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@article{Mestel:2019:10.1017/jfm.2019.440,
author = {Mestel, A and Mannix, P},
doi = {10.1017/jfm.2019.440},
journal = {Journal of Fluid Mechanics},
pages = {359--390},
title = {Weakly nonlinear mode-interactions in spherical Rayleigh-Benard convection},
url = {http://dx.doi.org/10.1017/jfm.2019.440},
volume = {874},
year = {2019}
}

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TY - JOUR
AB - In an annular spherical domain with separation d, the onset of convective motion occursat a critical Rayleigh number Ra = Rac. Solving the linear stability problem, it is shownthat degenerate points (d = dc; Rac) exist where two modes simultaneously becomeunstable. Considering the weakly nonlinear evolution of these modes, it is found thatspatial resonances play a crucial role in determining the preferred convection pattern forneighbouring modes (` : ` 1) and non-neighbouring even modes (` : ` 2). Derivingcoupled amplitude equations relevant at all degeneracies we outline the inuence ofchanges in d; Ra and Prandtl number Pr. A particular conclusion is that only evenmodes have pure mode solutions, and that odd modes exist only as a component of mixedmode solutions. The mode-dependent inuence of Pr on the saturation of mixed modesolutions is shown to be markedly di erent in the limits Pr ! 0 and Pr ! 1. Usingdirect numerical simulation (DNS) to verify all results, time periodic solutions are alsooutlined for small Pr. The 2 : 1 periodic signature observed to be general of oscillationsin a spherical annulus, is explained using the structure of the equations derived.
AU - Mestel,A
AU - Mannix,P
DO - 10.1017/jfm.2019.440
EP - 390
PY - 2019///
SN - 0022-1120
SP - 359
TI - Weakly nonlinear mode-interactions in spherical Rayleigh-Benard convection
T2 - Journal of Fluid Mechanics
UR - http://dx.doi.org/10.1017/jfm.2019.440
UR - http://hdl.handle.net/10044/1/72283
VL - 874
ER -

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