Rotating fluids frequently show nonlinear wave interactions and turbulence. This is true in particular for nonuniformly rotating systems. One example of such a nonuniform rotating object is the Earth. Due to its fast rotation it is not exactly spherical. As a result of the interaction with the Sun and Moon, the nonspherical Earth cannot rotate uniformly but shows precession and libration. This has consequences for the fluid enclosed in the outer Earth core. Due to the forcing it might become turbulent, one of the key factors in the present theories explaining the generation of the geomagnetic field. In the present paper we show experimental results from a system that is simpler than classical precession experiments but still shows very similar wave interactions and a collapse to turbulence. This system consists of a partly filled rotating annulus that rotates about its symmetry axis slightly tilted with respect to the gravity vector and allows us to explore Ekman numbers ranging from $7.9\times {10}^{-6}$ to $3.2\times {10}^{-5}$. In analogy to the more classical precession experiments, we also find a resonant collapse when the forcing frequency corresponds with a resonant frequency of the rotating tank. The forced mode and two free Kelvin modes give rise to triadic resonance. Besides the parametric triadic resonance we further observed a shear-type instability of the nonlinearly excited geostrophic flow. This instability gives rise to a barotropic mode that interacts with the forced mode and generates secondary modes. We also observed a dependency of the mode frequencies on the Ekman number, which can, at least partly, be explained by a Doppler shift due to the mean flow. Finally, we try to connect our data to a low-order dynamical system that describes the main features of single triad interaction in precession experiments. Although this model is originally not designed for the multiple triads we observe, it is still useful for a qualitative understanding of mode interactions, e.g., for the mechanism of geostrophic mode excitation.

• Received 27 June 2019
• Accepted 28 August 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.094801