Helical Flow Structure in a Precessing Sphere

A new kind of helical flow structure is observed in a precessing sphere. The Navier–Stokes equation for an incompressible viscous fluid of viscosity ν is solved numerically by a spectral method in a sphere of radius a which rotates with a constant spin angular velocity Ω s around an axis which rotates, orthogonally to itself, with another constant precession angular velocity Ω p . A variety of flow state is realized depending on two control parameters Re = a 2 Ω s /ν and Γ=Ω p /Ω s . Here we report the detailed flow structures at Re =10, 200, 330, and 500 for a fixed value of Γ=0.1, for which the flow is stationary in the precession frame. It is found numerically that each streamline winds helically on a torus, the shape of which becomes more and more complicated as Re increases. The spherical region is divided into many domains by the sense of streamline torsion. The number of domains varies depending on Re .