Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh-Bénard convection

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We explore the mechanisms of heat transfer in a turbulent constant heat flux-driven Rayleigh–Bénard convection flow, which exhibits a hierarchy of flow structures from granules to supergranules. Our computational framework makes use of time-dependent flow networks. These are based on trajectories of Lagrangian tracer particles that are advected in the flow. We identify coherent sets in the Lagrangian frame of reference as those sets of trajectories that stay closely together for an extended time span under the action of the turbulent flow. Depending on the choice of the measure of coherence, sets with different characteristics are detected. First, the application of a recently proposed evolutionary spectral clustering scheme allows us to extract granular coherent features that are shown to contribute significantly less to the global heat transfer than their spatial complements. Moreover, splits and mergers of these (leaking) coherent sets leave spectral footprints. Second, trajectories which exhibit a small node degree in the corresponding network represent objectively highly coherent flow structures and can be related to supergranules as the other stage of the present flow hierarchy. We demonstrate that the supergranular flow structures play a key role in the vertical heat transport and that they exhibit a greater spatial extension than the granular structures obtained from spectral clustering.
Original languageEnglish
JournalEuropean Journal of Mechanics, B/Fluids
Pages (from-to)69-85
Number of pages17
Publication statusAccepted/In press - 2023

Bibliographical note

Funding Information:
PPV and AK are supported by the Priority Programme DFG-SPP 1881 “Turbulent Superstructures” of the Deutsche Forschungsgemeinschaft, Germany . The authors thank Ambrish Pandey and Christiane Schneide for their previous contributions to this subject that helped to shape the present research. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( ) for funding this project by providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS Supercomputer JUWELS at Jülich Supercomputing Centre (JSC).

Publisher Copyright:
© 2023 The Author(s)

    Research areas

  • Mathematics - Lagrangian trajectory clustering, Rayleigh–Bénard convection