Convective pattern formation in a thermally heated rotating annulus with magnetic central force field

The earth, a sphere consisting of several layers like an onion is still up to now not fully understood. Gaining the fundamental knowledge to understand the mystery of global cell formation and large-scale convection in the interior or at the surface e.g. in our atmosphere is still of great interest from a meteorological point of view and of course in geophysics. However, laboratory experiments are still exposed to a significant problem – gravity. Establishing a radial force field e.g. in a sphere or annulus is still overpowered by gravity unless the experiment is carried out in a microgravity environment. Here, we show a potential application of a central force field induced by magnetic forces that acts on a magnetic fluid in a rotating thermally heated annulus to induce thermomagnetic convection and waves that are similar to the baroclinic annulus with the focus to study large scale atmospheric flow fields in a small laboratory system.

 

Thermomagnetic convection is based on non-isothermal variation of fluid magnetisation induced e.g. by a temperature gradient in the presence of an external magnetic field. After Currie’s law colder magnetic fluid exhibits a larger fluid magnetisation and is therefore attracted to higher magnetic field intensities. This phenomenon is used to induced convection in a thermally heated annulus filled with a magnetisable ferro-magnetic fluid. Here, we study a 2-dimensional numerical problem geometry where the fluid is cooled at the inner and heated at the outer cylinder. The system is forced with an increasing central force field such that colder fluid is attracted towards the outer boundary when a critical threshold is exceeded – the critical magnetic Rayleigh number an equivalent non-dimensional parameter to the classical Rayleigh number for natural convection.

 

Numerical results are obtained for two different radii ratios (0.35, 0.5). The parametric study included a range of magnetic Rayleigh numbers between 10³ to 7.5x10⁵ to induce a range of thermomagnetic convective cases. In addition, the thermally annulus is rotated at different speeds expressed via the Taylor number ranging from 10⁵ to 10⁶. The observed flow fields reveal similar flow structures as seen in the classical baroclinic wave tank but have a different physically interpretation. The observed modes range from mode number 2 to 8 with stable symmetric to oscillatory and chaotic behaviours. The results are summarised in a regime diagram that is spanned in the thermally forcing and rotation speed space. This may be able to classify certain structures that are used to study atmospheric flow fields for different rotation and thermal forcing states e.g. planetary waves.