scholarly journals The Effect of Filter Dimension on the Subgrid-Scale Stress, Heat Flux, and Tensor Alignments in the Atmospheric Surface Layer

2007 ◽  
Vol 24 (3) ◽  
pp. 360-375 ◽  
Author(s):  
Chad W. Higgins ◽  
Charles Meneveau ◽  
Marc B. Parlange
Keyword(s):  
Heat Flux ◽  
Surface Layer ◽  
Environmental Science ◽  
Field Experiments ◽  
Atmospheric Stability ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Subgrid Scale ◽  
Sonic Anemometers ◽  
Two Dimensional Filtering

Abstract In field experiments designed to study subgrid-scale parameterizations for large eddy simulation, the flow field is often measured and then filtered in two-dimensional planes. This two-dimensional filtering serves as a surrogate for three-dimensional filtering. The question of whether this will yield accurate results in subgrid-scale (SGS) models is addressed by analyzing data from a field experiment in which 16 sonic anemometers were deployed in a four by four grid. The experiment was held in July 2002 at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility in the Utah West Desert. The full SGS stress tensor and its parameterizations using both two- and three-dimensional filterings are obtained. Comparisons are given between two- and three-dimensional filterings of the field measurements based on probability density functions (PDFs) and energy spectra of the SGS stress elements. The PDFs reveal that quantities calculated with two-dimensional filtering exhibit greater intermittency than those computed with three-dimensional filtering at the same scale. From the spectra it is observed that the different filtering methods result in similar behavior, but that spectra of SGS stress components computed with a three-dimensional filter roll off at a slightly lower wavenumber than those computed with a two-dimensional filter. The PDFs and spectra of the stresses calculated with two- and three-dimensional filters can be made to collapse by reducing the three-dimensional filter scale according to Δ3−D = 0.84Δ2−D. Geometric alignment analyses are performed for the SGS heat flux, SGS stress, and filtered strain rate for the cases of stable, near-neutral, and unstable atmospheric stabilities. Under unstable and near-neutral atmospheric stability, two-dimensional filtering yields acceptable results; however, under stable atmospheric stability, a new approach is recommended and delineated.

Effect of Edge Conditions on Natural Convective Heat Transfer From a Narrow Vertical Flat Plate With a Uniform Surface Heat Flux

2007 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Jane T. Paul
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Surface Heat Flux ◽  
Three Dimensional ◽  
Surface Heat ◽  
Heated Plate ◽  
Two Dimensional ◽  
Adiabatic Surface

Two-dimensional natural convective heat transfer from vertical plates has been extensively studied. However, when the width of the plate is relatively small compared to its height, the heat transfer rate can be greater than that predicted by these two-dimensional flow results. Because situations that can be approximately modelled as narrow vertical plates occur in a number of practical situations, there exists a need to be able to predict heat transfer rates from such narrow plates. Attention has here been given to a plate with a uniform surface heat flux. The magnitude of the edge effects will, in general, depend on the boundary conditions existing near the edge of the plate. To examine this effect, two situations have been considered. In one, the heated plate is imbedded in a large plane adiabatic surface, the surfaces of the heated plane and the adiabatic surface being in the same plane while in the second there are plane adiabatic surfaces above and below the heated plate but the edge of the plate is directly exposed to the surrounding fluid. The flow has been assumed to be steady and laminar and it has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. It has also been assumed that the flow is symmetrical about the vertical centre-plane of the plate. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in terms of dimensionless variables. Results have only been obtained for a Prandtl number of 0.7. A wide range of the other governing parameters have been considered for both edge situations and the conditions under which three dimensional flow effects can be neglected have been deduced.

scholarly journals A Bayesian model to correct underestimated 3-D wind speeds from sonic anemometers increases turbulent components of the surface energy balance

2016 ◽  
Vol 9 (12) ◽  
pp. 5933-5953 ◽  
Author(s):  
John M. Frank ◽  
William J. Massman ◽  
Brent E. Ewers
Keyword(s):  
Heat Flux ◽  
Energy Balance ◽  
Bayesian Model ◽  
Field Experiments ◽  
Sonic Anemometer ◽  
Vertical Wind ◽  
State Variables ◽  
Data Set ◽  
Sonic Anemometers ◽  
Posterior Correction

