3,345 research outputs found
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 and . In parallel,
direct numerical simulations (DNS) have been performed for the same
configuration for Rayleigh numbers between and . 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
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 ( 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(Ca,Ba,Sr)MnO 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
- …