Wall modes in rotating penetrative internally heated convection
Abstract
Rotating internally heated convection has been studied almost exclusively in laterally periodic domains, which cannot support the sidewall-attached modes that appear for sufficient rotation rates in rotating Rayleigh--Bénard convection in containers. We conduct direct numerical simulations of internally heated convection with isothermal plates and an adiabatic sidewall in cylinders of aspect ratio Γ= 1/2, $1$, and $2$ at Ra = 108 and Pran = 1, comparing them with a doubly periodic layer. When rotation is strong enough to stabilise the flow in a doubly periodic layer at the same R (Ek lessapprox 2 × 10−5), the cylinders continue transporting heat via a wall mode down to Ek = 5.62 × 10−6. This mode consists of a wave attached to the sidewall, with a radial thickness of roughly $0.03$ layer depths independent of Γ, leaving a stationary interior. Although unstable stratification is confined to the upper half of the conductive state, the mode also penetrates the lower half while retaining stable mean stratification in the measured lower-layer interval. Its azimuthal wavenumber scales roughly with Γ, yielding a wall parallel wavelength on the order of the layer depth, and it drifts retrograde as a rigid wave slower in wider cylinders and at lower Ek. Analogous to rotating Rayleigh--Bénard convection, the wall modes reported here extend the observed range of sustained convection relative to the periodic reference and may complicate experimental comparisons.
Related
- Internal heating in rapidly rotating convection is not a shortcut to geostrophic turbulence
- Semi-convection in rotating spherical shells: flows, layers and dynamos
- Quasinormal modes of rotating black holes with ultralight scalar fields
- Quasibound modes of rotating acoustic black holes
- Quasi-normal Modes and Instabilities of Rotating Relativistic Stars
BibTeX
@misc{tarditti2026wall,
title = {{Wall modes in rotating penetrative internally heated convection}},
author = {Gabriel A. Tarditti and Rodolfo Ostilla-Mónico and Ali Arslan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36928},
eprint = {2610.36928},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36928},
}
RIS
TY - UNPB
TI - Wall modes in rotating penetrative internally heated convection
AU - Gabriel A. Tarditti
AU - Rodolfo Ostilla-Mónico
AU - Ali Arslan
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36928
UR - https://arxiv.org/abs/2610.36928
AB - Rotating internally heated convection has been studied almost exclusively in laterally periodic domains, which cannot support the sidewall-attached modes that appear for sufficient rotation rates in rotating Rayleigh--Bénard convection in containers. We conduct direct numerical simulations of internally heated convection with isothermal plates and an adiabatic sidewall in cylinders of aspect ratio Γ= 1/2, $1$, and $2$ at Ra = 10^8 and Pran = 1, comparing them with a doubly periodic layer. When rotation is strong enough to stabilise the flow in a doubly periodic layer at the same R (Ek lessapprox 2 × 10^−5), the cylinders continue transporting heat via a wall mode down to Ek = 5.62 × 10^−6. This mode consists of a wave attached to the sidewall, with a radial thickness of roughly $0.03$ layer depths independent of Γ, leaving a stationary interior. Although unstable stratification is confined to the upper half of the conductive state, the mode also penetrates the lower half while retaining stable mean stratification in the measured lower-layer interval. Its azimuthal wavenumber scales roughly with Γ, yielding a wall parallel wavelength on the order of the layer depth, and it drifts retrograde as a rigid wave slower in wider cylinders and at lower Ek. Analogous to rotating Rayleigh--Bénard convection, the wall modes reported here extend the observed range of sustained convection relative to the periodic reference and may complicate experimental comparisons.
ER -