**Turbulence**, a scientific term to describe certain complex and unpredictable motions of a fluid, is part of our daily experience and has been for a long time. No telescope or microscope is needed to contemplate the volutes of smoke from a cigarette, the elegant arabesques of cream poured into coffee and the vigorous eddies of a mountain stream. In an airplane we sometimes experience bursts of “clear air turbulence”. Ultrasonography can reveal turbulent blood flow in our arteries; satellite pictures may show turbulent meteorological perturbations; computer simulations reveal turbulent fluctuations of mass in the Universe on scales of tens of megaparsecs. Without turbulence, urban pollution would linger around for centuries, the heat produced by nuclear reactions in the interior of stars would not be able to escape on an acceptable time scale and meteorological phenomena would be predictable almost for ever.

Actually the word “turbulence” (Latin: turbulentia) originally refers to the disorderly motion of a crowd (turba). In the Middle Ages it was frequently used to mean just “trouble”, a word which derives from it. Even today “turbulent” may refer to social or personal behaviour. Its scientific usage refers to irregular and seemingly random motion of a fluid. This definition, which is far from exhaustive, tries to express in a synthetic way one of the most complex and fascinating phenomenon of natural science, from Antiquity to present days.

The subject has indeed a very long history. Lucretius described eddy motion in his De rerum natura. Subsequently, Leonardo was probably the first to use the word turbulence (in Italian turbolenza) with its modern meaning and to observe the slow decay of eddies formed behind the pillars of a bridge. Next, Euler wrote the equations of incompressible ideal or inviscid (zero-viscosity) flow in both two and three dimensions and realized the importance of vorticity. Years later Navier generalized these equation to include viscosity. Because of further work by Stokes, the equations are known as the Navier–Stokes equation.

In fluid dynamics, **turbulence** or **turbulent flow** is a fluid flow regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. A flow that is not turbulent is called laminar flow. The (dimensionless) Reynolds number characterizes whether flow conditions lead to laminar or turbulent flow.

The flow of water over a simple smooth object, such as a sphere, illustrates it. At very low speeds the flow is laminar; i.e., the flow is smooth (though it may involve vortices on a large scale). As the speed increases, at some point, the transition is made to turbulent (“chaotic”) flow. In turbulent flow, unsteady vortices appear on many scales and interact with each other. Drag due to boundary layer skin friction increases.

The structure and location of boundary layer separation often change, sometimes resulting in a reduction of overall drag. Because the laminar-turbulent transition is governed by Reynolds number, the same transition occurs if the size of the object is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is increased.