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Nonlinear interactions between an unstably stratified shear flow and a phase boundary

Published online by Cambridge University Press:  27 May 2021

S. Toppaladoddi Open the ORCID record for S. Toppaladoddi [Opens in a new window]
S. Toppaladoddi*
Affiliation:
All Souls College, OxfordOX1 4AL, UK Department of Physics, University of Oxford, OxfordOX1 3PU, UK Mathematical Institute, University of Oxford, OxfordOX2 6GG, UK
*
†Email address for correspondence: [email protected]
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Abstract

Well-resolved numerical simulations are used to study Rayleigh–Bénard–Poiseuille flow over an evolving phase boundary for moderate values of Péclet ($Pe \in [0, 50]$) and Rayleigh ($Ra \in [2.15 \times 10^3, 10^6]$) numbers. The relative effects of mean shear and buoyancy are quantified using a bulk Richardson number: $Ri_b = Ra \cdot Pr/Pe^2 \in [8.6 \times 10^{-1}, 10^4]$, where $Pr$ is the Prandtl number. For $Ri_b = O(1)$, we find that the Poiseuille flow inhibits convective motions, resulting in the heat transport being only due to conduction and, for $Ri_b \gg 1$, the flow properties and heat transport closely correspond to the purely convective case. We also find that for certain $Ra$ and $Pe$, such that $Ri_b \in [15,95]$, there is a pattern competition for convection cells with a preferred aspect ratio. Furthermore, we find travelling waves at the solid–liquid interface when $Pe \neq ~0$, in qualitative agreement with other sheared convective flows in the experiments of Gilpin et al. (J. Fluid Mech., vol. 99(3), 1980, pp. 619–640) and the linear stability analysis of Toppaladoddi & Wettlaufer (J. Fluid Mech., vol. 868, 2019, pp. 648–665).

JFM classification

Phase change: Solidification/melting
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A28
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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