The reversal mechanism of a dipole magnetic field generated by dynamo action in a rotating spherical shell is investigated by a three-dimensional nonlinear magnetohydrodynamic simulation as well as a linear stability analysis. The emphasis of the study is on understanding the relationship between dipole reversal and the symmetry properties of the dynamo solution. As a result, first, it is found that there is a threshold of the magnetic Prandtl number, below which the dipole field is never reversed, and above which the reversal occurs at irregular intervals like the paleomagnetic evolution of the geodynamo. Second, it is shown that the dynamo process responsible for the generation of a dipole field (called “a-dynamo” in this paper) consists only of the antimirror symmetric magnetic field and the mirror symmetric velocity field with respect to the equatorial plane. Third, it is found that the components of the opposite symmetry to the a-dynamo grow only during the polarity reversal events and quickly decay afterwards. This indicates that the dipole field reversal and the loss of equatorial symmetry are tightly connected. In fact, it is clearly demonstrated by numerical analyses that the a-dynamo process is linearly unstable for the perturbation of opposite symmetry when the magnetic Prandtl number exceeds the threshold for dipole reversal. Mode coupling between the longitudinal Fourier components plays a crucial role in creating the instability. Based on the above results, it is proposed that symmetry-breaking instability could be the mechanism for dipole field reversal in the geodynamo process. The energy conversion between components of different symmetry is also analyzed in the quasistable polarity phase and in the polarity reversal phase, respectively.

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Abstract. Flow visualization was used to investigate experimentally the evolution process of the instability in the separated shear layer behind an axisymmetric paraboloidal-nose cylinder at high angles of attack. The appearance of instability is observed as uniformly spaced vortex loops showing wavy folds of a shear layer. The distance between the counter-rotating primary and secondary vortices varies with time and the vortex loops always appear first in the region between the primary and secondary vortex at the time and place where these vortices approach closest together. The second vortex loops appear in the downstream of the first ones delayed by the appearance of the first vortex loops. It is suggested that the short wavelength perturbations of the preceding vortex loops advect on the outer surface of the primary vortex along the fluid path accompanied by the dominating vortex loops in downstream region. IntroductionA flow over a paraboloidal-nose cylinder at incidence provides the fundamental example of the simple body flow field seen in most high angle of attack flows and provides the model flow of three-dimensional separated flows. Three-dimensional flow separation about a slender body at incidence has been the subject of many studies, including topological structures for a body of revolution such as a slender cone [1], a round-nosed body [2], and a prolate spheroid [3,4]. The structures of the symmetric separated flow about a paraboloidal-nose cylinder at incidence with main, primary, and secondary vortices on the lee side has been well established in experiments and is illustrated in figure 1. The feeding shear layers roll up to form a pair of counter-rotating main vortices.It was shown by Riley & Lowson [5] that steady sub-vortical structures appear in the free shear layer over delta wings. They demonstrated that the smoke filaments formed near the leading edge of the wing spiral into the core of the main vortex as they pass downstream. They suggested that the steady sub-vortices are due to a local three-dimensional Kelvin-Helmholtz instability of the free shear layer.In the preset study, we investigate experimentally the instability of the flow behind a paraboloidal-nose cylinder with appearance of vortex loops in the feeding shear layer encircling the main vortices. This instability is unsteady in contrast to the steady sub-vortical structures over delta wings, and little data on this kind of instability were available in previous works. The present measurements were accomplished using flow visualizations together with PIV measurements in a towing system in a settled air chamber.

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