Abstract. Sonic anemometers are the principal instruments in micrometeorological studies of turbulence and ecosystem fluxes. Common designs underestimate vertical wind measurements because they lack a correction for transducer shadowing, with no consensus on a suitable correction. We reanalyze a subset of data collected during field experiments in 2011 and 2013 featuring two or four CSAT3 sonic anemometers. We introduce a Bayesian analysis to resolve the three-dimensional correction by optimizing differences between anemometers mounted both vertically and horizontally. A grid of 512 points (∼ ±5° resolution in wind location) is defined on a sphere around the sonic anemometer, from which the shadow correction for each transducer pair is derived from a set of 138 unique state variables describing the quadrants and borders. Using the Markov chain Monte Carlo (MCMC) method, the Bayesian model proposes new values for each state variable, recalculates the fast-response data set, summarizes the 5 min wind statistics, and accepts the proposed new values based on the probability that they make measurements from vertical and horizontal anemometers more equivalent. MCMC chains were constructed for three different prior distributions describing the state variables: no shadow correction, the Kaimal correction for transducer shadowing, and double the Kaimal correction, all initialized with 10 % uncertainty. The final posterior correction did not depend on the prior distribution and revealed both self- and cross-shadowing effects from all transducers. After correction, the vertical wind velocity and sensible heat flux increased  ∼ 10 % with  ∼ 2 % uncertainty, which was significantly higher than the Kaimal correction. We applied the posterior correction to eddy-covariance data from various sites across North America and found that the turbulent components of the energy balance (sensible plus latent heat flux) increased on average between 8 and 12 %, with an average 95 % credible interval between 6 and 14 %. Considering this is the most common sonic anemometer in the AmeriFlux network and is found widely within FLUXNET, these results provide a mechanistic explanation for much of the energy imbalance at these sites where all terrestrial/atmospheric fluxes of mass and energy are likely underestimated.

scholarly journals A Bayesian model to correct underestimated 3D wind speeds from sonic anemometers increases turbulent components of the surface energy balance

2016 ◽  
Author(s):  
John M. Frank ◽  
William J. Massman ◽  
Brent E. Ewers
Keyword(s):  
Heat Flux ◽  
Energy Balance ◽  
Bayesian Model ◽  
Field Experiments ◽  
Sonic Anemometer ◽  
Sensible Heat Flux ◽  
Vertical Wind ◽  
State Variables ◽  
Sonic Anemometers ◽  
Posterior Correction

Abstract. Sonic anemometers are the principal instruments in micrometeorological studies of turbulence and ecosystem fluxes. Recent studies have shown that common designs underestimate vertical wind measurements because they lack a correction for transducer shadowing, with no consensus on a suitable correction. We reanalyze a subset of data collected during field experiments in 2011 and 2013 featuring two or four CSAT3 sonic anemometers. We introduce a novel Bayesian analysis with the potential to resolve the three-dimensional correction by optimizing differences between anemometers mounted both vertically and horizontally. A grid of 512 points (~ ±5° resolution in wind location) is defined on a sphere around the sonic anemometer, from which the shadow correction for each transducer-pair is derived from a set of 138 unique state variables. Using the Markov chain Monte Carlo (MCMC) method, the Bayesian model proposes new values for each state variable, recalculates the fast-response dataset, summarizes the five-minute wind statistics, and accepts the proposed new values based on the probability that they make measurements from vertical and horizontal anemometers more equivalent. MCMC chains were constructed for three different prior distributions describing the state variables: no shadow correction, the Kaimal correction for transducer shadowing, and double the Kaimal correction, all initialized with 10 % uncertainty. The final posterior correction did not depend on the prior distribution and revealed both self- and cross-shadowing effects from all transducers. After correction, the vertical wind velocity and sensible heat flux increased ~ 10 % with ~ 2 % uncertainty, which was significantly higher than the Kaimal correction. We applied the posterior correction to eddy covariance data from various sites across North America and found that the turbulent components of the energy balance (sensible plus latent heat flux) increased on average between 8-12 %, with an average 95 % credible interval between 6-14 %. Considering this is the most common sonic anemometer in the AmeriFlux network and is found widely within FLUXNET, these results provide a mechanistic explanation for much of the energy imbalance at these sites where all terrestrial/atmospheric fluxes of mass and energy are likely underestimated.

scholarly journals Optimal heat transfer enhancement in plane Couette flow

2017 ◽  
Vol 835 ◽  
pp. 1157-1198 ◽  
Author(s):  
Shingo Motoki ◽  
Genta Kawahara ◽  
Masaki Shimizu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Heat Transfer Enhancement ◽  
Three Dimensional ◽  
Wall Heat Flux ◽  
Scalar Dissipation ◽  
Two Dimensional ◽  
Transfer Enhancement ◽  
Optimal State

