Description
The Omega-effect in the Omega-alpha solar dynamo model is characterised by the horizontally anisotropic flow in the solar tachocline which deforms the large-scale dipole magnetic field into an azimuthal configuration. This anisotropic flow is believed to be shear-driven due to the location of the tachocline between the uniformly rotating radiative zone below and the differentially rotating convective zone above, where the tachocline is additionally stably stratified. The effects of both stable stratification and a magnetic field on shear-driven instabilities are therefore pertinent to conditions in the solar tachocline, though remain an open problem in literature.
To address this, we study an idealised minimal fluid dynamical model in the Boussinesq framework to address how a horizontal magnetic field and stable stratification affect shear-driven instabilities, brought in via a plane-parallel Kolmogorov flow forcing. Full nonlinear simulations of our flow geometry show that for $P_{e}\gg1$ and $R_{m}\gg1$, that Kelvin cat’s eyes form at the inflection points of the Kolmogorov flow. At the onset of hydrodynamic instability, using weakly nonlinear theory in the limit of $P_{e}, R_{m}\gg1$, we derive a reduced model for Kelvin cat’s eyes. Through nonlinear pseudospectral simulation, we use this reduced model to show the formation and expansion of Kelvin cat’s eyes, whose growth is directly comparable to our linear stability results in the appropriate flow parameter regime.
