Wind and boundary layers in Rayleigh-Benard convection. I: analysis and modeling

The aim of this paper is to contribute to the understanding and to model the processes controlling the amplitude of the wind of Rayleigh-Benard convection. We analyze results from direct simulation of an L/H = 4 aspect-ratio domain with periodic sidewalls at Ra = 1e5; 1e6; 1e7; 1e8 and at Pr = 1 by decomposing independent realizations into wind and fluctuations. It is shown that deep inside the thermal boundary layer, horizontal heat-fuxes exceed the average vertical heat-fux by a factor 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 DNS results to parameterise 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

Spectral analysis of boundary layers in Rayleigh-Benard convection

A combined experimental and numerical study of the boundary layer in a 4:1 aspect-ratio Rayleigh-B\'{e}nard 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 (LDA) 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 $1.6 \times 10^7$ and $2.4 \times 10^9$. In parallel, direct numerical simulations (DNS) have been performed for the same configuration for Rayleigh numbers between $7.0 \times 10^4$ and $7.7 \times 10^7$. 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 $\textrm{Ra}$ 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.Comment: 10 pages, 6 figures, Accepted for publication in Phys. Rev.

Low Temperature Magnetic Properties of the Double Exchange Model

We study the {\it ferromagnetic} (FM) Kondo lattice model in the strong coupling limit (double exchange (DE) model). The DE mechanism proposed by Zener to explain ferromagnetism has unexpected properties when there is more than one itinerant electron. We find that, in general, the many-body ground state of the DE model is {\it not} globally FM ordered (except for special filled-shell cases). Also, the low energy excitations of this model are distinct from spin wave excitations in usual Heisenberg ferromagnets, which will result in unusual dynamic magnetic properties.Comment: 5 pages, RevTeX, 5 Postscript figures include

Spin Dynamics of the Magnetoresistive Pyrochlore Tl_2Mn_2O_7

Neutron scattering has been used to study the magnetic order and spin dynamics of the colossal magnetoresistive pyrochlore Tl_2Mn_2O_7. On cooling from the paramagnetic state, magnetic correlations develop and appear to diverge at T_C (123 K). In the ferromagnetic phase well defined spin waves are observed, with a gapless ($\Delta <0.04$ meV) dispersion relation E=Dq^{2} as expected for an ideal isotropic ferromagnet. As T approaches T_C from low T, the spin waves renormalize, but no significant central diffusive component to the fluctuation spectrum is observed in stark contrast to the La$_{1-x}$(Ca,Ba,Sr)$_x$MnO$_3$ system. These results argue strongly that the mechanism responsible for the magnetoresistive effect has a different origin in these two classes of materials.Comment: 4 pages (RevTex), 4 figures (encapsulated postscript), to be published in Phys. Rev. Let

Wind and boundary layers in Rayleigh-Benard convection. Part 2: boundary layer character and scaling

The effect of the wind of Rayleigh-Benard convection on the boundary layers is studied by direct numerical simulation of an L/H=4 aspect-ratio domain with periodic side boundary conditions for Ra={10^5, 10^6, 10^7} and Pr=1. It is shown that the kinetic boundary layers on the top- and bottom plate have some features of both laminar and turbulent boundary layers. A continuous spectrum, as well as significant forcing due to Reynolds stresses indicates undoubtedly a turbulent character, whereas the classical integral boundary layer parameters -- the shape factor and friction factor (the latter is shown to be dominated by the pressure gradient) -- scale with Reynolds number more akin to laminar boundary layers. This apparent dual behavior is caused by the large influence of plumes impinging onto and detaching from the boundary layer. The plume-generated Reynolds stresses have a negligible effect on the friction factor at the Rayleigh numbers we consider, which indicates that they are passive with respect to momentum transfer in the wall-parallel direction. However, the effect of Reynolds stresses cannot be neglected for the thickness of the kinetic boundary layer. Using a conceptual wind model, we find that the friction factor C_f should scale proportional to the thermal boundary layer thickness as C_f ~ lambda_Theta, while the kinetic boundary layer thickness lambda_u scales inversely proportional to the thermal boundary layer thickness and wind Reynolds number lambda_u ~ lambda_Theta^{-1} Re^{-1}. The predicted trends for C_f and \lambda_u are in agreement with DNS results

Synthesis of phosphatidic acids via cobalt(salen) catalyzed epoxide ring-opening with dibenzyl phosphate

With a CoIII(salen)OTs catalyst, dibenzyl phosphate ring-opens a variety of terminal epoxides with excellent regio-selectively and yields up to 85%. The reaction is used in a highly efficient synthesis of enantiopure mixed-diacyl phosphatidic acids, including a photoswitchable phosphatidic acid mimic