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O. M. Umurhan and J. Y-K. Cho
School of Mathematical Sciences
Queen Mary University of London
Recent calculations suggest that the ionization degree in the uppermost atmospheric layers of hot extrasolar giant planets (EGPs) may be significant enough to warrant a magneto-hydrodynamic description of the dynamics in those layers. We develop a two-layer magneto-quasigeostrophic model (mQG) on a β-plane to examine the nature and dynamics of vortices under conditions in which the upper layer is magnetized and the lower layer is not. The mQG model is similar to the shallow water magnetohydrodynamic equations developed to study the problem of the solar tachochline. Some properties of the multi-layer mQG equations are highlighted. In a parallel vein, recently reported single layer magnetized shallow water simulations on a sphere show that zonal jet profiles break-up into compact vortices, i.e., coherent structures that look like magnetically confined circular jets, when the magnetic fields in the layer become strong enough.
The mQG framework is used to understand the properties of idealized representations of these compact vortices. Linear stability analysis shows that these structures disintegrate due to the instability of counterpropagating Rossby edgewaves if the Alfven wavespeeds are less than the typical circular velocity scales. Numerical simulations are performed and confirm this feature. We also examine the nonlinear stability of these compact vortices in the two-layer setup where the lower unmagnetized layer is seeded with a turbulent geostrophic field and the upper layer is initialized with a single, otherwise, stable compact vortex. Results of the numerical experiments show that if the rms velocities of the lower layer’s flow field exceeds the Alfven speeds of the upper vortex then the structure is destroyed. The sensitivity and longevity of the compact vortices to the upper layer’s magnetic Reynolds number is also explored. This work suggests that compact vortices may be generic features of EGP atmosphere layers that are magnetized.
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