Laminar flow in low-viscosity fluids is relatively rare in nature and industry. Turbulent flow is among the most complicated and intriguing natural phenomena and is not well understood, despite more than a century of study. Nevertheless, out of necessity, investigators developed simple models that can be used for engineering design and analysis.

Turbulent flows at relatively high Reynolds numbers (fully turbulent flows) are characterized by extremely irregular fluctuations in velocity, temperature, pressure, and other properties. At each point the velocity and other properties fluctuate around a mean value.

Turbulent flows are characterized by eddies and vortices. Chunks of fluid covering a wide size range move randomly around with respect to the mean flow. Fluid particles move on irregular paths, and the result is very effective mixing. Even the smallest eddies are typically orders of magnitude larger than the molecular mean free path (MMFP) (in gases) and the intermolecular distances. Within the small eddies, molecular (laminar) transport processes take place, but the interaction among eddies often dominates the overall transport processes and make molecular transport effects unimportant.

With respect to analysis, the Navier–Stokes equations discussed earlier in principle can be applied to turbulent flow as well. However, to obtain a meaningful solution, these equations must be solved in such a way that the largest and smallest eddies in the flow field are resolved. This approach [direct numerical simulation (DNS)] is extremely computational intensive, and it is possible at this time only for simple flow configurations and low Reynolds numbers.