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Date
2024-08-25Type
- Journal Article
ETH Bibliography
yes
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Abstract
We consider an internally heated fluid between parallel plates with fixed thermal fluxes. For a large class of heat sources that vary in the direction of gravity, we prove that ⟨δT⟩ₕ ≥ σR⁻¹/³−μ, where ⟨δT⟩ₕ is the average temperature difference between the bottom and top plates, R is a ‘flux’ Rayleigh number and the constants σ,μ>0 depend on the geometric properties of the internal heating. This result implies that mean downward conduction (for which ⟨δT⟩ₕ < 0) is impossible for a range of Rayleigh numbers smaller than a critical value R₀ := (σ/μ)3. The bound demonstrates that R0 depends on the heating distribution and can be made arbitrarily large by concentrating the heating near the bottom plate. However, for any given fixed heating profile of the class we consider, the corresponding value of R0 is always finite. This points to a fundamental difference between internally heated convection and its limiting case of Rayleigh–Bénard convection with fixed-flux boundary conditions, for which ⟨δT⟩ₕ is known to be positive for all R. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000695389Publication status
publishedExternal links
Journal / series
Journal of Fluid MechanicsVolume
Pages / Article No.
Publisher
Cambridge University PressSubject
turbulent convection; variational methodsOrganisational unit
03734 - Jackson, Andrew / Jackson, Andrew
Funding
833848 - Unravelling Earth’s magnetic history and processes UEMHP (EC)
219247 - Dynamics of the Earth's core under the plesio-geostrophy paradigm (SNF)
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ETH Bibliography
yes
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