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arxiv: 2607.06350 · v1 · pith:F7F7UWWO · submitted 2026-07-07 · physics.flu-dyn

Suppressing wall modes in confined rotating turbulent convection

L\'azaro Mart\'inez-Ort\'iz , Maarten Minartz , Youri H. Lemm , Xander M. de Wit , Herman J. H. Clercx , Rudie P. J. Kunnen This is my paper

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classification physics.flu-dyn
keywords barriersbarriermodessidewallwallflownearturbulent
0
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The pith

Ring barriers suppress wall modes in rotating convection

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

In confined rotating turbulent convection, persistent wave-like structures called wall modes arise near the sidewalls of the container, producing the largest vertical velocities, biasing heat transport upward, and injecting radial jets into the bulk flow. These structures are problematic because they contaminate measurements and prevent clean access to the bulk dynamics that idealized (laterally periodic) simulations can reach. This paper shows, through combined laboratory experiments and direct numerical simulations in cylindrical cells, that mounting ring-shaped horizontal barriers on the inner sidewall suppresses the major signatures of wall modes. The barriers reduce near-wall vertical velocity peaks, disrupt the dominant azimuthal wave pattern, attenuate radial jet ejections, eliminate the boundary zonal flow (a cyclonic ring in the time-averaged azimuthal velocity), and shift global heat transport toward values characteristic of sidewall-free periodic domains. The suppression efficiency is governed by the ratio of the barrier width to the wall-mode length scale (set by the Ekman number): the barrier must be wider than the inner Stewartson layer scale but narrower than the outer wall-mode extent. A second barrier enhances suppression, particularly at stronger thermal forcing where wall modes re-emerge above and below a single barrier. The paper also identifies an unintended consequence: the thermal-conductivity mismatch between the barrier and the fluid bends isotherms near the barrier, misaligning them with isobars and inducing a steady baroclinic flow along the barrier faces. This secondary flow can be partially mitigated by using higher-conductivity barrier materials and rounded edge geometry.

Core claim

The central discovery is that the suppression of wall modes by sidewall barriers is controlled by a scale-matching condition: the barrier width must exceed the inner Stewartson layer thickness (scaling as Ekman number to the one-third power) but remain below the outer wall-mode extent (scaling as Ekman number to the one-quarter power). When this condition is met, a single barrier eliminates the dominant azimuthal mode, suppresses near-wall velocity peaks, removes the boundary zonal flow, and recovers heat-transport values close to those of laterally periodic domains. The barriers also induce a secondary baroclinic flow caused by isotherm-isobar misalignment at the barrier, which is a direct,

What carries the argument

wall modes

If this is right

  • Experiments in rapidly rotating convection can now isolate bulk dynamics from sidewall contamination by installing properly scaled ring barriers, enabling closer comparison with idealized periodic-domain simulations.
  • The scale-matching condition (barrier width between Ek^{1/3} and Ek^{1/4} times the cell height) provides a concrete design rule for future experimental facilities targeting geostrophic convection regimes.
  • The baroclinic flow induced by thermal-conductivity mismatch suggests that barrier material choice is a critical design parameter; high-conductivity barriers reduce secondary flows but may introduce other thermal artifacts.
  • At extreme Rayleigh numbers, single barriers become insufficient and multiple barriers or stronger rotational confinement are needed, indicating that suppression strategies must be tailored to the specific region of parameter space.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If wall modes are topologically protected (as prior work suggests), the barriers likely do not destroy them but rather prevent their nonlinear saturation and spatial organization, effectively trapping them below threshold — this distinction between suppression and elimination is not fully resolved in the paper.
  • The baroclinic flow asymmetry between DNS and experiments, attributed to centrifugal buoyancy, implies that even small physical effects normally neglected in simulations can qualitatively change local flow topology near obstacles, raising questions about the fidelity of volume-penalization methods for other barrier geometries.
  • The finding that barrier effectiveness depends on the ratio of barrier width to wall-mode scale suggests a potential scaling law for the minimum number of barriers needed as a function of Rayleigh and Ekman numbers, though the paper does not derive such a law explicitly.

Load-bearing premise

The direct numerical simulations assume the volume penalization method with a fixed penalization strength accurately represents the fluid-barrier interaction, and that neglecting centrifugal buoyancy and assuming the barrier has the same thermal conductivity as the fluid are sufficient simplifications — yet the DNS-experiment mismatch in the baroclinic flow asymmetry shows these second-order effects qualitatively change the local dynamics near the barrier.

