Multiple heat transport maxima in confined-rotating Rayleigh-Bénard convection

Hartmann, Robert; Verzicco, Roberto; Klein Kranenbarg, Liesbeth; Lohse, Detlef; Stevens, Richard J.A.M.

doi:10.1017/jfm.2021.1031

How rotation and confinement create three heat-transport maxima

R. Hartmann, R. Verzicco, L. Klein Kranenbarg, D. Lohse, and R.J.A.M. Stevens, Journal of Fluid Mechanics 939, A1 (2022).

The article and Figure 1 are open access under CC BY 4.0.

Main finding

At Ra = 7 × 10⁸ and Pr = 4.38, the sampled rotation-confinement DNS map contained three separated normalized heat-transport maxima: confinement-only, double-vortex, and single-vortex states. Across the four-Rayleigh-number matrix, the double-vortex maximum reached about 50% enhancement at lower Ra but less than 20% at the two higher Ra. The discrete, interpolated cylinder dataset does not define universal optima or uniquely isolate a mechanism.

Normalized heat transport across sampled inverse Rossby number and inverse aspect ratio at Rayleigh number 7 times 10 to the eighth, with three maxima labelled A, B, and C — **How to read the figure.** This is Figure 1(a) at Ra = 7 × 10⁸ and Pr = 4.38. The horizontal coordinate Ro⁻¹ increases rotation; the vertical coordinate Γ⁻¹ = H/D increases horizontal confinement. Circles are computed DNS cases, while the colored background is a cubic interpolation rather than additional evidence. A marks the non-rotating confinement maximum, B the double-vortex maximum, and C the single-vortex maximum. Warm colors indicate transport above the non-rotating Γ⁻¹ = 1 reference and cool colors indicate lower transport. The other Figure 1 panels supply correlated flow-state diagnostics; this crop does not independently establish those mechanisms. Open the full-resolution panel. Figure 1(a), cropped without resampling. R. Hartmann et al. (2022), CC BY 4.0.

Why this matters

Rotation and confinement each stabilize convection, but their heat-transport effects do not simply add. Their combination reorganizes the flow into different domain-spanning states, producing several local maxima in the joint control space. Optimizing one control while holding the other implicit can therefore miss the dominant regime or select a response that disappears as thermal driving changes.

Research context

The study contains 323 three-dimensional Boussinesq DNS in a rotating cylinder at fixed Pr = 4.38, four Rayleigh numbers from 2 × 10⁸ to 7 × 10⁹, 0 ≤ Ro⁻¹ ≤ 40, and 2 ≤ Γ⁻¹ ≤ 32. The authors associate the maxima with boundary-layer-controlled heat injection and stable domain-spanning bulk flow. Those contributions are correlated diagnostics, not independently manipulated causal effects. Sampling is discrete and nonuniform; the response-map backgrounds are interpolated, the single-vortex classifier contains an explicitly arbitrary threshold, and the plotted optimum-location bars elsewhere in the paper have no stated uncertainty construction. The simulations use one Prandtl number, cylindrical no-slip boundaries, and one numerical method, with no independent experiment, alternate solver, hysteresis study, initial-state ensemble, or universal scaling law for the coupled optima. The result establishes a nonseparable response within this matrix, not an engineering optimum or a universal transition boundary.

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