Efficient global resolvent analysis via the one-way Navier–Stokes equations
Bibliographic record
Abstract
Resolvent analysis is a powerful tool for modelling and analysing transitional and turbulent flows and, in particular, for approximating coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more than one inhomogeneous spatial coordinate remains computationally expensive. In this paper we show how efficient and accurate approximations of resolvent modes can be obtained using a well-posed spatial marching method for flows that contain a slowly varying direction, i.e. one in which the mean flow changes gradually. First, we derive a well-posed and convergent one-way equation describing the downstream-travelling waves supported by the linearized Navier–Stokes equations. The method is based on a projection operator that isolates downstream-travelling waves. Integrating these one-way Navier–Stokes (OWNS) equations in the slowly varying direction, which requires significantly less CPU and memory resources than a direct solution of the linearized Navier–Stokes equations, approximates the action of the resolvent operator on a forcing vector. Second, this capability is leveraged to compute approximate resolvent modes using an adjoint-based optimization framework in which the forward and adjoint OWNS equations are marched in the downstream and upstream directions, respectively. This avoids the need to solve direct and adjoint globally discretized equations, therefore bypassing the main computational bottleneck of a typical global resolvent calculation. The method is demonstrated using the examples of a simple acoustics problem, a Mach 1.5 turbulent jet and a Mach 4.5 transitional zero-pressure-gradient flat-plate boundary layer. The optimal OWNS results are validated against corresponding global calculations, and the close agreement demonstrates the near-parabolic nature of these flows.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".