Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise‐Constant Coastlines
Abstract Coastlines in most ocean general circulation models are piecewise constant. Accurate representation of boundary currents along staircase‐like coastlines is a long‐standing issue in ocean modeling. Pioneering work by Adcroft and Marshall (1998, https://doi.org/10.3402/tellusa.v50i1.14514) re...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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American Geophysical Union (AGU)
2023-05-01
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| Series: | Journal of Advances in Modeling Earth Systems |
| Subjects: | |
| Online Access: | https://doi.org/10.1029/2022MS003594 |
| _version_ | 1797800192031850496 |
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| author | Antoine‐Alexis Nasser Gurvan Madec Casimir deLavergne Laurent Debreu Florian Lemarié Eric Blayo |
| author_facet | Antoine‐Alexis Nasser Gurvan Madec Casimir deLavergne Laurent Debreu Florian Lemarié Eric Blayo |
| author_sort | Antoine‐Alexis Nasser |
| collection | DOAJ |
| description | Abstract Coastlines in most ocean general circulation models are piecewise constant. Accurate representation of boundary currents along staircase‐like coastlines is a long‐standing issue in ocean modeling. Pioneering work by Adcroft and Marshall (1998, https://doi.org/10.3402/tellusa.v50i1.14514) revealed that artificial indentation of model coastlines, obtained by rotating the numerical mesh within an idealized square basin, generates a spurious form drag that slows down the circulation. Here, we revisit this problem and show how this spurious drag may be eliminated. First, we find that physical convergence to spatial resolution (i.e., the main characteristics of the flow are insensitive to the increase of the mesh resolution) allows simulations to become independent of the mesh orientation. An advection scheme with a wider stencil also reduces sensitivity to mesh orientation from coarser resolution. Second, we show that indented coastlines behave as straight and slippery shores when a true mirror boundary condition on the flow is imposed. This finding applies to both symmetric and rotational‐divergence formulations of the stress tensor, and to both flux and vector‐invariant forms of the equations. Finally, we demonstrate that the detachment of a vortex flowing past an outgoing corner of the coastline is missed with a free‐slip (zero vorticity) condition at the corner. These results provide guidance for a better numerical treatment of coastlines (and isobaths) in ocean general circulation models. |
| first_indexed | 2024-03-13T04:31:25Z |
| format | Article |
| id | doaj.art-d619b7d588604aa583ce82fce0c90073 |
| institution | Directory Open Access Journal |
| issn | 1942-2466 |
| language | English |
| last_indexed | 2024-03-13T04:31:25Z |
| publishDate | 2023-05-01 |
| publisher | American Geophysical Union (AGU) |
| record_format | Article |
| series | Journal of Advances in Modeling Earth Systems |
| spelling | doaj.art-d619b7d588604aa583ce82fce0c900732023-06-19T13:40:46ZengAmerican Geophysical Union (AGU)Journal of Advances in Modeling Earth Systems1942-24662023-05-01155n/an/a10.1029/2022MS003594Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise‐Constant CoastlinesAntoine‐Alexis Nasser0Gurvan Madec1Casimir deLavergne2Laurent Debreu3Florian Lemarié4Eric Blayo5Univ. Grenoble Alpes Inria, CNRS, Grenoble INP, LJK Grenoble FranceUniv. Grenoble Alpes Inria, CNRS, Grenoble INP, LJK Grenoble FranceLOCEAN Laboratory Sorbonne University‐CNRS‐IRD‐MHNM Paris FranceUniv. Grenoble Alpes Inria, CNRS, Grenoble INP, LJK Grenoble FranceUniv. Grenoble Alpes Inria, CNRS, Grenoble INP, LJK Grenoble FranceUniv. Grenoble Alpes Inria, CNRS, Grenoble INP, LJK Grenoble FranceAbstract Coastlines in most ocean general circulation models are piecewise constant. Accurate representation of boundary currents along staircase‐like coastlines is a long‐standing issue in ocean modeling. Pioneering work by Adcroft and Marshall (1998, https://doi.org/10.3402/tellusa.v50i1.14514) revealed that artificial indentation of model coastlines, obtained by rotating the numerical mesh within an idealized square basin, generates a spurious form drag that slows down the circulation. Here, we revisit this problem and show how this spurious drag may be eliminated. First, we find that physical convergence to spatial resolution (i.e., the main characteristics of the flow are insensitive to the increase of the mesh resolution) allows simulations to become independent of the mesh orientation. An advection scheme with a wider stencil also reduces sensitivity to mesh orientation from coarser resolution. Second, we show that indented coastlines behave as straight and slippery shores when a true mirror boundary condition on the flow is imposed. This finding applies to both symmetric and rotational‐divergence formulations of the stress tensor, and to both flux and vector‐invariant forms of the equations. Finally, we demonstrate that the detachment of a vortex flowing past an outgoing corner of the coastline is missed with a free‐slip (zero vorticity) condition at the corner. These results provide guidance for a better numerical treatment of coastlines (and isobaths) in ocean general circulation models.https://doi.org/10.1029/2022MS003594ocean modelingidealized configurationcoastlinetopographyboundary current |
| spellingShingle | Antoine‐Alexis Nasser Gurvan Madec Casimir deLavergne Laurent Debreu Florian Lemarié Eric Blayo Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise‐Constant Coastlines Journal of Advances in Modeling Earth Systems ocean modeling idealized configuration coastline topography boundary current |
| title | Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise‐Constant Coastlines |
| title_full | Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise‐Constant Coastlines |
| title_fullStr | Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise‐Constant Coastlines |
| title_full_unstemmed | Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise‐Constant Coastlines |
| title_short | Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise‐Constant Coastlines |
| title_sort | sliding or stumbling on the staircase numerics of ocean circulation along piecewise constant coastlines |
| topic | ocean modeling idealized configuration coastline topography boundary current |
| url | https://doi.org/10.1029/2022MS003594 |
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