Exact Intermittent Solutions in a Turbulence Multi-Branch Shell Model
Reproducing complex phenomena with simple models marks our understanding of the phenomena themselves, and this is what Jack Herring’s work demonstrated multiple times. In that spirit, this work studies a turbulence shell model consisting of a hierarchy of structures of different scales <inline-fo...
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| Format: | Article |
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MDPI AG
2023-08-01
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| Series: | Atmosphere |
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| Online Access: | https://www.mdpi.com/2073-4433/14/8/1316 |
| _version_ | 1797585540934008832 |
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| author | Ben Ajzner Alexandros Alexakis |
| author_facet | Ben Ajzner Alexandros Alexakis |
| author_sort | Ben Ajzner |
| collection | DOAJ |
| description | Reproducing complex phenomena with simple models marks our understanding of the phenomena themselves, and this is what Jack Herring’s work demonstrated multiple times. In that spirit, this work studies a turbulence shell model consisting of a hierarchy of structures of different scales <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mi>n</mi></msub></semantics></math></inline-formula> such that each structure transfers its energy to two substructures of scale <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>ℓ</mo><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mo>ℓ</mo><mi>n</mi></msub><mo>/</mo><mi>λ</mi></mrow></semantics></math></inline-formula>. For this model, we construct exact inertial range solutions that display intermittency, i.e., absence of self-similarity. Using a large ensemble of these solutions, we investigate how the probability distributions of the velocity modes change with scale. It is demonstrated that, while velocity amplitudes are not scale-invariant, their ratios are. Furthermore, using large deviation theory, we show how the probability distributions of the velocity modes can be re-scaled to collapse in a scale-independent form. Finally, we discuss the implications the present results have for real turbulent flows. |
| first_indexed | 2024-03-11T00:07:34Z |
| format | Article |
| id | doaj.art-86e8c7ff7ebb49c6890efbed62569bba |
| institution | Directory Open Access Journal |
| issn | 2073-4433 |
| language | English |
| last_indexed | 2024-03-11T00:07:34Z |
| publishDate | 2023-08-01 |
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| series | Atmosphere |
| spelling | doaj.art-86e8c7ff7ebb49c6890efbed62569bba2023-11-19T00:13:44ZengMDPI AGAtmosphere2073-44332023-08-01148131610.3390/atmos14081316Exact Intermittent Solutions in a Turbulence Multi-Branch Shell ModelBen Ajzner0Alexandros Alexakis1Laboratoire de Physique de l’Ecole Normale Supérieure, Université PSL, Centre National de la Recherche Scientifique, Sorbonne Université, Université de Paris, F-75005 Paris, FranceLaboratoire de Physique de l’Ecole Normale Supérieure, Université PSL, Centre National de la Recherche Scientifique, Sorbonne Université, Université de Paris, F-75005 Paris, FranceReproducing complex phenomena with simple models marks our understanding of the phenomena themselves, and this is what Jack Herring’s work demonstrated multiple times. In that spirit, this work studies a turbulence shell model consisting of a hierarchy of structures of different scales <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mi>n</mi></msub></semantics></math></inline-formula> such that each structure transfers its energy to two substructures of scale <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>ℓ</mo><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mo>ℓ</mo><mi>n</mi></msub><mo>/</mo><mi>λ</mi></mrow></semantics></math></inline-formula>. For this model, we construct exact inertial range solutions that display intermittency, i.e., absence of self-similarity. Using a large ensemble of these solutions, we investigate how the probability distributions of the velocity modes change with scale. It is demonstrated that, while velocity amplitudes are not scale-invariant, their ratios are. Furthermore, using large deviation theory, we show how the probability distributions of the velocity modes can be re-scaled to collapse in a scale-independent form. Finally, we discuss the implications the present results have for real turbulent flows.https://www.mdpi.com/2073-4433/14/8/1316turbulenceintermittency |
| spellingShingle | Ben Ajzner Alexandros Alexakis Exact Intermittent Solutions in a Turbulence Multi-Branch Shell Model Atmosphere turbulence intermittency |
| title | Exact Intermittent Solutions in a Turbulence Multi-Branch Shell Model |
| title_full | Exact Intermittent Solutions in a Turbulence Multi-Branch Shell Model |
| title_fullStr | Exact Intermittent Solutions in a Turbulence Multi-Branch Shell Model |
| title_full_unstemmed | Exact Intermittent Solutions in a Turbulence Multi-Branch Shell Model |
| title_short | Exact Intermittent Solutions in a Turbulence Multi-Branch Shell Model |
| title_sort | exact intermittent solutions in a turbulence multi branch shell model |
| topic | turbulence intermittency |
| url | https://www.mdpi.com/2073-4433/14/8/1316 |
| work_keys_str_mv | AT benajzner exactintermittentsolutionsinaturbulencemultibranchshellmodel AT alexandrosalexakis exactintermittentsolutionsinaturbulencemultibranchshellmodel |