Introduction

Fluids and flows are pervading our daily lives without our conscious perception. The air we breathe, the shower in the bathroom with the shampoo, coffee or tea, the blood in our vascular tree including the heart and the brain, the ingredients of food like mayonnaise, oil, vinegar, yogurt, etc. The design and the engineering of new materials like polymers, plastics, ceramics, foams, etc., have produced complex fluids because the materials processing based on extrusion, molding, blowing, etc. is using them in the fluid state. Note that in polymers the presence of long molecular chains and their entanglement affect the mechanical behavior of the fluid. Therefore fluids are flowing around us in a swirl of natural events and of technological applications. Most flows in nature are complex due to their turbulent character: river and ocean currents, waves on a beach, storms, hurricanes, tsunamis, … . Many technological applications use turbulence to achieve the goal of the design, for example homogeneous mixing in materials processing. Moreover the understanding of the turbulent phenomena may lead to avoid them or reduce their intensity and thereby their effects, for example, in the design of hydraulic machines. These flows and fluids are reputed as complex. Therefore we need to better understand the meaning of this epithet.