Rayleigh-Bénard convection at high Rayleigh number and infinite Prandtl number: Asymptotics and numerics

Vynnycky, Michael; Masuda, Yoshio

doi:10.1063/1.4829450

Cited by 12 publications

(7 citation statements)

References 20 publications

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“…Here we consider only the former case, following JZ87 with some changes of notation. More recent asymptotic analyses of high Rayleighnumber RBC with both free-slip and no-slip horizontal boundaries (Fowler, 2011;Vynnycky and Masuda, 2013) find excellent agreement with JZ87's results for the free-slip case.…”

Section: Flow In the Isothermal Coresupporting

confidence: 63%

Theoretical Mantle Dynamics

Ribe

2018

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Geodynamics is the study of the deformation and flow of the solid Earth and other planetary interiors. Focusing on the Earth's mantle, this book provides a comprehensive, mathematically advanced treatment of the continuum mechanics of mantle processes and the craft of formulating geodynamical models to approximate them. Topics covered include slow viscous flow, elasticity and viscoelasticity, boundary-layer theory, long-wave theories including lubrication theory and shell theory, two-phase flow, and hydrodynamic stability and thermal convection. A unifying theme is the utility of powerful general methods (dimensional analysis, scaling analysis, and asymptotic analysis) that can be applied in many specific contexts. Featuring abundant exercises with worked solutions for graduate students and researchers, this book will make a useful resource for Earth scientists and applied mathematicians with an interest in mantle dynamics and geodynamics more broadly.

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Section: Flow In the Isothermal Coresupporting

confidence: 63%

Theoretical Mantle Dynamics

Ribe

2018

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“…The more accurate approach for a boundary layer flow solution by Vynnycky and Masuda (2013) might produce better quantitative agreement with the numerical results, but it requires more computation and was not followed. Although the present boundary layer solution does not give close quantitative comparison with numerical results, it has a simplicity that allows it to be used for teaching and communicating the dynamics to those in other disciplines .…”

Section: Summary and Discussionmentioning

confidence: 99%

Convection driven by temperature and composition flux with the same diffusivity

Whitehead

2017

Geophysical & Astrophysical Fluid Dynamics

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Temperature, pressure, and composition determine density of fluids within the earth, the ocean, our atmosphere, stars and planets. In some cases, variation of composition component C competes equally with temperature T to determine buoyancy-driven flow. Properties of two-dimensional cellular convection are calculated with density difference between top and bottom boundaries determined by difference of temperature T (Dirichlet boundary conditions, quantified by Rayleigh number Ra that is positive destabilising), fluxes of C (Neumann boundary conditions quantified by Raf that is positive stabilising), and Prandtl number P r. Numerical solutions in a 2-dimensional rectangular chamber are analysed for Prandtl numbers P r = 1, ∞. For Ra and Raf > 0 and Raf above approximately 300, subcritical instability separates T -driven convection from C-dominated stagnation. The flow is steady but a sudden change in Ra or Raf produces decaying pulsations to the new flow. A boundary layer solution for rapid flow exists in which T , which has the Dirichlet condition, is more sensitive to flow speed than C with the Neumann condition. A new type of pulsating flow occurs for Ra and Raf < 0. The pulsations are characterised by slow flow with gradually strengthening compositional plumes in a thermally stratified flow interrupted by rapid flow with gradually weakening compositional plumes. In this slow speed range, C is more sensitive to speed than T .

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“…This laminar regime should not be mistaken for that of viscous convection of an infinite-Prandtl or Schmidt fluid in the limit of large Rayleigh numbers. For such a case, the scaling Sh w ∼ Ra 1/5 w is expected between (no-slip) solid surfaces [51,52] (cf. regime I > ∞ of the Grossmann-Lohse theory [53]) and Sh w ∼ Ra 1/3 w between (zero shear stress) free surfaces [51,52,54].…”

Section: A Effect Of Convective Dissolutionmentioning

confidence: 98%

“…For such a case, the scaling Sh w ∼ Ra 1/5 w is expected between (no-slip) solid surfaces [51,52] (cf. regime I > ∞ of the Grossmann-Lohse theory [53]) and Sh w ∼ Ra 1/3 w between (zero shear stress) free surfaces [51,52,54]. However, the robustness of the 1/4 exponent present in all the aforementioned cases of laminar convection hints that neither the no-shear boundary condition nor the cell geometry impact the scaling significantly.…”

Section: A Effect Of Convective Dissolutionmentioning

confidence: 98%

Slug bubble growth and dissolution by solute exchange

et al. 2021

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In many environmental and industrial applications, the mass transfer of gases in liquid solvents is a fundamental process during the generation of bubbles for specific purposes or, vice versa, the removal of entrapped bubbles. We address the growth dynamics of a trapped slug bubble in a vertical glass cylinder under a water barrier. In the studied process, the ambient air atmosphere is replaced by a CO 2 atmosphere at the same or higher pressure. The asymmetric exchange of the gaseous solutes between the CO 2 -rich water barrier and the air-rich bubble always results in net bubble growth. We refer to this process as solute exchange. The dominant transport of CO 2 across the water barrier is driven by a combination of diffusion and convective dissolution. The experimental results are compared to and explained with a simple numerical model, with which the underlying mass transport processes are quantified. Analytical solutions that accurately predict the bubble growth dynamics are subsequently derived. The effect of convective dissolution across the water layer is treated as a reduction of the effective diffusion length, in accordance with the mass transfer scaling observed in laminar or natural convection. Finally, the binary water-bubble system is extended to a ternary water-bubble-alkane system. It is found that the alkane (n-hexadecane) layer bestows a buffering (hindering) effect on bubble growth and dissolution. The resulting growth dynamics and underlying fluxes are characterized theoretically.

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Rayleigh-Bénard convection at high Rayleigh number and infinite Prandtl number: Asymptotics and numerics

Cited by 12 publications

References 20 publications

Theoretical Mantle Dynamics

Theoretical Mantle Dynamics

Convection driven by temperature and composition flux with the same diffusivity

Slug bubble growth and dissolution by solute exchange

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