Mathematical modeling of frazil ice formation and evolution
Bibliographic record
Abstract
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".