Grand Séminaire d'Institut

Vendredi 26 Janvier 2018 à 11h00.

Boundary layers in fluid mechanics: basics, techniques et some applications

''Although the bases of fluid mechanics are well established since the beginning of the nineteenth century, the subtle role of viscosity in inertia-dominated flows has long been overlooked. The role of inertia and viscosity in flows are compared by a dimensionless quantity, the Reynolds number. If this number is large, it seemed reasonable to neglect viscosity. However, this lead to major inconsistencies, the most known being d'Alembert's paradox, namely the incapacity of the theory to predict the drag experienced by vehicles or planes. Ludwig Prandtl (1875-1953), a German engineer and physicist, solved this problem by recognising that however high the Reynolds number be, viscosity remains essential in a thin region close to solid boundaries. This is the basis of the so-called boundary-layer theory.
I will first briefly present these ideas purely qualitatively, then I will review the three key technical ideas associated to boundary layers, namely rescaling, asymptotic matching and self-similarity, on a very simple mathematical example. I will finally present several examples of the occurrence of boundary layers in physics, in particular their importance in determining the rate of evaporation of water surfaces [Dollet & Boulogne, Phys. Rev. Fluids (2017)]''