Nonlocal Convective PBL Model Based on New Third- and Fourth-Order Moments

2005 ◽  
Vol 62 (7) ◽  
pp. 2189-2204 ◽  
Author(s):  
Y. Cheng ◽  
V. M. Canuto ◽  
A. M. Howard
Keyword(s):  
Fourth Order ◽  
Potential Temperature ◽  
Turbulence Models ◽  
Second Order ◽  
Order Moment ◽  
Third Order ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Analytic Expressions ◽  
Aircraft Data

Abstract The standard approach to studying the planetary boundary layer (PBL) via turbulence models begins with the first-moment equations for temperature, moisture, and mean velocity. These equations entail second-order moments that are solutions of dynamic equations, which in turn entail third-order moments, and so on. How and where to terminate (close) the moments equations has not been a generally agreed upon procedure and a variety of models differ precisely in the way they terminate the sequence. This can be viewed as a bottom-up approach. In this paper, a top-down procedure is suggested, worked out, and justified, in which a new closure model is proposed for the fourth-order moments (FOMs). The key reason for this consideration is the availability of new aircraft data that provide for the first time the z profile of several FOMs. The new FOM expressions have nonzero cumulants that the model relates to the z integrals of the third-order moments (TOMs), giving rise to a nonlocal model for the FOMs. The new FOM model is based on an analysis of the TOM equations with the aid of large-eddy simulation (LES) data, and is verified by comparison with the aircraft data. Use of the new FOMs in the equations for the TOMs yields a new TOM model, in which the TOMs are damped more realistically than in previous models. Surprisingly, the new FOMs with nonzero cumulants simplify, rather than complicate, the TOM model as compared with the quasi-normal (QN) approximation, since the resulting analytic expressions for the TOMs are considerably simpler than those of previous models and are free of algebraic singularities. The new TOMs are employed in a second-order moment (SOM) model, a numerical simulation of a convective PBL is run, and the resulting mean potential temperature T, the SOMs, and the TOMs are compared with several LES data. As a final consistency check, T, SOMs, and TOMs are substituted from the PBL run back into the FOMs, which are again compared with the aircraft data.

The infra-red spectra of crystals

1960 ◽  
Vol 258 (1294) ◽  
pp. 377-401 ◽  
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Order Moment ◽  
Order Effects ◽  
Ionic Crystals ◽  
Third Order ◽  
Main Band ◽  
The Third ◽  
Cross Terms ◽  
Infra Red

The higher-order effects in the intrinsic infra-red absorption of crystals are investigated in a systematic way. In agreement with a previous paper which dealt with the static dielectric constant, it is found that in the case of ionic crystals the third- and fourth-order potential, the second- and the third-order dipole moment, and the cross-terms between the second-order moment and the third-order potential, all contribute terms of the same order to the infra-red spectrum. In the lowest approximation, the third-order moment and the fourth-order potential only affect the absorption in the immediate neighbourhood of the maximum and hence have little effect on the shape of the spectrum. The broadening of the main band is due mainly to the third-order potential, while the side bands may be caused by the second-order moment as well as by the third-order potential and by cross-terms between the two. But due to an internal field effect, in strongly ionic crystals a large second-order moment automatically leads to a large third-order potential; thus a large second-order moment may increase the width of the main band as well as the intensity of the side bands. Although the intrinsic infra-red absorption of valency crystals, such as diamond or germaniam, is due to the second-order moment only, nevertheless, there is a strong similarity between the expressions for the infra-red absorption of valency crystals and for the side-band absorption of ionic crystals. This similarity suggests that the spectra of all ionic crystals should exhibit a number of secondary maxima. The available experimental evidence does not seem sufficient to decide whether this suggestion is correct.

scholarly journals Method for Measuring the Second-Order Moment of Atmospheric Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 564
Author(s):  
Hong Shen ◽  
Longkun Yu ◽  
Xu Jing ◽  
Fengfu Tan
Keyword(s):  
Atmospheric Turbulence ◽  
Weighting Function ◽  
Structure Constant ◽  
Turbulence Models ◽  
Second Order ◽  
Index Structure ◽  
Order Moment ◽  
Site Testing ◽  
Optical Effects ◽  
Novel Method