What would settle it

If barriers with width satisfying the stated scale-matching condition fail to reduce near-wall vertical velocity peaks or heat-transport bias in an independent experimental apparatus at the same parameters, the suppression mechanism would not be robust.

Figures

Figures reproduced from arXiv: 2607.06350 by Herman J. H. Clercx, L\'azaro Mart\'inez-Ort\'iz, Maarten Minartz, Rudie P. J. Kunnen, Xander M. de Wit, Youri H. Lemm.

Figure 1
Figure 1. Figure 1: (a) Parameter space 𝑅𝑎 versus 𝐸 𝑘, summarizing the conducted experiments and simulations (for more details, consult [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Vertical velocity field for the no barrier case. Strong vertical velocities are observed near the left (𝑥/𝐷 = 0) and right (𝑥/𝐷 = 1) walls.(b) Under the same conditions, a single barrier is placed at mid-height. Vertical velocities recover bulk values across the cross section; the barrier appears as a white band where it obstructs a small portion of the field of view. (c) Vertical velocity profiles alo… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Azimuthally averaged DNS fields of 𝑅𝑒𝑧 for the no-barrier, one barrier, and two barrier configurations at 𝑅𝑎 = 7.8 × 109 and 𝐸 𝑘 = 1.1 × 10−6 . The fields are shown in cylindrical coordinates, with the symmetry axis located at 𝑥/𝐷 = 0.5 and the sidewalls at 𝑥/𝐷 = 1. (b) Vertically averaged 𝑅𝑒𝑧 profiles at fixed 𝐸 𝑘 = 1.4 × 10−6 for different values of 𝑅𝑎. The no barrier cases exhibit a nearly uniform b… view at source ↗
Figure 4
Figure 4. Figure 4: (a) Effect of varying the barrier width at fixed 𝑅𝑎 = 7.8 × 109 and 𝐸 𝑘 = 1.1 × 10−6 . (b) Colour profiles showing the effect of a single barrier as 𝐸 𝑘 is decreased and 𝑅𝑎 is increased while maintaining 𝑅𝑜 = 𝐸 𝑘√︁ 𝑅𝑎/𝑃𝑟 = 4.27 × 10−2 . The gray profile corresponds to weaker rotational confinement at the higher Rossby number, 𝑅𝑜 = 9.55 × 10−2 . In all cases, 𝑑/𝐷 = 0.05 is fixed. All results are obtained fr… view at source ↗
Figure 5
Figure 5. Figure 5: (a) Dependence of the time-averaged 𝑁𝑢 on 𝑅𝑎 at fixed 𝐸 𝑘 = 1.1 × 10−6 from DNS. (b) Same as in (a), but for fixed 𝑅𝑜 = 4.27 × 10−2 . Here, 𝑅𝑎 is varied as in (a), while 𝐸 𝑘 is decreased accordingly (see [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Instantaneous radial velocity component for 𝑅𝑎 = 1.6 × 109 , 𝐸 𝑘 = 2.5 × 10−6 , without barrier. Azimuthally, two dominant regions of opposite sign (inward and outward) are observed. (b) Full structure of the wall modes is recovered; the vertical cross-section shows maximum upward and downward velocities near the walls, while the horizontal cross-section isolates the 𝑚 = 2 Fourier component of the radi… view at source ↗
Figure 7
Figure 7. Figure 7: (a) Cross-section of the time-averaged azimuthal velocity field at 𝑧 = 𝐻/3, obtained experimentally at 𝑅𝑎 = 1.57×109 and 𝐸 𝑘 = 5.0×10−6 . An anticyclonic bulk region and a cyclonic near-wall ring corresponding to the BZF are observed. (b) Same as (a), but with one barrier. The cyclonic BZF ring is no longer present, and the mean field exhibits a fully anticyclonic cross-section. (c) Time- and azimuthally a… view at source ↗
Figure 8
Figure 8. Figure 8: (a) Time and azimuthally averaged √︁ 𝑅𝑎/𝑃𝑟 𝑢˜𝜙 profiles in regions located 5 mm above and below the barrier. In both cases, an anticyclonic bulk region is observed. Above the barrier, a cyclonic near-wall region develops (stars indicate the position of the maximum in the profiles), whereas below the barrier an anticyclonic near-wall region is observed. The purple curve corresponds to the DNS; the remaining… view at source ↗
Figure 9
Figure 9. Figure 9: (a) Straight-cut plexiglass and aluminium barriers are employed. Owing to the higher thermal conductivity of aluminium, the baroclinic flow intensity is reduced compared to geometrically identical plexiglass barrier. (b) Barriers with a smoother, rounded finish are also effective; the combination of rounded geometry and aluminium material provides the strongest control, reducing the intensity of the barocl… view at source ↗
Figure 10
Figure 10. Figure 10: (a) Azimuthally averaged fields of 𝑅𝑒𝑧 for the no-barrier and one barrier configurations obtained from DNS at 𝑅𝑎 = 3.2×1011 and 𝐸 𝑘 = 10−7 . The fields are shown in cylindrical coordinates, with the rotation axis located at 𝑥/𝐷 = 0.5 and the sidewall at 𝑥/𝐷 = 1. (b) Time-averaged ⟨𝑁𝑢⟩𝑡 as a function of 𝑅𝑎 at fixed 𝐸 𝑘 = 10−7 . Appendix B. Baroclinic flow and effects of centrifugal buoyancy In the main tex… view at source ↗
Figure 11
Figure 11. Figure 11: (a) Sketch showing isotherms and isobars near the barrier. The curvature of the isotherms, which sets the direction of the temperature gradient, determines the sign of the baroclinic vorticity above and below the barrier, owing to the corresponding sign of the cross product ∇𝑝×∇𝜃 > 0 above the barrier and ∇𝑝×∇𝜃 < 0 below. (b) Heat maps of the time averaged azimuthal velocity from DNS for the no-barrier, o… view at source ↗
read the original abstract

