Richard J.A.M. Stevens

Physics of Fluids · University of Twente

Publication 21 · Thermal convection

Comparison between two and three dimensional Rayleigh-Bénard convection

E.P. van der Poel, R.J.A.M. Stevens, D. Lohse, J. Fluid Mech. 736, 177-194 (2013).

Main finding

Two-dimensional transfer is regime- and observable-specific; agreement in Nu does not establish equivalence of flow, Reynolds number, or boundary layers.

Compensated Reynolds number against Rayleigh and Prandtl number in two and three dimensions
How to read the figure. Compensated Reynolds number against Rayleigh number and Prandtl number, in two-dimensional and three-dimensional convection. The two-dimensional flow runs about a factor of three faster throughout, even where the two agree on heat transport. Matching the Nusselt number therefore does not establish that the flow, the Reynolds number or the boundary layers agree; Figure 8 makes the boundary-layer half of the point. Open the full-resolution figure. Figure 7. E.P. van der Poel et al. (2013). No separate licence is stated here; consult the original publication and credited source before reuse.

Why this matters

Similar global heat flux in two- and three-dimensional convection can conceal different flow structures, Reynolds numbers, and boundary layers.

Research context

The comparison spans two-dimensional rectangular and three-dimensional cylindrical simulations across different Rayleigh- and Prandtl-number ranges. Agreement is regime- and observable-specific; the constant-factor heat-transfer comparison is empirical.

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