Transition control of the blasius boundary layer using linear robust control theory
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Bibliographic record
Abstract
Abstract The paper considers control system design for linearized three-dimensional perturbations about a nominal laminar boundary layer over a flat plate (the Blasius profile). The objective is prevention of the laminar to turbulent transition using appropriate inputs, outputs, and feedback controllers. They are synthesized with a view to reducing transient energy growth, a known precursor to important transition scenarios. The linearized Navier–Stokes equations are reduced to the Orr–Sommerfeld and Squire equations with wall-normal velocity actuation entering through the boundary conditions on the wall. The sensor output is taken to be the wall-normal derivative of the wall-normal vorticity measured on the plate. Several multivariable output controllers are examined, including simple constant gain output feedback, loop transfer recovery, and $$H_{\infty }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> loop shaping. Reduced order compensators are developed using balanced truncation and analyzed for robustness using the gap metric between reduced order models and full order models. It is demonstrated that the level of minimum transient energy growth that can be achieved is similar for these diverse controller methodologies but falls short of that which can be achieved using optimal state feedback.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it