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

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 small 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 flow which is driven randomly. The purpose of the present proposal is 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 how the statistical moments in the transition range are affected by the present boundary layer dynamics. The flow that will be studied here, is a Rayleigh-Bénard convection flow where thermal plumes detach from the walls and drive statistical fluctuations of velocity and velocity derivatives in the bulk of the layer.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Katepalli Sreenivasan, Ph.D.