Boundary layer structure in turbulent Rayleigh-Benard convection

Abstract

The structure of the boundary layers in turbulent Rayleigh-Benard convection is studied by means of three-dimensional direct numerical simulations. We consider convection in a cylindrical cell at an aspect ratio one for Rayleigh numbers of Ra=3e+9 and 3e+10 at fixed Prandtl number Pr=0.7. Similar to the experimental results in the same setup and for the same Prandtl number, the structure of the laminar boundary layers of the velocity and temperature fields is found to deviate from the prediction of the Prandtl-Blasius-Pohlhausen theory. Deviations decrease when a dynamical rescaling of the data with an instantaneously defined boundary layer thickness is performed and the analysis plane is aligned with the instantaneous direction of the large-scale circulation in the closed cell. Our numerical results demonstrate that important assumptions which enter existing classical laminar boundary layer theories for forced and natural convection are violated, such as the strict two-dimensionality of the dynamics or the steadiness of the fluid motion. The boundary layer dynamics consists of two essential local dynamical building blocks, a plume detachment and a post-plume phase. The former is associated with larger variations of the instantaneous thickness of velocity and temperature boundary layer and a fully three-dimensional local flow. The post-plume dynamics is connected with the large-scale circulation in the cell that penetrates the boundary region from above. The mean turbulence profiles taken in localized sections of the boundary layer for both dynamical phases are also compared with solutions of perturbation expansions of the boundary layer equations of forced or natural convection towards mixed convection. Our analysis of both boundary layers shows that the near-wall dynamics combines elements of forced Blasius-type and natural convection.

arXiv comment23 pages, 19 Postscript figures (Figs. 1,8,12,14,15,17 in reduced quality)

References in corpus (17)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Scaling in thermal convection: A unifying theory
• Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
• Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection
• Plume motion and large-scale circulation in a cylindrical Rayleigh-Bénard cell
• The cause of oscillations of the large-scale circulation of turbulent Rayleigh-B{é}nard convection
• Fine-scale statistics of temperature and its derivatives in convective turbulence
• Measured Instantaneous Viscous Boundary Layer in Turbulent Rayleigh-Bénard Convection
• Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-Bénard convection
• Dynamics of reorientations and reversals of large scale flow in Rayleigh-Benard convection
• Statistical and geometrical properties of thermal plumes in turbulent Rayleigh-Bénard convection
• Thermal boundary layer profiles in turbulent Rayleigh-Bénard convection in a cylindrical sample
• Horizontal Structures of Velocity and Temperature Boundary Layers in 2D Numerical Turbulent Rayleigh-Bénard Convection
• Wind and boundary layers in Rayleigh-Benard convection. I: analysis and modeling
• Wind and boundary layers in Rayleigh-Benard convection. Part 2: boundary layer character and scaling
• Low-dimensional model of turbulent Rayleigh-Benard convection in a Cartesian cell with square domain
• Lagrangian tracer dynamics in a closed cylindrical turbulent convection cell

Cited by in corpus (30)

• Comparison between two and three dimensional Rayleigh-Bénard convection
• Resolving the fine-scale structure in turbulent Rayleigh-Benard convection
• Thermal Boundary Layer Equation for Turbulent Rayleigh-Benard Convection
• Turbulent Rayleigh-Bénard convection in spherical shells
• Local boundary layer scales in turbulent Rayleigh-Benard convection
• Combined measurement of velocity and temperature in liquid metal convection
• Koopman analysis of the long-term evolution in a turbulent convection cell
• Transitional boundary layers in low-Prandtl-number convection
• Complexity of viscous dissipation in turbulent thermal convection
• Competing forces in liquid metal electrodes and batteries
• Logarithmic mean temperature profiles and their connection to plume emissions in turbulent Rayleigh-Bénard convection
• Thermal boundary layer structure in low-Prandtl-number turbulent convection
• Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection
• Mean Temperature Profiles in Turbulent Thermal Convection
• Viscous boundary layer properties in turbulent thermal convection in a cylindrical cell: the effect of cell tilting
• Revisiting Reynolds and Nusselt numbers in turbulent thermal convection
• Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models
• Kinetic Energy Transport in Rayleigh--Bénard Convection
• Dynamics of line plumes on horizontal surfaces in turbulent convection
• No sustained mean velocity in the boundary region of plane thermal convection
• Similarity model for corner roll in turbulent Rayleigh-Benard convection
• Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection
• Scaling and spatial intermittency of thermal dissipation in turbulent convection
• Boundary layer structure in turbulent Rayleigh-Bénard convection in a slim box
• Role of critical points of the skin friction field in formation of plumes in thermal convection
• Plane-layer Rayleigh-Bénard convection up to $Ra=10^{11}$: Near-wall fluctuations and role of initial conditions
• Boundary layer evolution in turbulent Rayleigh-Benard convection
• Influence of plume activity on thermal convection in a rectangular cell
• Horizontal velocity field near the hot plate in turbulent natural convection
• Predicting transition ranges to turbulent viscous boundary layers in low Prandtl number convection flows