Orateur
Description
Co-authors: Yinshen Xu (UCD), Tiziana Comito (UCD), Johan Hoffman (KTH), John D. Gibbon (Imperial)
Abstract: Consider incompressible inviscid flow past an object. D'Alembert (1752) proved that for potential flow, the object experiences no drag force. However, experimental observations find significant drag at high Reynolds numbers, leading to the famous d'Alembert's paradox in fluid mechanics. Prandtl (1904) proposed a milestone solution to this paradox through his boundary layer theory, which attributes drag primarily to the viscous boundary layer.
Recently, Hoffman and Johnson (2010) revisited the paradox, bypassing the use of viscosity. In a computational "weak" solution of the 3D Euler equations of flow past a cylinder with slip boundary conditions, they found turbulence to be the primary source of drag.
We prove this analytically, showing that Gibbon et al.'s (1999) stagnation-point-like solution of the 3D Euler equations, with appropriate inflow conditions, holds at the rear separation zone. Via a linear instability, nonlinear (stable) streamwise helical vortices form, causing drag.