In generic rotating Rayleigh-Bénard convection (RRBC), wallmodes develop in domains with an impermeable lateral boundary [1]. Their onset occurs typically at a lower Rayleigh number than the critical Rayleigh number for the onset of convection in an infinite plane layer, and they carry a significant fraction of the total heat flux. Because of this, they are a hindrance in the experimental study of Rayleigh-Bénard convection, since lateral walls are unavoidable in experiments [2].
On the other hand, RRBC experiments in cylinders have a specific relevance to convection in planetary interiors because they mimic so-called Tangent Cylinders. In planets with a liquid core surrounding a solid core, such as the Earth, TCs are imaginary surfaces extruded from the solid core along the rotation axis. They tend to become impermeable because of the Taylor-Proudman constraint imposed by rotation. However, this constraint relaxes in the presence of inertia, or of an external magnetic field, so TCs do not exactly behave like impermeable walls. Since they are not perfectly impermeable, the question arises of whether wallmodes develop along them, and, if so, whether they are similar to wallmodes found in solid cylinders.
Experiments on the "Little Earth Experiment" [3] deliver seemingly contradictory insights into that question: In experiments in a hemispherical dome, representing the cold, core-mantle boundary, and a raised heater mimicking the hot solid core, structures akin to wallmodes have been noticed at the TC above the heater [4]. When the outer dome is replaced by a tight outer cylinder, however, no wallmodes are present [5]. To understand whether wallmodes can indeed exist along TCs, and under which conditions, we use DNS and linear stability analysis in LEE's exact configuration. These simulations tell us whether the base flow is subject to an instability leading to wallmodes.


[1] Zhong, F., Ecke, R., & Steinberg, V., 1991. Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection, Phys. Rev. Lett., 67(18), 2473

[2] Ecke, R. & Shishkina, O., 2023. Turbulent rotating Rayleigh–Bénard convection, Annu. Rev. Fluid Mech., 55, 603–638.

[3] Aujogue, K., Pothérat, A., Bates, I., Debray, F., & Sreenivasan, B., 2016. Little Earth Experiment: An instrument to model planetary
cores, Rev. Sci. Instrum., 87(8).

[4] Aujogue, K., Pothérat, A., Sreenivasan, B., & Debray, F., 2018.
Experimental study of the convection in a rotating tangent cylin-
der, J. Fluid Mech., 843, 355–381.

[5]. Agrawal, R., Hodlsworth, M. & Pothérat, A. Regimes of rotating convection in an experimental model of the Earth's tangent cylinder. 2024. ArXiv preprint 2408.07837