Journal article
Structure of mushy layers grown from perfectly and imperfectly conducting boundaries. Part 2. Onset of convection
- Abstract:
-
We study linear convective instability in a mushy layer formed by solidification of a binary alloy, cooled by either an isothermal perfectly conducting boundary or an imperfectly conducting boundary where the surface temperature depends linearly on the surface heat flux. A companion paper (Hitchen & Wells, J. Fluid Mech., 2025, in press) showed how thermal and salinity conditions impact mush structure. We here quantify the impact on convective instability, described by a Rayleigh number characterising the ratio of buoyancy to dissipative mechanisms. Two limits emerge for a perfectly conducting boundary. When the salinity-dependent freezing-point depression is large versus the temperature difference across the mush, convection penetrates throughout the depth of a high-porosity mush. The other limit, which we will call the Stefan limit, has small freezing-point depression and inhibits convection, which localises at onset to a high-porosity boundary layer near the mush–liquid interface. Scaling arguments characterise variation of the critical Rayleigh number and wavenumber based on the potential energy contained in order-one aspect ratio convective cells over the high-porosity regions. The Stefan number characterises the ratio of latent and sensible heats, and has moderate impact on stability via modification of the background temperature and porosity. For imperfectly conducting boundaries, the changing surface temperature causes stability to decrease over time in the limit of large freezing-point depression, but in the Stefan limit combines with the decreasing porosity to yield non-monotonic variation of the critical Rayleigh number. We discuss the implications for convection in growing sea ice.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Version of record, pdf, 3.1MB, Terms of use)
-
- Publisher copy:
- 10.1017/jfm.2024.809
Authors
- Publisher:
- Cambridge University Press
- Journal:
- Journal of Fluid Mechanics More from this journal
- Volume:
- 1002
- Article number:
- A26
- Publication date:
- 2025-01-03
- Acceptance date:
- 2024-05-18
- DOI:
- EISSN:
-
1469-7645
- ISSN:
-
0022-1120
- Language:
-
English
- Keywords:
- Pubs id:
-
2011460
- Local pid:
-
pubs:2011460
- Deposit date:
-
2024-07-02
Terms of use
- Copyright holder:
- Hitchen and Wells
- Copyright date:
- 2025
- Rights statement:
- © The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
- Notes:
- This research was funded in in part by the Natural Environment Research Council UK Grant numbers NE/L501530/1 and NE/I528493/1, and through the research program of the European Union FP7 award PCIG13-GA-2013-618610 SEA-ICE-CFD. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.
- Licence:
- CC Attribution (CC BY)
If you are the owner of this record, you can report an update to it here: Report update to this record