In confined turbulent rotating convection, the largest vertical velocities are found near the sidewalls in the form of wave-like structures known as wall modes. These structures persist deep into the turbulent regime, bias heat transport, and disrupt bulk flow organisation through radial jets. Controlling or suppressing wall modes is, therefore, essential for accessing bulk dynamics free from wall-induced effects. Here, we combine experiments and direct numerical simulations to investigate wall modes control in cylindrical cells equipped with ring-shaped sidewall barriers. Barriers suppress vertical-velocity maxima near the sidewall and disrupt the characteristic wave-like pattern. Simulations further show that the barriers reduce the wall-mode-induced enhancement of heat transport, shifting it towards values characteristic of laterally periodic domains. The suppression efficiency is governed by the ratio of the barrier width to the wall-mode scale and is enhanced by the addition of a second barrier. In the horizontal plane, radial jet ejections are attenuated, while the time-averaged flow reveals suppression of the boundary zonal flow (BZF), a ring-shaped region of positive azimuthal velocity near the sidewall, provided measurements are taken away from the immediate vicinity of the barriers. In this region, isotherms bend toward the poorly conducting barrier, creating a local misalignment with the isobars and inducing a baroclinic flow adjacent to the barrier faces. This effect weakens with increasing barrier conductivity or smoother geometry. These results demonstrate that sidewall barriers provide a robust route for suppressing wall modes signatures in experimental turbulent rotating convection, while locally inducing secondary baroclinic flows near the barriers. Their use enables access to extreme rotating-convection regimes with reduced sidewall influence.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 8 minor

Summary. This manuscript investigates the suppression of wall modes in confined rotating Rayleigh–Bénard convection using ring-shaped sidewall barriers, combining PIV experiments and DNS. The central claim is that barriers suppress the characteristic signatures of wall modes—near-wall vertical velocity peaks, heat-transport bias, radial jet ejections, and the boundary zonal flow—when the barrier width exceeds the Stewartson inner-layer scale δ_m ~ Ek^{1/3}. The paper also characterizes a secondary baroclinic flow induced near the barriers due to thermal conductivity mismatch and proposes mitigation strategies. The experimental and DNS results show good quantitative agreement for the vertical, radial, and azimuthal velocity components, while the heat-transport results are DNS-only.

