Richard J.A.M. Stevens

Physics of Fluids

University of Twente

Publication 111 · Thermal convection

Why the optimal rotation reverses at large Rayleigh number

R. Hartmann, G.S. Yerragolam, R. Verzicco, D. Lohse, and R.J.A.M. Stevens, Physical Review Fluids 8, 083501 (2023).

The displayed figure is cropped from the CC BY 4.0 arXiv v2 author manuscript. The APS version of record has separate publisher terms.

Main finding

Across the tested rotating-convection DNS, the inverse Rossby number giving the sampled maximum normalized heat transport first increased and then decreased with Rayleigh number. For Pr = 4.38 and 6.4, the maximum enhancement fell from roughly 20%–30% at lower Rayleigh number to about 5% by Ra = 10¹⁰.

Normalized heat transport versus inverse Rossby number at Prandtl numbers 4.38 and 6.4, showing weaker maxima and lower optimal rotation at Rayleigh number 10 to the tenth
How to read the figure. Panels (a) and (b) plot heat transport normalized by the nonrotating value, Nu/Nu0, against inverse Rossby number for Pr = 4.38 and 6.4. Each color represents a Rayleigh number. Open symbols are simulations reused from Yang et al. (2020); filled symbols are new simulations in this study. As Ra increases through the sampled range, the peak first moves toward faster rotation and then returns toward lower inverse Rossby number, while its height falls from roughly 1.2–1.3 to about 1.05. The figure establishes the response trend, not the proposed vortex-coherence or wall-shear mechanism. Open the full-resolution figure. Figure 2(a,b), cropped without resampling from the arXiv v2 author manuscript. R. Hartmann et al. (2023), CC BY 4.0.

Why this matters

At lower Rayleigh number, the rotation giving the largest heat-transfer enhancement is associated with matching the kinetic and thermal boundary-layer thicknesses. That rule continues to organize the layer ratio at larger Rayleigh number but no longer locates the observed maximum. The simulations instead show vertically coherent, Ekman-fed vortices becoming vertically decorrelated while bulk thermal dissipation increases. These diagnostics support a changing bulk-flow limitation, although their covariance does not identify wall shear as a unique cause.

Research context

The study uses three-dimensional Boussinesq DNS in a horizontally periodic cell with no-slip isothermal plates, 10⁷ ≤ Ra ≤ 10¹⁰, 0 ≤ Ro−1 ≤ 40, and Pr = 4.38 or 6.4. It combines 81 new simulations with data from Yang et al. (2020), so those subsets are one evidence chain rather than independent replication. The broad maxima retain rotation-rate sampling uncertainty, and the Pr = 6.4, Ra = 10¹⁰ value uses an estimated nonrotating Nu0 = 125.5. The simulations provide no independent experiment or solver test of the proposed threshold. Two nearby waterlike Prandtl numbers do not establish a universal compensated optimum, and the data do not prove that enhancement vanishes beyond Ra = 10¹⁰.

Read the version of record Open-access arXiv manuscript View in the complete publication list Related rotating-convection research