28 research outputs found
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
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.
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
Stochastic parameterization of shallow cumulus convection estimated from high-resolution data
In this paper, we report on the development of a methodology for stochastic parameterization of convective transport by shallow cumulus convection in weather and climate models. We construct a parameterization based on Large-Eddy Simulation (LES) data. These simulations resolve the turbulent fluxes of heat and moisture and are based on a typical case of non-precipitating shallow cumulus convection above sea in the trade-wind region. Using clustering, we determine a finite number of turbulent flux pairs for heat and moisture that are representative for the pairs of flux profiles observed in these simulations. In the stochastic parameterization scheme proposed here, the convection scheme jumps randomly between these pre-computed pairs of turbulent flux profiles. The transition probabilities are estimated from the LES data, and they are conditioned on the resolved-scale state in the model column. Hence, the stochastic parameterization is formulated as a data-inferred conditional Markov chain (CMC), where each state of the Markov chain corresponds to a pair of turbulent heat and moisture fluxes. The CMC parameterization is designed to emulate, in a statistical sense, the convective behaviour observed in the LES data. The CMC is tested in single-column model (SCM) experiments. The SCM is able to reproduce the ensemble spread of the temperature and humidity that was observed in the LES data. Furthermore, there is a good similarity between time series of the fractions of the discretized fluxes produced by SCM and observed in LES
Stochastic Parameterization of Convective Area Fractions with a Multicloud Model Inferred from Observational Data
Observational data of rainfall from a rain radar in Darwin, Australia, are combined with data defining the
large-scale dynamic and thermodynamic state of the atmosphere around Darwin to develop a multicloud
model based on a stochastic method using conditional Markov chains. The authors assign the radar data to
clear sky, moderate congestus, strong congestus, deep convective, or stratiform clouds and estimate transition
probabilities used by Markov chains that switch between the cloud types and yield cloud-type area fractions.
Cross-correlation analysis shows that the mean vertical velocity is an important indicator of deep convection.
Further, it is shown that, if conditioned on the mean vertical velocity, the Markov chains produce fractions
comparable to the observations. The stochastic nature of the approach turns out to be essential for the correct
production of area fractions. The stochastic multicloud model can easily be coupled to existing moist convectio