Modulated rotating waves and triadic resonances in spherical fluid systems: The case of magnetized spherical Couette flow

TL;DR

This paper investigates how triadic resonances and modulated rotating waves develop in magnetized spherical Couette flow, revealing their connection to radial jet instability and bifurcation processes in spherical fluid systems.

Contribution

It introduces a general framework for triadic resonance generation via successive Hopf bifurcations, emphasizing the role of non-inertial, equatorially antisymmetric modes.

Findings

Resonant modes are linked to radial jet instability, not inertial waves.

Triadic resonances are generated through successive Hopf bifurcations.

Nonlinear coupling among modes is analyzed using spherical harmonics.

Abstract

The existence of triadic resonances in the magnetized spherical Couette system (MSC) is related to the development of modulated rotating waves, which are quasiperiodic flows understood in terms of bifurcation theory in systems with symmetry. In contrast to previous studies in spherical geometry the resonant modes are not inertial waves but related with the radial jet instability which is strongly equatorially antisymmetric. We propose a general framework in which triadic resonances are generated through successive Hopf bifurcations from the base state. The study relies on an accurate frequency analysis of different modes of the flow, for solutions belonging to two different bifurcation scenarios. The azimuthal and latitudinal nonlinear coupling among the resonant modes is analysed and interpreted using spherical harmonics and the results are compared with previous studies in spherical geometry.