Turbulence

Turbulence is a feature of fluid flow characterized by chaotic, irregular fluctuations in velocity and pressure. In turbulent regions the flow exhibits rapid mixing, high levels of momentum and heat transfer, and substantial spatial and temporal variability, in contrast to laminar flow, which is smooth and orderly.

Most turbulent flows arise at high Reynolds numbers or near obstacles. The motion contains a wide range of interacting length and time scales. Energy is typically injected at large scales and cascades to progressively smaller scales until viscous dissipation converts it to heat. Kolmogorov's theory provides a statistical framework for the small-scale structure, predicting an inertial range where statistics depend only on the rate of energy transfer and viscosity, and leading to universal scaling in the appropriate limit. But real flows near boundaries or with strong shear deviate from this idealization.

Governing equations and closure: Turbulence is governed by the Navier-Stokes equations. Averaging these equations introduces Reynolds stresses, creating a closure problem that necessitates turbulence models. The state of turbulence is commonly quantified by the Reynolds number, Re = UL/ν, where U and L are characteristic velocity and length scales and ν is kinematic viscosity; as Re increases, flows tend to become turbulent.

Applications and measurement: Turbulence influences aerodynamic drag, heat and mass transfer, mixing, and weather and ocean dynamics. It is studied using experiments and simulations, including hot-wire anemometry and particle image velocimetry, and computational approaches such as direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds-averaged Navier–Stokes (RANS) with closure models.