Water-at-Rest Equilibrium Stability Analysis of a first-moment Shallow Water Exner Moment Model with Sediment Entrainment and Deposition: Extended Technical Report
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arXiv
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| Format: | Preprint |
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2026
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| author | Parvin, Afroja Samaey, Giovanni Koellermeier, Julian |
| author_facet | Parvin, Afroja Samaey, Giovanni Koellermeier, Julian |
| contents | We derive the first-moment Shallow Water Exner Moment model with sediment entrainment and deposition (SWEMED1) and show that the full source term has a fully-settled water-at-rest equilibrium manifold. We prove that the model is only weakly hyperbolic at this equilibrium, which prevents the use of Yong's structural stability framework. However, a linear spectral analysis and numerical results do not indicate instability. Based on numerical results, we introduce a fast-slow scaling of the source term, and for the fast limit, we derive a new suspended water-at-rest equilibrium manifold, which has a different structure but is still only weakly hyperbolic. Our results show that the remaining obstruction is linked to the transport closure of the SWEMED1, and we give a constructive direction for the derivation of new closures leading to models with more desirable analytical properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29554 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Water-at-Rest Equilibrium Stability Analysis of a first-moment Shallow Water Exner Moment Model with Sediment Entrainment and Deposition: Extended Technical Report Parvin, Afroja Samaey, Giovanni Koellermeier, Julian Analysis of PDEs Numerical Analysis We derive the first-moment Shallow Water Exner Moment model with sediment entrainment and deposition (SWEMED1) and show that the full source term has a fully-settled water-at-rest equilibrium manifold. We prove that the model is only weakly hyperbolic at this equilibrium, which prevents the use of Yong's structural stability framework. However, a linear spectral analysis and numerical results do not indicate instability. Based on numerical results, we introduce a fast-slow scaling of the source term, and for the fast limit, we derive a new suspended water-at-rest equilibrium manifold, which has a different structure but is still only weakly hyperbolic. Our results show that the remaining obstruction is linked to the transport closure of the SWEMED1, and we give a constructive direction for the derivation of new closures leading to models with more desirable analytical properties. |
| title | Water-at-Rest Equilibrium Stability Analysis of a first-moment Shallow Water Exner Moment Model with Sediment Entrainment and Deposition: Extended Technical Report |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2605.29554 |