DNS of transitional and turbulent flows in rectangular ducts
Pith reviewed 2026-05-24 19:40 UTC · model grok-4.3
The pith
Reynolds number based on short-side half-length makes critical value for duct transition independent of aspect ratio for AR greater than one.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Direct numerical simulations of transitional and turbulent flows in rectangular ducts with fixed cross-sectional area and flow rate demonstrate that the Reynolds number based on the half length of the short side produces a critical Reynolds number independent of aspect ratio for ducts with aspect ratio greater than one. Mean and root-mean-square wall-normal velocity profiles collapse when scaled with the local friction velocity. At high friction Reynolds numbers the Reynolds-number dependence of the statistics matches that found in turbulent plane channels, while at low Reynolds numbers the profiles deviate from two-dimensional channel results because of interactions among flow structures of
What carries the argument
Reynolds number defined with the half-length of the shorter duct side as the characteristic length, which removes aspect-ratio dependence from the critical value for transition when area and flow rate are held constant.
If this is right
- Mean and rms wall-normal velocity profiles scale with the local friction velocity across the range of aspect ratios examined.
- At high friction Reynolds numbers the statistics follow the same Reynolds-number dependence observed in plane channel flow.
- At low Reynolds numbers the profiles differ from those in two-dimensional channels because structures of different sizes interact.
- Projection of velocity and Reynolds stress onto the eigenvectors of the strain-rate tensor reduces apparent anisotropy and yields simpler turbulent kinetic energy budgets.
Where Pith is reading between the lines
- Rectangular ducts could be used to map Reynolds-number effects on turbulence with fewer separate simulations than are needed for plane channels at high Re.
- The short-side scaling may indicate that the narrowest dimension controls the onset of turbulence in other non-circular duct shapes.
- The observed low-Re differences suggest that geometry-specific structure interactions must be accounted for when modeling transitional flows in ducts.
Load-bearing premise
Holding cross-sectional area and flow rate fixed while varying aspect ratio isolates the effect of geometry on transition without introducing confounding changes in effective length scales or boundary-layer development.
What would settle it
Direct numerical simulations or experiments at two different aspect ratios greater than one, both run at the same Reynolds number based on short-side half-length, that produce visibly different transition behavior would falsify the claimed independence.
read the original abstract
We carry out Direct Numerical Simulation (DNS) of flows in closed rectangular ducts with several aspect ratios. The Navier-Stokes equations are discretized through a second-order finite difference scheme, with non-uniform grids in two directions. The duct cross-sectional area is maintained constant as well as the flow rate, which allows to investigate which is the appropriate length scale in the Reynolds number for a good scaling in the laminar and in the fully turbulent regimes. We find that the Reynolds number based on the half length of the short side leads to a critical Reynolds number which is independent on the aspect ratio (AR), for ducts with AR>1. The mean and rms wall-normal velocity profiles are found to scale with the local value of the friction velocity. At high friction Reynolds numbers, the Reynolds number dependence is similar to that in turbulent plane channels, hence flows in rectangular ducts allow to investigate the Reynolds number dependency through a reduced number of simulations. At low Re the profiles of the statistics differ from those in the two-dimensional channel due to the interaction of flow structures of different size. The projection of the velocity vector and of the Reynolds stress tensor along the eigenvectors of the strain-rate tensor yields reduced Reynolds stress anisotropy, and simple turbulent kinetic energy budgets.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports direct numerical simulations (DNS) of transitional and turbulent flows in rectangular ducts with varying aspect ratios (AR), using a second-order finite-difference scheme on non-uniform grids. Cross-sectional area and mass flow rate are held fixed while AR is varied. The central claim is that the Reynolds number based on the half-length of the short side produces a critical Reynolds number independent of AR for AR > 1. Additional results include scaling of mean and rms wall-normal velocity profiles with local friction velocity, similarity to plane-channel Re dependence at high friction Reynolds numbers, differences at low Re due to interacting flow structures, and reduced Reynolds-stress anisotropy obtained by projecting onto strain-rate eigenvectors.
Significance. If the results hold, the identification of an AR-independent critical Re based on short-side half-height provides a practical length scale for duct transition studies. The fixed-area, fixed-flow-rate design allows direct discrimination among candidate scales without additional parameters. The standard DNS method and the absence of fitted parameters or self-referential definitions in the scaling claims are strengths. The observation that high-Re duct statistics collapse onto channel behavior suggests the geometry can be used to explore Re dependence with a reduced simulation campaign.
major comments (1)
- [Methods] Methods section: the manuscript should report the grid resolutions (in wall units) and any convergence checks or error estimates used to establish the critical Re values; without these, the independence claim rests on unquantified numerical accuracy.
minor comments (2)
- [Abstract] Abstract: the sentence describing the critical-Re result is long; splitting it would improve readability.
- The phrase 'the Reynolds number dependence is similar to that in turbulent plane channels' should cite the specific channel data or references used for comparison.
Simulated Author's Rebuttal
We thank the referee for the constructive review and the recommendation of minor revision. The single major comment concerns additional documentation in the Methods section, which we address below and will incorporate in the revised manuscript.
read point-by-point responses
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Referee: [Methods] Methods section: the manuscript should report the grid resolutions (in wall units) and any convergence checks or error estimates used to establish the critical Re values; without these, the independence claim rests on unquantified numerical accuracy.
Authors: We agree that explicit reporting of grid resolutions in wall units and convergence details strengthens the critical-Re independence claim. In the revised manuscript we will add to the Methods section a table listing the streamwise, wall-normal and spanwise resolutions in wall units (based on the local friction velocity) for every aspect ratio and Reynolds number simulated. We will also describe the convergence procedure: for each AR we performed a sequence of runs at successively doubled resolutions until the location of the laminar-turbulent transition (identified by the sudden rise in friction factor and the appearance of sustained turbulent fluctuations) ceased to change within 1 %; the difference between the two finest grids supplies the error bar on the reported critical Re. These additions quantify the numerical accuracy underlying the AR-independent threshold for AR > 1. revision: yes
Circularity Check
No significant circularity detected
full rationale
The paper's central claims, including the aspect-ratio independence of the critical Reynolds number based on short-side half-height for AR>1, are presented as direct outcomes of DNS integration of the Navier-Stokes equations with fixed cross-sectional area and mass flow rate. No load-bearing steps reduce to self-definition, fitted inputs renamed as predictions, or self-citation chains; the numerical discretization and scaling hypotheses are independent of the reported empirical findings, rendering the derivation self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
axioms (2)
- standard math Incompressible Navier-Stokes equations accurately describe the flow at the simulated Reynolds numbers
- domain assumption Second-order finite-difference scheme on non-uniform grids is adequate to resolve transitional and turbulent structures
discussion (0)
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