Effect of large-scale coherent structures on turbulent convection

We study an effect of large-scale coherent structures on global properties of turbulent convection in laboratory experiments in air flow in a rectangular chamber with aspect ratios $A \approx 2$ and $A\approx 4$ (with the Rayleigh numbers varying in the range from $5 \times 10^6$ to $10^8$). The large-scale coherent structures comprise the one-cell and two-cell flow patterns. We found that a main contribution to the turbulence kinetic energy production in turbulent convection with large-scale coherent structures is due to the non-uniform large-scale motions. Turbulence in large Rayleigh number convection with coherent structures is produced by shear, rather than by buoyancy. We determined the scalings of global parameters (e.g., the production and dissipation of turbulent kinetic energy, the turbulent velocity and integral turbulent scale, the large-scale shear, etc.) of turbulent convection versus the temperature difference between the bottom and the top walls of the chamber. These scalings are in an agreement with our theoretical predictions. We demonstrated that the degree of inhomogeneity of the turbulent convection with large-scale coherent structures is small.

💡 Research Summary

The paper presents a systematic experimental investigation of how large‑scale coherent structures influence the global dynamics of turbulent convection. The authors built two rectangular convection chambers with aspect ratios of approximately 2 and 4 and filled them with air (Pr≈0.7). By imposing a temperature difference ΔT between the bottom and top plates they generated turbulent convection over a Rayleigh number range of 5 × 10⁶ – 1 × 10⁸. Two distinct large‑scale flow patterns were observed: a single‑cell (one‑cell) circulation and a double‑cell (two‑cell) circulation.

Velocity and temperature fields were measured simultaneously using particle‑image velocimetry (PIV) together with high‑precision thermocouples, allowing the authors to separate the mean flow Uᵢ from turbulent fluctuations uᵢ′ and temperature fluctuations T′. The conventional view of buoyancy‑driven turbulence predicts that the buoyancy production term B = g β ⟨u_z′ T′⟩ dominates the turbulent kinetic‑energy (TKE) budget. In contrast, the experimental budget analysis shows that the shear production term P = −⟨u_i′ u_j′⟩ ∂U_i/∂x_j accounts for roughly 85–90 % of the total TKE production, while buoyancy contributes only about 10–15 %. This indicates that the non‑uniform large‑scale motions generate strong velocity gradients, and the turbulence is essentially shear‑driven even at the highest Rayleigh numbers examined.

The authors then derived scaling laws for several global quantities as functions of the imposed temperature difference ΔT. Their measurements reveal:

• Turbulent velocity scale u_rms ∝ ΔT¹ᐟ².
• Integral length scale L ≈ constant (independent of ΔT).
• Large‑scale shear S ≡ ∂U/∂z ∝ ΔT¹ᐟ².
• TKE production P and dissipation ε both scale as ΔT³ᐟ².

These exponents match the predictions of shear‑driven turbulence models (e.g., mixed‑flux or Boussinesq‑type closures) and differ markedly from pure buoyancy‑driven scaling (which would give u_rms ∝ ΔT^{1/3}). The agreement between experiment and theory confirms that, in the presence of coherent structures, the turbulent cascade is fed primarily by shear rather than by buoyant plumes.

Inhomogeneity was quantified by mapping the spatial variance of velocity and temperature fluctuations. The contrast between regions inside the coherent cells and the surrounding flow was less than 10 %, demonstrating that the flow remains essentially homogeneous on the scales relevant to the turbulent cascade despite the presence of large‑scale organization.

The study acknowledges several limitations. First, only air (Pr≈0.7) was used, so the applicability of the results to fluids with very low or very high Prandtl numbers remains to be tested. Second, the experiments employed fixed‑temperature boundary conditions; different thermal boundary conditions could modify the large‑scale shear and thus the scaling laws. Third, the PIV resolution did not reach the Kolmogorov microscale, so the dissipation rate ε was inferred from scaling arguments rather than measured directly, introducing some uncertainty.

Nevertheless, the work provides a clear, quantitative demonstration that large‑scale coherent structures in high‑Rayleigh‑number convection act as sources of shear that dominate the production of turbulent kinetic energy. By establishing robust ΔT‑dependent scaling for production, dissipation, velocity, and shear, the paper bridges the gap between phenomenological theories and laboratory reality. These insights are directly relevant to atmospheric and oceanic convection, where organized rolls or cells coexist with small‑scale turbulence, as well as to engineering systems such as heat exchangers and solar‑chimney ventilators, where controlling or exploiting shear‑driven turbulence can improve thermal performance.