Richard J.A.M. Stevens

Physics of Fluids

University of Twente

Thermal convection

“Turbulence” is often used as a synonym for “complexity.” It is a multiscale phenomenon that shows chaotic behavior in both space and time, but it is also a phenomenon in which self-organization plays a central role. Weather, climate, and ocean flow are prime examples of both turbulence and complexity. An advantage in turbulence research is that the underlying dynamical equations are well known. An important way to drive turbulent flow is through buoyancy, as in the atmosphere and oceans. The paradigmatic example is Rayleigh-Bénard flow: a fluid-filled cell heated from below and cooled from above. Besides the width-to-height aspect ratio Γ, the central control parameters are the Rayleigh number Ra, which measures the strength of buoyant forcing relative to viscous and thermal diffusion, and the Prandtl number Pr, the ratio of kinematic viscosity to thermal diffusivity.

Grossmann–Lohse (GL) theory describes heat transfer in Rayleigh-Bénard flow by combining exact global balances for kinetic and thermal dissipation with scaling estimates for boundary-layer and bulk contributions. The resulting regimes depend on which contributions dominate and predict the Rayleigh- and Prandtl-number dependence of the Nusselt number. Prandtl–Blasius boundary-layer scaling enters the classical formulation but is not the whole theory. Figure 1 shows the corresponding regimes in Ra–Pr parameter space.

The following topics are specifically addressed:
High Rayleigh number thermal convection
Rotating Rayleigh-Bénard convection
2D Rayleigh-Bénard convection

Phase diagram in the Rayleigh number-Prandtl number plane showing turbulent convection regimes

Figure 1: Phase diagram in Ra-Pr plane indicating the different turbulent regimes. The data points indicate where Nu has been measured or numerically calculated, figure from Ref. [3] where details about the shown data points can be found.

References

  1. X. Zhu, E. Phillips, V. Spandan, J. Donners, G. Ruetsch, J. Romero, R. Ostilla-Mónico, Y. Yang, D. Lohse, R. Verzicco, M. Fatica, R.J.A.M. Stevens,
    AFiD-GPU: A versatile Navier–Stokes solver for wall-bounded turbulent flows on GPU clusters,
    Comput. Phys. Commun. 229, 199-210 (2018).
  2. G.L. Kooij, M. A. Botchev, E.M.A. Frederix, B.J. Geurts, S. Horn, D. Lohse, E.P. van der Poel, O. Shishkina, R.J.A.M. Stevens, R. Verzicco,
    Comparison of computational codes for direct numerical simulations of turbulent Rayleigh-Bénard convection,
    Computers & Fluids 166, 1-8 (2018)
  3. X. Zhu, R.J.A.M. Stevens, R. Verzicco, D. Lohse,
    Roughness-facilitated local 1/2 scaling does not imply the onset of the ultimate regime of thermal convection,
    Phys. Rev. Lett. 119, 154501 (2017).
  4. J. Lülff, M. Wilczek, R.J.A.M. Stevens, R. Friedrich, D. Lohse,
    Turbulent Rayleigh-Bénard convection described by projected dynamics in phase space,
    J. Fluid Mech. 781, 276- 297 (2015).
  5. R.J.A.M. Stevens, E.P. van der Poel, S. Grossmann, D. Lohse,
    The unifying theory of scaling in thermal convection: The updated prefactors,
    J. Fluid Mech. 730, 295-308 (2013).
  6. R.J.A.M. Stevens, Q. Zhou, S. Grossmann, R. Verzicco, K.-Q Xia, D. Lohse,
    Thermal boundary layer profiles in turbulent Rayleigh-Bénard convection in a cylindrical sample,
    Phys. Rev. E 85, 027301 (2012).