Chaotic Orbits of Tumbling Ellipsoids in Viscous and Inviscid Fluids*

Aref(1993) showed that the dynamics of an immersed tri-axial ellipsoid should be chaotic under certain inviscid conditions. We use analytical and numerical methods to determine occurrence and conditions of chaotic orbits in viscous and inviscid environments. Our numerical work uses Gerris(Popinet et al, 2003) augmented with a fully-coupled solver for fluid-solid interaction with 6 degrees-of-freedom (6DOF). Its adaptive Cartesian mesh scores over traditional algorithms in convergence and also require fewer mesh adaption steps whilst using the immersed boundary method. For inviscid conditions, our numerical results agree with the solution of Kirchhoff’s equations. Our results show that chaos is a strong function of density ratio and the initial energy ratio even for inviscid environments. Using recurrence quantification (Marwanet al, 2007) methods, we also characterise chaos and identify regime shifts from being periodic to quasi-periodic to chaotic. In viscous systems, we have also noted evidence of chaotic orbits for symmetric ellipsoids. We will discuss vortex shedding behaviour in this context.