Turbulence

Turbulence is irregular fluid motion marked by interacting vortices and fluctuations across a range of scales. It transports momentum, heat, and material in ways that are difficult to predict precisely.

Reynolds number: A dimensionless ratio of inertial forces to viscous forces in fluid flow. It helps predict when a flow becomes susceptible to turbulence.
Fluid mechanics: The study of fluids and the forces and motion that govern them. Turbulence is a complex regime of fluid motion.
Boundary layer: A thin region near a surface where fluid velocity changes from the surface value to the outer flow. Turbulent boundary layers strongly affect drag and surface heat transfer.
Laminar flow: Fluid motion in smooth layers with little mixing between adjacent layers. It contrasts with turbulence’s irregular fluctuations and vigorous mixing.
Turbulence modeling: The development of mathematical approximations for turbulent effects in fluid-flow calculations. Engineering predictions depend on models for unresolved turbulent motion.
Vortex stretching: The amplification of vorticity when a three-dimensional fluid element stretches along its rotation axis. It transfers energy into smaller-scale rotational motion in three-dimensional turbulence.
Viscosity: A fluid property that measures resistance to deformation and internal flow. It dissipates turbulent motion, especially at the smallest scales.
Atmospheric boundary layer: The lowest part of the atmosphere, directly influenced by the surface over timescales of about an hour or less. Its turbulence mixes heat, moisture, and pollutants between the ground and air.
Transition to turbulence: The process by which a flow changes from laminar motion to turbulence. It identifies the route into turbulence, rather than turbulence’s fully developed state.
Navier–Stokes existence and smoothness: A Millennium Prize Problem asking whether three-dimensional incompressible Navier–Stokes solutions exist globally and remain smooth. Its mathematical questions concern equations that also govern many turbulent flows.

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