Significance. The problem addressed is well-motivated: wall modes contaminate heat-transport measurements and bulk flow organization in rotating convection experiments, and a practical suppression strategy is needed. The combination of laboratory experiments and DNS across multiple velocity components is a strength, as is the identification and partial mitigation of the secondary baroclinic flow. The scaling criterion d > δ_m = Ek^{1/3} provides a falsifiable, parameter-free design rule grounded in established Stewartson-layer theory. The extension to extreme parameter regimes (Appendix A) and the systematic variation of barrier width (Fig. 4, Fig. 5d) add value. The paper builds directly on the numerical proposal of Terrien et al. (2023) and provides the first experimental validation, which is a meaningful contribution to the field.

major comments (2)
  1. §3.2, Fig. 5: The heat-transport claim (pillar 2 of the central result) is supported by DNS alone; no experimental Nu measurements are presented. The DNS treats the barrier thermal diffusivity as identical to the fluid's (Eq. 2.4, §2.2), while the experimental Plexiglas barriers have κ approximately κ_water/3. The paper itself demonstrates in §3.5 that this conductivity mismatch substantially alters local barrier dynamics (isotherm bending, baroclinic flow intensity changing with aluminium vs. Plexiglas barriers, Fig. 9). Since the heat-transport modification depends on how the barrier redistributes convective transport in the near-wall region—precisely where the thermal-conductivity simplification matters most—the Nu results in Fig. 5 carry an unquantified systematic uncertainty. The authors should either (i) provide an estimate of the sensitivity of Nu to the barrier conductivity (e.g.
  2. a DNS comparison with a contrasting conductivity, even if approximate), or (ii) explicitly state this limitation in §3.2 and temper the claim that Nu shifts toward 'values characteristic of laterally periodic domains.' As written, the abstract and conclusion state the heat-transport shift as an established result without flagging that it rests on an idealized barrier model whose simplifications the paper itself shows to be consequential for local dynamics.
minor comments (8)
  1. §2.2: The penalization strength ζ=100 is stated as adequate based on a previous study (Martínez-Ortíz et al. 2026). A brief note on whether convergence with respect to ζ was checked for the present barrier geometry would strengthen confidence, since the barrier–fluid interaction is the central object of study.
  2. Fig. 3(b): The experimental and DNS profiles are at slightly different Ek (1.4×10⁻⁶ vs. 1.13×10⁻⁶) and different Ra. The agreement is described as 'excellent' but the parameter mismatch should be noted explicitly.
  3. §3.5, Fig. 8(a): The scaling δ_b ~ Ek^{0.20} is based on only four data points. The exponent should be labeled as preliminary, and the range of Ek over which it was measured should be stated. It is unclear whether this is a fitted exponent or merely empirical.
  4. Fig. 5(d): The barrier width axis uses d/D, while the scaling criterion is expressed in terms of d/δ_m or d/H. Adding a secondary axis in units of d/δ_m would make the figure self-consistent with the text and more interpretable.
  5. Appendix B, Fig. 11(f): The caption states 'Note the difference in Ek in bot cases' — the DNS and experimental Ek values used for this comparison should be stated explicitly in the caption or text, since the comparison involves centrifugal buoyancy effects that depend on Fr.
  6. §3.1: The statement 'predicting an exact relation for the number and characteristics of the barriers is not straightforward' is honest but could be sharpened. The paper does provide a useful criterion (δ_m < d < δ); clarifying whether this is intended as a necessary condition, a sufficient condition, or a heuristic would help the reader.
  7. Table 1: The grid resolution column uses notation like '193×385×[577,769]²' which is ambiguous. Clarify whether the bracket notation indicates two grid levels or a range.
  8. The abstract states 'shifting it towards values characteristic of laterally periodic domains' without qualification. Given that this is a DNS-only result with the conductivity simplification noted above, a qualifier such as 'in DNS' or 'under the idealized barrier model' would be appropriate.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee's single major comment concerns the heat-transport results in §3.2, which are DNS-only and rely on a barrier thermal diffusivity matched to the fluid rather than to the experimental Plexiglas. We agree this limitation should be made explicit and are happy to revise the manuscript accordingly.

read point-by-point responses

  1. Referee: §3.2, Fig. 5: The heat-transport claim (pillar 2 of the central result) is supported by DNS alone; no experimental Nu measurements are presented. The DNS treats the barrier thermal diffusivity as identical to the fluid's (Eq. 2.4, §2.2), while the experimental Plexiglas barriers have κ approximately κ_water/3. The paper itself demonstrates in §3.5 that this conductivity mismatch substantially alters local barrier dynamics (isotherm bending, baroclinic flow intensity changing with aluminium vs. Plexiglas barriers, Fig. 9). Since the heat-transport modification depends on how the barrier redistributes convective transport in the near-wall region—precisely where the thermal-conductivity simplification matters most—the Nu results in Fig. 5 carry an unquantified systematic uncertainty. The authors should either (i) provide an estimate of the sensitivity of Nu to the barrier conductivity (e.g.

