Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes
The incorporation of vapor transport has become a key demand for snowpack modeling in which accompanied phase changes give rise to a new, nonlinear coupling in the heat and mass equations. This coupling has an impact on choosing efficient numerical schemes for 1D snowpack models which are naturally...
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2022
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ftdoajarticles:oai:doaj.org/article:051e48d9331f45d6ac01b7ee6aede0a9 2023-05-15T18:32:27+02:00 Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes K. Schürholt J. Kowalski H. Löwe 2022-03-01T00:00:00Z https://doi.org/10.5194/tc-16-903-2022 https://doaj.org/article/051e48d9331f45d6ac01b7ee6aede0a9 EN eng Copernicus Publications https://tc.copernicus.org/articles/16/903/2022/tc-16-903-2022.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-16-903-2022 1994-0416 1994-0424 https://doaj.org/article/051e48d9331f45d6ac01b7ee6aede0a9 The Cryosphere, Vol 16, Pp 903-923 (2022) Environmental sciences GE1-350 Geology QE1-996.5 article 2022 ftdoajarticles https://doi.org/10.5194/tc-16-903-2022 2022-12-31T07:44:21Z The incorporation of vapor transport has become a key demand for snowpack modeling in which accompanied phase changes give rise to a new, nonlinear coupling in the heat and mass equations. This coupling has an impact on choosing efficient numerical schemes for 1D snowpack models which are naturally not designed to cope with mathematical particularities of arbitrary, nonlinear partial differential equations (PDEs). To explore this coupling we have implemented a stand-alone finite element solution of the coupled heat and mass equations in snow using the computing platform FEniCS. We focus on the nonlinear feedback of the ice phase exchanging mass with a diffusing vapor phase with concurrent heat transport in the absence of settling. We demonstrate that existing continuum-mechanical models derived through homogenization or mixture theory yield similar results for homogeneous snowpacks of constant density. When snow density varies significantly with depth, we show that phase changes in the presence of temperature gradients give rise to nonlinear advection of the ice phase amplifying existing density variations. Eventually, this advection triggers a wave instability in the continuity equations. This is traced back to the density dependence of the effective transport coefficients as revealed by a linear stability analysis of the nonlinear PDE system. The instability is an inherent feature of existing continuum models and predicts, as a side product, the formation of a low-density (mechanical) weak layer on the sublimating side of an ice crust. The wave instability constitutes a key challenge for a faithful treatment of solid–vapor mass conservation between layers, which is discussed in view of the underlying homogenization schemes and their numerical solutions. Article in Journal/Newspaper The Cryosphere Directory of Open Access Journals: DOAJ Articles The Cryosphere 16 3 903 923 |
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Open Polar |
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Directory of Open Access Journals: DOAJ Articles |
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ftdoajarticles |
language |
English |
topic |
Environmental sciences GE1-350 Geology QE1-996.5 |
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Environmental sciences GE1-350 Geology QE1-996.5 K. Schürholt J. Kowalski H. Löwe Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes |
topic_facet |
Environmental sciences GE1-350 Geology QE1-996.5 |
description |
The incorporation of vapor transport has become a key demand for snowpack modeling in which accompanied phase changes give rise to a new, nonlinear coupling in the heat and mass equations. This coupling has an impact on choosing efficient numerical schemes for 1D snowpack models which are naturally not designed to cope with mathematical particularities of arbitrary, nonlinear partial differential equations (PDEs). To explore this coupling we have implemented a stand-alone finite element solution of the coupled heat and mass equations in snow using the computing platform FEniCS. We focus on the nonlinear feedback of the ice phase exchanging mass with a diffusing vapor phase with concurrent heat transport in the absence of settling. We demonstrate that existing continuum-mechanical models derived through homogenization or mixture theory yield similar results for homogeneous snowpacks of constant density. When snow density varies significantly with depth, we show that phase changes in the presence of temperature gradients give rise to nonlinear advection of the ice phase amplifying existing density variations. Eventually, this advection triggers a wave instability in the continuity equations. This is traced back to the density dependence of the effective transport coefficients as revealed by a linear stability analysis of the nonlinear PDE system. The instability is an inherent feature of existing continuum models and predicts, as a side product, the formation of a low-density (mechanical) weak layer on the sublimating side of an ice crust. The wave instability constitutes a key challenge for a faithful treatment of solid–vapor mass conservation between layers, which is discussed in view of the underlying homogenization schemes and their numerical solutions. |
format |
Article in Journal/Newspaper |
author |
K. Schürholt J. Kowalski H. Löwe |
author_facet |
K. Schürholt J. Kowalski H. Löwe |
author_sort |
K. Schürholt |
title |
Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes |
title_short |
Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes |
title_full |
Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes |
title_fullStr |
Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes |
title_full_unstemmed |
Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes |
title_sort |
elements of future snowpack modeling – part 1: a physical instability arising from the nonlinear coupling of transport and phase changes |
publisher |
Copernicus Publications |
publishDate |
2022 |
url |
https://doi.org/10.5194/tc-16-903-2022 https://doaj.org/article/051e48d9331f45d6ac01b7ee6aede0a9 |
genre |
The Cryosphere |
genre_facet |
The Cryosphere |
op_source |
The Cryosphere, Vol 16, Pp 903-923 (2022) |
op_relation |
https://tc.copernicus.org/articles/16/903/2022/tc-16-903-2022.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-16-903-2022 1994-0416 1994-0424 https://doaj.org/article/051e48d9331f45d6ac01b7ee6aede0a9 |
op_doi |
https://doi.org/10.5194/tc-16-903-2022 |
container_title |
The Cryosphere |
container_volume |
16 |
container_issue |
3 |
container_start_page |
903 |
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923 |
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1766216570995998720 |