Phase transition to intermittent velocity gradient statistics in thermal convection

• Applicant: Professor Dr. Jörg Schumacher
• Subject Area: Fluid Mechanics ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 417275129

• Final Report Year: 2023

Final Report Abstract

The question of small-scale universality is one of the fundamental problems in turbulence research. It is a main ingredient of all turbulence models which rely on the assumption that there is a generic cascade of kinetic energy from large to small scales at which velocity fluctuations then are dissipated following the same statistical laws. Rather than studying therefore the statistics in the fully developed cascade range at high Reynolds numbers, the interest has turned in the past years to analyses of the Reynolds number dependence of statistical moments of velocity derivatives which are mainly supported at the smallest scales. Recently, a phase transition to an intermittent, non-Gaussian velocity gradient statistics for Reynolds numbers as small as 100 has been predicted and found for an isotropic box turbulence flow which is driven randomly. The 1st purpose of the present project was to investigate if such a phase transition to non-Gaussian statistical behavior of velocity derivatives can be generalized to turbulent flows in the presence of walls and if yes how the statistical moments in the transition range are affected by the presence of boundary layers. The flow that was selected here, is a Rayleigh-Bénard convection flow where thermal plumes detach from the walls at top and bottom and drive statistical fluctuations of velocity and velocity derivatives in the bulk of the layer. The 2nd purpose was to model the resulting convection flow statistics by data-driven reduced-order models, such as by recurrent machine learning algorithms or Markov state models.

Publications

• A perspective on machine learning in turbulent flows. Journal of Turbulence, 21(9-10), 567-584.
  Pandey, Sandeep; Schumacher, Jörg & Sreenivasan, Katepalli R.
  
• Reservoir computing model of two-dimensional turbulent convection. Physical Review Fluids, 5(11).
  Pandey, Sandeep & Schumacher, Jörg
  
• Connecting boundary layer dynamics with extreme bulk dissipation events in Rayleigh-Bénard flow (a). EPL (Europhysics Letters), 134(3), 34004.
  Valori, Valentina & Schumacher, Jörg
  
• Direct data-driven forecast of local turbulent heat flux in Rayleigh–Bénard convection. Physics of Fluids, 34(4).
  Pandey, Sandeep; Teutsch, Philipp; Mäder, Patrick & Schumacher, Jörg
  
• Extreme vorticity events in turbulent Rayleigh-Bénard convection from stereoscopic measurements and reservoir computing. Physical Review Research, 4(2).
  Valori, Valentina; Kräuter, Robert & Schumacher, Jörg
  
• Large-scale flow in a cubic Rayleigh–Bénard cell: long-term turbulence statistics and Markovianity of macrostate transitions. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380.
  Maity, Priyanka; Koltai, Péter & Schumacher, Jörg
  
• Collective variables between large-scale states in turbulent convection. Physical Review Research, 5(3).
  Maity, Priyanka; Bittracher, Andreas; Koltai, Péter & Schumacher, Jörg