem; it is the measurement of the initial conditions fed into those models. The well-known butterfly effect is at work or more formally the nature of the system (and therefore any model of it) is chaotic, which means acute sensitivity to initial conditions. Essentially our weather forecasts and many environmentally driven simulations (e.g. pollution plumes from power stations) are hindered by our inability to provide accurate initial conditions.