Richard J.A.M. Stevens

Physics of Fluids · University of Twente

Publication 33 · Thermal convection

Turbulent Rayleigh-Bénard convection described by projected dynamics in phase space

J. Lülff, M. Wilczek, R.J.A.M. Stevens, R. Friedrich, D. Lohse, J. Fluid Mech. 781, 276-297 (2015).

Main finding

The PDF transport identity is exact, but the practical phase-space vector field is empirical because its conditional terms come from finite DNS samples. Characteristics describe conditional ensemble-mean evolution and share one-point statistics with the Eulerian fields; they are not trajectories of individual material particles.

Phase-space vector field with the closed characteristic curve of the convection cycle
How to read the figure. The vector field governing the characteristics in temperature-height phase space, coloured by probability density, with a closed characteristic drawn on it. The loop describes the conditional ensemble-mean cycle; it is not the path of any individual fluid particle. Open the full-resolution figure. Figure 5. J. Lülff et al. (2015). No separate licence is stated here; consult the original publication and credited source before reuse.

Why this matters

The framework links exact one-point PDF transport to an interpretable mean convection cycle without mistaking the characteristics for material-particle trajectories.

Research context

The characteristics describe conditional ensemble-mean cycling through temperature–height phase space. They complement direct roll and plume diagnostics but are not trajectories of individual material particles.

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