Prime modes of fluid circulation in large-aspect-ratio turbulent Rayleigh-Bénard convection.

Based on a detailed experimental investigation in an aspect-ratio-4 rectangular cell in the range 3.7 x 10(7)

Wind and boundary layers in Rayleigh-Bénard convection. I. Analysis and modeling.

The aim of this paper is to contribute to the understanding of and to model the processes controlling the amplitude of the wind of Rayleigh-Bénard convection. We analyze results from direct simulation of an L/H=4 aspect-ratio domain with periodic sidewalls at Ra=(10(5), 10(6), 10(7), 10(8)) and at Pr=1 by decomposing independent realizations into wind and fluctuations. It is shown that, deep inside the thermal boundary layer, horizontal heat fluxes exceed the average vertical heat flux by a factor of 3 due to the interaction between the wind and the mean temperature field. These large horizontal heat fluxes are responsible for spatial temperature differences that drive the wind by creating pressure gradients. The wall fluxes and turbulent mixing in the bulk provide damping. Using the direct numerical simulation results to parametrize the unclosed terms, a simple model capturing the essential processes governing the wind structure is derived. The model consists of two coupled differential equations for wind velocity and temperature amplitude. The equations indicate that the formation of a wind structure is inevitable due to the positive feedback resulting from the interaction between the wind and temperature field. Furthermore, the wind velocity is largely determined by the turbulence in the bulk rather than by the wall-shear stress. The model reproduces the Ra dependence of wind Reynolds number and temperature amplitude.

Wind and boundary layers in Rayleigh-Bénard convection. II. Boundary layer character and scaling.

The scaling of the kinematic boundary layer thickness lambda(u) and the friction factor C(f) at the top and bottom walls of Rayleigh-Bénard convection is studied by direct numerical simulation (DNS). By a detailed analysis of the friction factor, a new parameterisation for C(f) and lambda(u) is proposed. The simulations were made of an L/H=4 aspect-ratio domain with periodic lateral boundary conditions at Ra=(10(5), 10(6), 10(7), 10(8)) and Pr=1. The continuous spectrum, as well as significant forcing due to Reynolds stresses, clearly indicates a turbulent character of the boundary layer, while viscous effects cannot be neglected, judging from the scaling of classical integral boundary layer parameters with Reynolds number. Using a conceptual wind model, we find that the friction factor C(f) should scale proportionally to the thermal boundary layer thickness as C(f) proportional variant lambda(Theta)/H, while the kinetic boundary layer thickness lambda(u) scales inversely proportionally to the thermal boundary layer thickness and wind Reynolds number lambda(u)/H proportional variant (lambda(Theta)/H)(-1)Re(-1). The predicted trends for C(f) and lambda(u) are in agreement with DNS results.

Spectral analysis of boundary layers in Rayleigh-Bénard convection.

A combined experimental and numerical study of the boundary layer in a 4:1 aspect-ratio Rayleigh-Bénard cell over a four-decade range of Rayleigh numbers has been undertaken aimed at gaining a better insight into the character of the boundary layers. The experiments involved the simultaneous laser Doppler anemometry measurements of fluid velocity at two locations, i.e., in the boundary layer and far away from it in the bulk, for Rayleigh numbers varying between 1.6x10(7) and 2.4x10(9) . In parallel, direct numerical simulations have been performed for the same configuration for Rayleigh numbers between 7.0x10(4) and 7.7x10(7) . The temperature and velocity probability density functions and the power spectra of the horizontal velocity fluctuations measured in the boundary layer and in the bulk flow are found to be practically identical. Except for the smallest Rayleigh numbers, the spectra in the boundary layer and in the bulk central region are continuous and have a wide range of active scales. This indicates that both the bulk and the boundary layers are turbulent in the Ra number range considered. However, molecular effects can still be observed and the boundary layer does not behave like a classical shear-driven turbulent boundary layer.

Oscillating large-scale circulation in turbulent Rayleigh-Bénard convection.

We report on the dynamics and structure of the turbulent velocity field in a high-Rayleigh-number (Ra = 5.9 x 10(8))thermal convection cell with an aspect ratio of 4. Spectral density functions (measured with laser Doppler velocimetry) indicated the existence of a large-scale periodic component. The long-time mean flow field (measured with particle image velocimetry) revealed that the large-scale circulation in the aspect-ratio-4 cell consists of two corotating rolls. The periodicity in the flow could be traced back to the alternating growth and decay of these rolls.