Mathematical modeling of frazil ice formation and evolution
Notice bibliographique
Résumé
In cold regions the production of fraztl ice in supercooled turbulent water has a profound impact on the design, operation and maintenance of water resources infrastructure.Studies on frazil ice formation are therefore important and imperative for ice engineering.This study mainly focuses on the development of mathematical models for frazil ice formation and evolution, which is an important part of modeling ice formation in a river.A general mathematical model is formulated that includes the modeling of flow and turbulence, heat transfer, and frazil ice transport in open chan¡rel flow.ln addition the methodologies to model the physical processes of ice formation are described.Three mathematical models to simulate the supercooling process and frazil ice evolution were developed based on the general mathematical model and frazll ice dynamics.A zero-dimensional mathematical model was able to simulate water temperature history, frazil ice number evolution in the well-mixed water and the varied size distribution of frazil ice during the supercooling process.A vertical one-dimensional mathematical model was able to simulate water temperature variation with time at the different water depths, velocity and turbulent intensity distribution over the water depth, and the vertical distribution of frazil ice number concentration.The variation of mean size of fraztl ice particle is also simulated.An extended one-dimensional mathematical model was developed from the vertical one-dimensional model by including the size distribution of frazil ice and the complicated physical processeS.The three mathematical models developed are calibrated and verified using experimental data. Mathematical Modeling of Frazil lce Formatio, onã E oliffiGeneral Description research is divided into two areas: the study of river ice and the study of sea ice, both of which involve similar physical processes although salinity and strongly nonlinear waves are involved in the formation of sea ice.This study will be confined to the formation of river ice.River ice phenomena include the formation, evolution, transport, accumulation, and deterioration of various forms of ice (Shen, L996).River ice processes involve complex interactions between the hydrod5mamics, mechanics, and the thermal dynamics.Several reviews of river ice processes and the state-of-research are available (e.g., Ashton, 1986;Gerard, 1990; Prowse, L993;Beltaos, 1995;and Shen, 1996), in which it is stated that the studies of frazil ice formation and anchor ice formation are very limited, and that more attention and effort are required in these two areas.Frazil ice is defined as a fine, small, needle-like structure or thin, flat, circular plates of ice suspended in water (USA CRREL, lgg7),and it is the origin of almost all the others forms of river ice (Ettema et al., 1984).Early studies of frazil ice usually focused on the supercooling process, nucleation, frazll ice growth and evolution both from an experimental and a mathematical perspective.Mathematical modeling has been useful in predicting the ice formation and its corresponding consequences, while the experimental study often provided useful data for the development of the mathematical models and for elucidating unclear mechanisms about ice formation. Mathematical Modeling of Frazil lce Form.ation and Evolution
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Comment cette classification a été obtenuedéplier
Prédiction machine sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Le volet Gemma est une étiquette directe du modèle pour chaque travail de la base, lue sur la notice réduite au titre. Le volet Codex est un classifieur appris des 10 348 étiquettes directes de Codex et calibré sur les taux pondérés de l'échantillon; les champs sans appui suffisant ne portent aucun appel Codex. Le mode candidate est l'union des deux volets; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont pas des étiquettes humaines.
Scores du classifieur distillé par catégorie (deux têtes)
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,000 | 0,001 |
| Méta-épidémiologie (sens strict) | 0,001 | 0,000 |
| Méta-épidémiologie (sens large) | 0,001 | 0,001 |
| Bibliométrie | 0,001 | 0,001 |
| Études des sciences et des technologies | 0,000 | 0,001 |
| Communication savante | 0,001 | 0,001 |
| Science ouverte | 0,001 | 0,001 |
| Intégrité de la recherche | 0,001 | 0,001 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,001 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule source (Gemma direct ou Codex distillé), pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».