The turbulence moment of order m (μm) is defined as the refractive index structure constant Cn2 integrated over the whole path z with path-weighting function zm. Optical effects of atmospheric turbulence are directly related to turbulence moments. To evaluate the optical effects of atmospheric turbulence, it is necessary to measure the turbulence moment. It is well known that zero-order moments of turbulence (μ0) and five-thirds-order moments of turbulence (μ5/3), which correspond to the seeing and the isoplanatic angles, respectively, have been monitored as routine parameters in astronomical site testing. However, the direct measurement of second-order moments of turbulence (μ2) of the whole layer atmosphere has not been reported. Using a star as the light source, it has been found that μ2 can be measured through the covariance of the irradiance in two receiver apertures with suitable aperture size and aperture separation. Numerical results show that the theoretical error of this novel method is negligible in all the typical turbulence models. This method enabled us to monitor μ2 as a routine parameter in astronomical site testing, which is helpful to understand the characteristics of atmospheric turbulence better combined with μ0 and μ5/3.

scholarly journals Prediction of flow and dispersion in cross–ventilated buildings

2019 ◽  
Vol 128 ◽  
pp. 05002
Author(s):  
Ali Cemal Benim ◽  
Michael Diederich ◽  
Ali Nahavandi
Keyword(s):  
Computational Analysis ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Turbulence Structure ◽  
Detached Eddy Simulation ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Large Eddy ◽  
The Mean ◽  
Grid Independence

The present paper presents a detailed computational analysis of flow and dispersion in a generic isolated single–zone buildings. First, a grid generation strategy is discussed, that is inspired by a previous computational analysis and a grid independence study. Different turbulence models are appliedincluding two-equation turbulence models, the differential Reynolds Stress Model, Detached Eddy Simulation and Zonal Large Eddy Simulation. The mean velocity and concentration fields are calculated and compared with the measurements. A satisfactory agreement with the experiments is not observed by any of the modelling approaches, indicating the highly demanding flow and turbulence structure of the problem.

Attenuated microvascular alterations in coarctation hypertension

1989 ◽  
Vol 256 (1) ◽  
pp. H213-H221 ◽  
Author(s):  
D. L. Stacy ◽  
R. L. Prewitt
Keyword(s):  
Fourth Order ◽  
Vascular Tone ◽  
Structural Parameters ◽  
Renal Hypertension ◽  
Second Order ◽  
Hypertensive Rats ◽  
Third Order ◽  
Flow Dependence ◽  
Vascular Beds ◽  
Microvascular Alterations

Arteriolar vasoconstriction, structural reductions in dilated diameter, and rarefaction have been observed in vascular beds with chronic renal hypertension. To determine their pressure or flow dependence, these functional and structural parameters were studied in the developing and chronic stages of coarctation hypertension in the cremaster muscle, a normotensive skeletal muscle bed that is protected from the effects of elevated microvascular pressures. Hypertension was produced in rats by placing a silver clip around the abdominal aorta above the branches of the renal arteries. In hypertensive rats, resting diameters were reduced in second-order arterioles after 4 and 8 wk, in third-order arterioles after 2, 4, and 8 wk, and in fourth-order arterioles after 4 and 8 wk, vs. controls. Vascular tone was elevated in second-order arterioles after 2, 4, and 8 wk and in third- and fourth-order arterioles after 8 wk in hypertensive rats. No increases in medial-intimal area were found at any stage of hypertension in any arteriolar order. The density of small arterioles (3rd-5th orders) was reduced by 20% in hypertensive rats at 8 wk but was unchanged at the other time periods. These arteriolar alterations, especially the absence of structural reductions in diameter, are attenuated compared with those observed in one-kidney, one-clip hypertension and suggest that most of the arteriolar alterations that occur in renal hypertension are pressure or flow dependent.