Optimal heat transfer enhancement has been explored theoretically in plane Couette flow. The vector field (referred to as the ‘velocity’) to be optimised is time independent and divergence free, and temperature is determined in terms of the velocity as a solution to an advection-diffusion equation. The Prandtl number is set to unity, and consistent boundary conditions are imposed on the velocity and the temperature fields. The excess of a wall heat flux (or equivalently total scalar dissipation) over total energy dissipation is taken as an objective functional, and by using a variational method the Euler–Lagrange equations are derived, which are solved numerically to obtain the optimal states in the sense of maximisation of the functional. The laminar conductive field is an optimal state at low Reynolds number $Re\sim 10^{0}$. At higher Reynolds number $Re\sim 10^{1}$, however, the optimal state exhibits a streamwise-independent two-dimensional velocity field. The two-dimensional field consists of large-scale circulation rolls that play a role in heat transfer enhancement with respect to the conductive state as in thermal convection. A further increase of the Reynolds number leads to a three-dimensional optimal state at $Re\gtrsim 10^{2}$. In the three-dimensional velocity field there appear smaller-scale hierarchical quasi-streamwise vortex tubes near the walls in addition to the large-scale rolls. The streamwise vortices are tilted in the spanwise direction so that they may produce the anticyclonic vorticity antiparallel to the mean-shear vorticity, bringing about significant three-dimensionality. The isotherms wrapped around the tilted anticyclonic vortices undergo the cross-axial shear of the mean flow, so that the spacing of the wrapped isotherms is narrower and so the temperature gradient is steeper than those around a purely streamwise (two-dimensional) vortex tube, intensifying scalar dissipation and so a wall heat flux. Moreover, the tilted anticyclonic vortices induce the flow towards the wall to push low- (or high-) temperature fluids on the hot (or cold) wall, enhancing a wall heat flux. The optimised three-dimensional velocity fields achieve a much higher wall heat flux and much lower energy dissipation than those of plane Couette turbulence.

Evolution of Ground Level Scalar Concentrations Through a Compact Cylinder Array Embedded in the Atmospheric Surface Layer

2002 ◽  
Author(s):  
Heidi E. Miner ◽  
Adam Rasmussen
Keyword(s):  
Surface Layer ◽  
Atmospheric Surface Layer ◽  
Field Experiments ◽  
Initial Conditions ◽  
Atmospheric Stability ◽  
Ground Level ◽  
Stability Conditions ◽  
Plume Dispersion ◽  
Gas Dispersion ◽  
Stable Conditions

Experiments for this study were designed to understand gas dispersion in the presence of surface mounted obstacles. To this end, model field experiments were conducted in a compact barrel array employing a spatial distribution of concentration sensors. Specific aims were to explore the effects of atmospheric stability and plume source initial conditions on the plume dispersion through the barrel array. The present results indicate a relaxation towards Gaussian behavior along the plume centerline. The rate of this Gaussian-like behavior is dependent upon atmospheric stability conditions. Plume dispersion through the array appears to be independent of source initial conditions under neutrally stable conditions.

scholarly journals Turbulence in the Atmosphere of B-Type Stars

1980 ◽  
Vol 51 ◽  
pp. 170-171
Author(s):  
Keiichi Kodaira
Keyword(s):  
Surface Layer ◽  
Velocity Field ◽  
Differential Rotation ◽  
Meridional Circulation ◽  
Three Dimensional ◽  
Scale Height ◽  
Small Scale ◽  
Two Dimensional ◽  
Viscosity Term ◽  
Pressure Scale

AbstractThe stationary turbulent surface layer, whose depth is of the order of the pressure scale height in the subphotospheric layer, was investigated for B-type stars, using the momentum and the continuity equations with the inertia term neglected but the turbulence-viscosity term included. The mean velocity field is dominated by the horizontal component of the meridional circulation, driven by the pressure-density unbalance in the radiative envelope of the rotating star, and the differential rotation induced by the Coriolis force.The model calculation for a B3IV-V star with the equatorial rotational velocity of 200 km/s led to the conclusions that the velocity field due to the differential rotation is of the order of 0.1-1 km/s, the velocity field of the meridional circulation itself is negligible, the velocity field of the three-dimensional shear turbulence is of the order of 0.1 km/s, and i t s scale is comparable to or less than the pressure scale height, the velocity field of the horizontal two-dimensional turbulence is of the order of 1-10 km/s, and i t s maximum scale ranges from a few times the pressure scale height to one-fiftieth of the stellar radius. If the index of the energy density law is close to 3.5, the turbulent surface layer may be dominated by the large scale (two-dimensional) barotropic eddies whose energy is fed by the small scale (three-dimensional) baroclinic turbulence in a way similar to the planetary atmospheres. In this case we may expect the tangential macroturbulence of the order of 1-10 km/s, though the interaction between this and the small-scale three-dimensional turbulence still remains to be investigated.

On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow

1970 ◽  
Vol 42 (2) ◽  
pp. 295-307 ◽  
Author(s):  
Ruby Krishnamurti
Keyword(s):  
Heat Flux ◽  
Time Dependence ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Prandtl Numbers ◽  
Rayleigh Numbers ◽  
Discrete Change ◽  
Flux Curve

In a horizontal convecting layer several distinct transitions occur before the flow becomes turbulent. These are studied experimentally for several Prandtl numbers from 1 to 104. Cell size plan form, transitions in plan form, transition to time-dependence, as well as the heat flux, are measured for Rayleigh numbers from 103to 105. The second transition, occurring at around 12 times the critical Rayleigh number, is one from steady two-dimensional rolls to a steady regular cellular pattern. There is associated with this a discrete change of slope of the heat flux curve, coinciding with the second transition observed by Malkus. Transitions to time-dependence will be discussed in part 2.

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