The influence of the large scale circulation on the transition to the "Ultimate state of thermal convection"
Geophysics
Atmospheric Science
Final Report Abstract
We have investigated the interplay between buoyancy and shear in a viscose boundary layer (BL) that develops on top of a heated horizontal plate. The project was originally motivated by the transition e from the classical to the ultimate regime in Rayleigh-B´nard convection (RBC) which is triggered when the laminar BL turns turbulent under sufficiently strong driving. While the results gained from our investigation on thermally unstable boundary layers are very relevant for the initial questions, this project has deviate a bit from RBC and has addressed more general questions about the heat transport in forced vs free convection. For this project, we have built an entire new experiment almost from scratch. The experiment consisted of a flat horizontal plate that was heated from below uniformely and that was placed inside an open air wind tunnel. The plate consisted of two aluminum plates with a thin polycarbonate plate sandwiched between them. With 42 thermistors equally distributed in the aluminum plates we could measure the temperature drop across the polycarbonate plate and hence detect the vertical heat flux spatially resolved. We investigated the normalised heat transport (Nusselt number - Nux) as a function of the wind speed (experessed in the Reyndols number - Rex) and the provided heating power (expressed by the Grashof number - Grx). In the data, we saw a clear transition from the buoyancy dominated regime (natural convection) when Grx is large and Rex is small to the shear dominated regime (forced convection) for 0.25 small Grx and large Rex. We have investigated the flow close to the plate for various Rex and Grx, both qualitatively by visualising the flow with oil particles and a light sheet as well a quantitatively using hot wire velocimetry. With this, we have measured velocity statistics inside the boundary layer and found for the largest Rex a reduction in the flow speed and the velocity rms very close to the plate when the plate is heated. Since in this regime buoyancy is small compared to the shear, we believe that this observation is caused by an increased kinematic viscosity due to the increased temperature. For smaller Rex , buoyancy becomes important and we see that fluctuations are enhanced and the boundary layer is also larger with increasing Grx. In another project related to the priority program on ”Turbulent superstructures”, we have used the diffusion maps embedding to detect and analyse the turbulent superstructure in Rayleigh-Bénard convection, namely the large scale circulation role - LSC. We could show that indeed this novel approach that does not include any physical information can detect structure in the rather chaotic system. This was the first time that diffusion maps embedding has been successfully applied to RBC and we could show that it does not only detect the LSC, correctly but also allows for an analysis of its dynamic and stability, such as the temporal transition from a single to a double role state, its diffusive azimuthal drift or its constant drift inside a slowly rotating cylinder. We are confident that this research also paves the road for the application of the diffusion maps method or similar methods to detect structure in other turbulent or chaotic systems.
Publications
- Manifold learning and transition matrix analysis of the large-scale flow structure in turbulent Rayleigh–Bénard convection, Nonlinearity, 33, 1723 (2020)
P. Koltai and S. Weiss
(See online at https://doi.org/10.1088/1361-6544/ab6a76)
