Abstract
Precession driven flows are of great interest for both, industrial and geophysical applications. While cylindrical, spherical and spheroidal geometries have been investigated in great detail, the numerically and theoretically more challenging case of a non-axisymmetric cavity has received less attention. We report experimental results on the flows in a precessing triaxial ellipsoid, with a focus on the base flow of uniform vorticity, which we show to be in good agreement with existing theoretical models. As predicted, the uniform vorticity component exhibits two branches of solutions leading to a hysteresis cycle as a function of the Poincaré number. The first branch is observed at low forcing and characterized by large amplitude of the total fluid rotation and a moderate tilt angle of the fluid rotation axis. In contrast, the second branch displays only a moderate fluid rotation and a large tilt angle of the fluid rotation axis, which tends to align with the precession axis. In addition, we observe the occurrence of parametric instabilities early in the first branch, which saturate in the second branch, where we observe the same order of the kinetic energy in the base flow and instabilities.
Highlights
The term precession denotes the slow, gyroscopic motion of a spinning object, resulting from a torque that tends to tilt the object’s rotation axis
We start with a discussion of the uniform vorticity component and define four important quantities that characterize the rotation of the fluid: first, the time averaged total rotation of the fluid Ω t, second, the time averaged differential rotation between the fluid and the container, δω t, third, the time average rotation of the fluid along the spin axis Ωz t and, the time averaged tilt angle of the fluid rotation axis with respect to the container axis, θ t
We have experimentally investigated the flows in a triaxial ellipsoid subject to precession at an angle of 90◦
Summary
The term precession denotes the slow, gyroscopic motion of a spinning object, resulting from a torque that tends to tilt the object’s rotation axis. Under the assumption that the vorticity is uniform and steady in the frame of precession, they derived an inviscid solution in the form of a tilted solid body rotation, which is complemented by a gradient flow. In non-axisymmetric, i.e. triaxial, ellipsoids, the flow of uniform vorticity has been investigated theoretically and numerically by Noir & Cébron (2013) and experimentally and numerically by Cebron, Le Bars & Meunier (2010). The former treat the true geophysical problem of a solid container with a fixed shape in the rotating frame, while the latter consider a deformable container with a shape fixed in the frame of precession, yet both approaches share similar dynamics.
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