Turbulence refers to the chaotic, irregular motion of fluid (gases or liquids) that is characterized by vortices, eddies, and rapid changes in pressure and velocity. It contrasts with laminar flow, where fluid moves in smooth, orderly layers. In different contexts, turbulence can be described as follows: 1. **Physics and Fluid Dynamics**: In fluid mechanics, turbulence is seen when the Reynolds number—a dimensionless quantity that predicts flow patterns in different fluid flow situations—is high.
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Turbulence is fluid flow with irregular, interacting velocity fluctuations over a range of lengths and times. An unsteady laminar flow also has a time-dependent velocity field; the important distinction is the organization and interaction of the fluctuations. In many flows a large Reynolds number allows nonlinear advection to distort the motion before kinematic viscosity smooths it, but transition depends on geometry and disturbances as well as the chosen Reynolds number.
The Reynolds pipe-and-dye experiment makes the distinction visible. A narrow band of colored water can remain coherent in a glass pipe, then break into irregular structures and spread across the pipe as the discharge increases. The inlet and pre-existing disturbances matter, so the observation does not establish a universal transition value.[ref]
https://personalpages.manchester.ac.uk/staff/jdjackson/Osborne%20Reynolds/oreynb.htm. University of Manchester historical account, 1883 experiments and Figures 9–10
In a three-dimensional forward energy cascade, nonlinear interactions transfer kinetic energy towards smaller scales until viscous dissipation converts it into heat. This transfer helps explain why a turbulent flow mixes a passive scalar efficiently, although final molecular homogenization still requires molecular diffusion. After Reynolds averaging, correlations of fluctuating velocities produce the Reynolds stress, an additional momentum flux. Predicting that flux from mean quantities is the turbulence closure problem; a model for it is an extra physical assumption.