Richard J.A.M. Stevens

Physics of Fluids · University of Twente

Publication 7 · Thermal convection

Radial boundary layer structure and Nusselt number in Rayleigh-Bénard convection

R.J.A.M. Stevens, R. Verzicco, D. Lohse, J. Fluid Mech. 643, 495-507 (2010).

Main finding

This is strong evidence that integral Nu agreement is an insufficient DNS-fidelity test and that local sidewall plume resolution and exact thermal balance are essential. It is not proof that all tabulated finest grids are fully resolved or that one universal resolution formula applies.

Kinetic and thermal dissipation fields and their difference between two grid resolutions
How to read the figure. Kinetic (top) and thermal (bottom) dissipation rate against radius and height in a cylindrical cell at Ra = 2 x 10^9: the high-resolution field (left), its difference from a coarser simulation (middle), and that difference relative to the high-resolution value (right). The error concentrates at the plates and against the sidewall, where the plumes are - regions a globally averaged Nusselt number cannot see. Agreement in the integral heat transport is therefore not sufficient evidence that a simulation is resolved. Open the full-resolution figure. Figure 2. R.J.A.M. Stevens et al. (2010). No separate licence is stated here; consult the original publication and credited source before reuse.

Why this matters

A plausible global answer can hide unresolved local physics.

Research context

Verzicco–Camussi/Amati DNS supplies the disputed high-Nu lineage; Prandtl-, Rayleigh-, and Rossby-Number dependence of heat transport in… supplies the imported Γ=1 multi-Pr comparison and related code lineage. Later and parallel papers: Boundary layer structure in turbulent thermal convection and its… formalizes resolution guidance partly from this campaign; Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent… and Horizontal structures of velocity and temperature boundary layers in… test PB profiles under dynamic rescaling; Comparison of computational codes for direct numerical simulations of… later demonstrates across codes that plausible Nu can conceal local under-resolution. Boundary layers in rotating weakly turbulent Rayleigh-Bénard convection uses related boundary-layer diagnostics in rotating convection.

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