Direct numerical simulation of turbulent slope flows up to Grashof number
Bibliographic record
Abstract
Stably stratified turbulent flows over an unbounded, smooth, planar sloping surface at high Grashof numbers are examined using direct numerical simulations (DNS). Four sloping angles ( $\unicode[STIX]{x1D6FC}=15^{\circ },30^{\circ },60^{\circ }$ and $90^{\circ }$ ) and three Grashof numbers ( $\mathit{Gr}=5\times 10^{10},1\times 10^{11}$ and $2.1\times 10^{11}$ ) are considered. Variations in mean flow, second-order statistics and budgets of mean- (MKE) and turbulent-kinetic energy (TKE) are evaluated as a function of $\unicode[STIX]{x1D6FC}$ and $Gr$ at fixed molecular Prandtl number $(Pr=1)$ . Dynamic and energy identities are highlighted, which diagnose the convergence of the averaging operation applied to the DNS results. Turbulent anabatic (upward moving warm fluid along the slope) and katabatic (downward moving cold fluid along the slope) regimes are identical for the vertical wall set-up (up to the sign of the along-slope velocity), but undergo a different transition in the mechanisms sustaining turbulence as the sloping angle decreases, resulting in stark differences at low $\unicode[STIX]{x1D6FC}$ . In addition, budget equations show how MKE is fed into the system through the imposed surface buoyancy, and turbulent fluctuations redistribute it from the low-level jet (LLJ) nose towards the boundary and outer flow regions. Analysis of the TKE budget equation suggests a subdivision of the boundary layer of anabatic and katabatic flows into four distinct thermodynamical regions: (i) an outer layer, corresponding approximately to the return flow region, where turbulent transport is the main source of TKE and balances dissipation; (ii) an intermediate layer, bounded below by the LLJ and capped above by the outer layer, where the sum of shear and buoyant production overcomes dissipation, and where turbulent and pressure transport terms are a sink of TKE; (iii) a buffer layer, located at $5\lessapprox z^{+}\lessapprox 30$ , where TKE is provided by turbulent and pressure transport terms, to balance viscous diffusion and dissipation; and (iv) a laminar sublayer, corresponding to $z^{+}\lessapprox 5$ , where the influence of viscosity is significant. $(\cdot )^{+}$ denotes a quantity rescaled in inner units. Interestingly, a zone of global backscatter (energy transfer from the turbulent eddies to the mean flow) is consistently found in a thin layer below the LLJ in both anabatic and katabatic regimes.
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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 | 0.000 | 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 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".