Flow of Wall Jet Near Channel Exit at Moderate Reynolds Number
Bibliographic record
Abstract
The wall jet flow near channel exit at moderate Reynolds Number, emerging from a two-dimensional channel, is examined theoretically in this study. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow and stress fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface, flow in the outer layer region and the flow in the core region. The fluid is assumed to be Newtonian and it is found that the jet contracts downstream from the channel exit. The influence of inertia on the shape of free surface, the velocity and stress is emphasized and the higher order boundary layer is explored. To leading order, the problem is similar to the case of the free jet (Tillett) [1] with different boundary conditions. A similarity solution can be carried out using a similarity variable problem which is then solved as an initial-value problem, where the equation is integrated subject to the boundary conditions and a guessed value of the slope at the origin. The slope is adjusted until reasonable matching is achieved between the solution and the asymptotic form at large θ. The level of contraction is essentially independent of inertia, but the contraction moves further downstream with increasing Reynolds number. The present work provides the correct conditions near exit, which are required to determine the jet structure further downstream. If the jet becomes thin far downstream, a boundary layer formulation can be used with the presently predicted boundary conditions for steady and possibly transient flows.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".