Role of critical points of the skin friction field in formation of plumes in thermal convection

Abstract

The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-Bénard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-Bénard convection in a closed cylindrical cell of aspect ratio $\Gamma =1$ and focused on the critical points of the skin friction field. We identify triplets of critical points, which are composed of two unstable nodes and a saddle between them, as the characteristic building block of the skin friction field. Isolated triplets as well as networks of triplets are detected. The majority of the ridges of line-like thermal plumes coincide with the unstable manifolds of the saddles. From a dynamical Lagrangian perspective, thermal plumes are formed together with an attractive hyperbolic Lagrangian Coherent Structure of the skin friction field. We also discuss the differences from the skin friction field in turbulent channel flows from the perspective of the Poincaré-Hopf index theorem for two-dimensional vector fields.

References in corpus (7)

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• Boundary layer structure in turbulent Rayleigh-Benard convection
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• Local boundary layer scales in turbulent Rayleigh-Benard convection
• Large-scale mean patterns in turbulent convection
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Cited by in corpus (5)

• Turbulent superstructures in Rayleigh-Bénard convection
• Transitional boundary layers in low-Prandtl-number convection
• Extreme dissipation event due to plume collision in a turbulent convection cell
• Connecting boundary layer dynamics with extreme bulk dissipation events in Rayleigh-Bénard flow
• The multi-scale nature of Wall shear stress fluctuations in turbulent Rayleigh-Benard convection