Turbulence is the state of vortex fluid motion where the velocity, pressure and other properties of the flow field vary in time and space sharply and irregularly and, it can be assumed, randomly.

Turbulent flows surround us, in the atmosphere, in the oceans, in engineering systems and sometimes in biological objects. A contrasting class of fluid motions, when the fluid moves in distinguishable layers (laminae in Latin) and the flow-field properties vary smoothly in time and space, is known as laminar flow. In Figure 11.1 an example of the time dependence of the velocity in a turbulent flow is presented. For laminar flow the time dependence would be a smooth line.

Leonardo da Vinci already knew about and clearly distinguished these two types of flow. Leonardo even used the term “turbulenza”. However, his observations and thoughts were buried in his notebooks, solemnly and carefully preserved in the Royal and Papal archives. They were not published until recently and therefore most regrettably did not influence future studies.

The systematic scientific study of turbulence began only in the nineteenth century, and here two names should be mentioned in particular, those of the French applied mathematician Joseph Boussinesq and the British physicist Osborne Reynolds. Boussinesq was a student of A. Barré de Saint Venant, who, in his turn, was a devoted disciple of C. L. M. H. Navier, the originator of the mathematical models for both Newtonian viscous fluid flows and the deformation of perfectly elastic bodies.