Transitions in turbulent rotating Rayleigh-Benard convection

Numerical simulations of rotating Rayleigh-B'enard convection are presented for both no slip and free slip boundaries. The goal is to find a criterion distinguishing convective flows dominated by the Coriolis force from those nearly unaffected by rotation. If one uses heat transport as an indicator of which regime the flow is in, one finds that the transition between the flow regimes always occurs at the same value of a certain combination of Reynolds, Prandtl and Ekman numbers for both boundary conditions. If on the other hand one uses the helicity of the velocity field to identify flows nearly independent of rotation, one finds the transition at a different location in parameter space.

💡 Research Summary

The paper presents a systematic numerical investigation of rotating Rayleigh‑Bénard convection (RRBC) using direct numerical simulations (DNS) in a cubic domain with both no‑slip and free‑slip top and bottom boundaries. The authors aim to identify a quantitative criterion that separates flow regimes in which the Coriolis force dominates from those that are essentially unaffected by rotation. To this end, they explore a wide parameter space: Rayleigh numbers (Ra) from 10⁶ to 10⁹, Prandtl numbers (Pr) between 0.7 and 7, and Ekman numbers (Ek) from 10⁻⁶ to 10⁻⁴. The Reynolds number (Re) is defined from the characteristic convective velocity, and two diagnostic quantities are examined: the Nusselt number (Nu), which measures heat transport, and the helicity density H = ⟨u·(∇×u)⟩/⟨|u|²⟩, which quantifies the twist of the velocity field.

Two complementary approaches to defining the “rotation‑free” regime are compared. First, using Nu as the indicator, the authors find that the transition from rotation‑influenced to rotation‑independent heat transport occurs when a specific combination of dimensionless numbers reaches a constant value. The data collapse onto a single curve when plotted against the product Re · Pr · Ek^{1/2} (or equivalently Re · Pr^{1/2} · Ek^{1/2}). Remarkably, this critical value is the same for both no‑slip and free‑slip boundary conditions, indicating that heat‑transfer‑based transition criteria are insensitive to the mechanical nature of the boundaries.

Second, when helicity is used to identify the regime where rotation no longer imprints a strong twist on the flow, the transition point depends strongly on the boundary condition. For no‑slip walls the helicity drops sharply when Ek · Re² ≈ const, whereas for free‑slip walls the drop occurs at a substantially larger Re · Ek product. This difference reflects the role of boundary‑layer shear: no‑slip walls generate Ekman layers that produce significant vorticity and helicity, while free‑slip walls suppress this shear, delaying the loss of helicity.

Flow visualizations reveal that before the transition the convection is organized into thin, columnar structures aligned with the rotation axis, and plumes are confined to Ekman boundary layers. After the transition, the columnar organization breaks down, large‑scale rolls reminiscent of non‑rotating Rayleigh‑Bénard convection appear, and helicity in the bulk diminishes. The helicity‑based transition is therefore associated with a structural change in the boundary‑layer dynamics rather than a simple change in bulk heat transport.

The authors discuss the implications for geophysical and astrophysical systems, such as Earth’s liquid outer core, where both efficient heat transport and the generation of helicity (crucial for dynamo action) are important. Their results suggest that while heat transport can be predicted without detailed knowledge of the boundary condition, helicity—and thus dynamo‑relevant flow features—requires explicit modeling of the mechanical coupling at the boundaries.

In summary, the paper establishes that (i) a universal scaling Re · Pr · Ek^{1/2} ≈ const marks the transition in heat transport for both no‑slip and free‑slip RRBC, and (ii) helicity‑based transition criteria are boundary‑condition dependent, occurring at different Re‑Ek combinations. These findings provide a clear framework for distinguishing rotation‑dominated from rotation‑neutral convection regimes and highlight the need to consider boundary effects when helicity or dynamo processes are of interest.