GIANMARCO SPERONE - POLITECNICO DI MILANO - SOME REMARKS ON THE FORCES EXERTED BY VISCOUS FLUID ON A BLUFF BODY

The theory of flight developed by Kutta, Lanchester and Zhukovsky is mainly based on the idea that a cambered surface produces lift through its ability to generate a vortex about itself. Since fluid flows around an obstacle generate vortices which are difficult to locate and to describe, in this talk we analyze the Stokes and Navier-Stokes equations for the two-dimensional motion of a viscous fluid in the exterior of a fixed obstacle.
Firstly, we discuss nonstandard boundary conditions for the Stokes equations on a smooth obstacle, allowing for the generation of turbulence behind the body. Secondly, after studying the connection between the appearance of lift and the unique solvability of the Navier-Stokes equations, we show some numerical results that compare the aerodynamic response of different non-smooth obstacles, as the inlet velocity is increased until reaching the critical Reynolds number. The talk accounts for results contained in two articles prepared in collaboration with Filippo Gazzola (Politecnico di Milano) and Andrei Fursikov (Moscow State University).