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DY: Fachverband Dynamik und Statistische Physik

DY 18: Pattern Formation

DY 18.2: Vortrag

Dienstag, 18. März 2025, 14:15–14:30, H47

Wavelength selection mechanism for turbulent superstructures in Rayleigh Bénard convection — •Fabián Alvarez-Garrido and Michael Wilczek — University of Bayreuth, Bayreuth, Germany

Large-scale flow patterns coexist with small-scale turbulence in high-aspect-ratio Rayleigh-Bénard cells. These flow patterns, known as turbulent superstructures, are significantly larger than convection rolls that emerge at the onset of convection. Direct numerical simulations of the Oberbeck-Boussinesq equations reveal that the size of these structures increases with the Rayleigh number. However, the mechanism behind this increase has not been elucidated.

Small-scale turbulence plays an important role in the redistribution of heat across the system. Motivated by how the background temperature gradient profile varies between the boundary layers and the bulk, we formulate effective equations for the large scales introducing a height-dependent turbulent thermal diffusivity. A sharp increase in the diffusivity renders the boundary layers effectively thermally insulating boundaries, fundamentally modifying how the fluid exchanges heat with its surroundings. A linear stability analysis of our model shows that this change in boundary conditions goes along with a change of the type of instability, which then leads to an increased wavelength of the flow patterns. These findings provide a mechanism to understand the increasing size of turbulent superstructures.

Keywords: Turbulence; Superstructures; Patterns