    Authors: We thank the referee for raising this important point, which we fully acknowledge as a genuine limitation of the current study. The referee is correct on both counts: the Nu results in Fig. 5 are DNS-only, and the DNS assumes the barrier thermal diffusivity is identical to that of the fluid (Eq. 2.4), whereas the experimental Plexiglas barriers have a thermal conductivity roughly one-third that of water. We also agree that §3.5 demonstrates that the conductivity mismatch has consequential local effects on the isotherm bending and baroclinic flow intensity near the barrier. We address the referee's two suggested remedies in turn. Regarding option (i) — a DNS comparison with contrasting conductivity: we have in fact already begun such a comparison. In Appendix B, we include DNS with centrifugal buoyancy included (varying Froude number), which was necessary to recover the experimentally observed asymmetry in the baroclinic flow above and below the barrier. In that appendix, we explicitly note that differences in thermal diffusivity between the barrier and the fluid are an additional mechanism not captured in the main-text DNS and likely contribute to the observed symmetry breaking. However, a full DNS parameter study varying the barrier thermal diffusivity independently is not feasible within the revision timeframe, as each additional simulation at the relevant parameters (Ra ~ 10^9–10^10, Ek ~ 10^-6) requires substantial computational resources, and the volume penalisation method as currently implemented does not straightforwardly support a spatially varying thermal diffusivity field within the penalised region. We therefore adopt option (ii). We will revise §3.2 to explicitly state that the Nu results rest on an idealised barrier model in which the thermal diffusivity is revision: no

Circularity Check

0 steps flagged

No significant circularity: the paper's central claims are grounded in independent experimental measurements and DNS, with the scaling relation derived from established Stewartson layer theory rather than postulated to make results work.

full rationale

The paper's central claim — that sidewall barriers suppress wall modes — is supported by independent experimental PIV measurements (Figs. 2, 3b, 6, 7) and DNS (Figs. 3a, 4, 5), with quantitative agreement between the two. The scaling relation d > δ_m = Ek^{1/3} is derived from established Stewartson layer theory (Stewartson 1957, 1966; Kunnen et al. 2011), not defined in terms of the suppression result. The heat-transport shift toward periodic-domain Nu (Fig. 5) is DNS-only, but this is a limitation of experimental coverage, not circularity: the DNS solves the full Navier-Stokes equations (Eq. 2.2-2.4) with independently specified boundary conditions, and the Nu is computed from the resulting fields, not fitted to a target. The baroclinic flow mechanism (§3.5) is explained physically via isotherm-isobar misalignment (∇p × ∇θ), not defined circularly. The one self-citation (Martínez-Ortíz et al. 2026) merely justifies the penalization strength ζ=100, a numerical parameter choice that does not load-bear the central physical claims. The DNS-experiment mismatch in baroclinic flow asymmetry (§3.5, Appendix B) is openly acknowledged and investigated, not hidden. No step in the derivation chain reduces to its inputs by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 0 invented entities

The paper introduces no new physical entities or forces. The free parameters are geometric and numerical choices, not fitted constants in a theoretical model. The axioms are standard domain assumptions, though the volume penalization accuracy is a notable modeling assumption.

free parameters (3)
  • Barrier width d = 0.0125 to 0.2 (d/D)
    Varied systematically in DNS to find the suppression threshold relative to the wall mode scale.
  • Number of barriers = 1 or 2
    Varied to test suppression efficiency.
  • Penalisation strength ζ = 100
    Set ad hoc based on a previous study (Martínez-Ortíz et al. 2026) to enforce vanishing velocity inside the barrier.
axioms (3)
  • domain assumption Boussinesq approximation
    Standard in rotating RBC, invoked in §2.2.
  • standard math Stewartson layer scaling (δ_m/H = Ek^(1/3), δ/H = Ek^(1/4))
    Used to define the wall mode region and the suppression threshold for barrier width (§3.1).
  • domain assumption Volume penalization method accurately represents solid barriers
    Assumed in §2.2; the DNS-experiment mismatch in baroclinic flow (§3.5) suggests this is an approximation.

pith-pipeline@v1.1.0-glm · 28627 in / 2519 out tokens · 355706 ms · 2026-07-08T08:40:50.108776+00:00 · methodology

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