Richard J.A.M. Stevens

Professor at the University of Twente

Wind energy · Turbulence · Environmental flows

Publication 5 · Thermal convection

Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution

O. Shishkina, R.J.A.M. Stevens, S. Grossmann, D. Lohse, New J. Phys. 12, 075022 (2010).

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Main finding

Boundary-layer thickness and local dissipation estimates provide a lower-bound grid-design rule for convection DNS. Satisfying the proposed node-count equations does not by itself guarantee an accurate simulation.

Minimum boundary layer node count against Rayleigh number for thermal and viscous layers
How to read the figure. The minimum number of grid nodes needed inside the thermal (a) and viscous (b) boundary layers, against the Rayleigh number, derived from a Prandtl-Blasius description of the near-wall flow. The requirement rises with Rayleigh number: the more intense the turbulent heat transport, the finer the near-wall resolution has to be. This is a lower bound and a design rule, not a universal node count, and meeting it is not by itself proof that a simulation is resolved. Open the full-resolution figure. Figure 4. O. Shishkina et al. (2010). No separate licence is stated here; consult the original publication and credited source before reuse.

Why this matters

Finer near-wall resolution is needed as turbulent heat transport intensifies.

Research context

Grossmann–Lohse scaling and classical Prandtl–Blasius theory provide the analytical framework. Radial boundary layer structure and Nusselt number in Rayleigh-Bénard… (read the finding) supplies the reused cylindrical DNS thickness diagnostic and empirical grid-sensitivity context; Optimal Prandtl number for heat transfer in rotating Rayleigh-Bénard… (read the finding) uses related kinetic/thermal boundary-layer diagnostics. Later or parallel papers that extend, revise, or test it: Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent… (read the finding) tests dynamically rescaled temperature and velocity profiles against Prandtl–Blasius forms; Horizontal structures of velocity and temperature boundary layers in… (read the finding) resolves horizontal structure in 2D DNS; Comparison of computational codes for direct numerical simulations of… (read the finding) compares independent computational codes.

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