On the Convexity Correction Approximation in Pricing Volatility Swaps and VIX Futures

2018 ◽  
Vol 14 (03) ◽  
pp. 383-401
Author(s):  
Song-Ping Zhu ◽  
Guang-Hua Lian
Keyword(s):  
Theoretical Analysis ◽  
Fourth Order ◽  
Taylor Expansion ◽  
Second Order ◽  
Approximation Technique ◽  
Third Order ◽  
Numerical Examples ◽  
Taylor Expansions ◽  
Vix Futures ◽  
Validity Condition

Convexity correction is a well-known approximation technique used in pricing volatility swaps and VIX futures. However, the accuracy of the technique itself and the validity condition of this approximation have hardly been addressed and discussed in the literature. This paper shows that, through both theoretical analysis and numerical examples, this type of approximations is not necessarily accurate and one should be very careful in using it. We also show that a better accuracy cannot be achieved by extending the convexity correction approximation from a second-order Taylor expansion to third-order or fourth-order Taylor expansions. We then analyze why and when it deteriorates, and provide a validity condition of applying the convexity correction approximation. Finally, we propose a new approximation, which is an extension of the convexity correction approximation, to achieve better accuracies.

scholarly journals What Causes the Divergences in Local Second-Order Closure Models?

2005 ◽  
Vol 62 (5) ◽  
pp. 1645-1651 ◽  
Author(s):  
V. M. Canuto ◽  
Y. Cheng ◽  
A. M. Howard
Keyword(s):  
Ad Hoc ◽  
Coefficient Of Thermal Expansion ◽  
Potential Temperature ◽  
Turbulence Models ◽  
Turnover Time ◽  
Second Order ◽  
Dimensionless Temperature ◽  
Gravitational Acceleration ◽  
Buoyancy Driven Flows ◽  
Large Eddies

Abstract It has been known for three decades that in the case of buoyancy-driven flows the widely used second-order closure (SOC) level-2.5 turbulence models exhibit divergences that render them unphysical in certain domains. This occurs when the dimensionless temperature gradient Gh (defined below) approaches a critical value Gh(cr) of the order of 10; thus far, the divergences have been treated with ad hoc limitations of the typewhere τ is the eddy turnover time scale, g is the gravitational acceleration, α is the coefficient of thermal expansion, T is the mean potential temperature, and z is the height. It must be noted that large eddy simulation (LES) data show no such limitation. The divergent results have the following implications. In most of the ∂T/∂z < 0 portion of a convective planetary boundary layer (PBL), a variety of data show that τ increases with z, −∂T/∂z decreases with z, and Gh decreases with z. As one approaches the surface layer from above, at some zcr (∼0.2H, H is the PBL height), Gh approaches Gh(cr) and the model results diverge. Below zcr, existing models assume the displayed equation above. Physically, this amounts to artificially making the eddy lifetime shorter than what it really is. Since short-lived eddies are small eddies, one is essentially changing large eddies into small eddies. Since large eddies are the main contributors to bulk properties such as heat, momentum flux, etc., the artificial transformation of large eddies into small eddies is equivalent to underestimating the efficiency of turbulence as a mixing process. In this paper the physical origin of the divergences is investigated. First, it is shown that it is due to the local nature of the level-2.5 models. Second, it is shown that once an appropriate nonlocal model is employed, all the divergences cancel out, yielding a finite result. An immediate implication of this result is the need for a reliable model for the third-order moments (TOMs) that represent nonlocality. The TOMs must not only compare well with LES data, but in addition, they must yield nondivergent second-order moments.

Adaptive Detached-Eddy Simulation of Three-Dimensional Diffusers

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Paul Durbin ◽  
Zifei Yin ◽  
Elbert Jeyapaul
Keyword(s):  
Pressure Coefficient ◽  
Three Dimensional ◽  
Side Wall ◽  
Turbulence Models ◽  
Adaptive Method ◽  
Detached Eddy Simulation ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Default Data

An adaptive method for detached-eddy simulation (DES) is tested by simulations of flow in a family of three-dimensional (3D) diffusers. The adaptive method either adjusts the model constant or defaults to a bound if the grid is too coarse. On the present grids, the adaptive method adjusts the model constant over most of the flow, without resorting to the default. Data for the diffuser family were created by wall-resolved, large-eddy simulation (LES), using the dynamic Smagorinsky model, for the purpose of testing turbulence models. The family is a parameterized set of geometries that allows one to test whether the pattern of separation is moving correctly from the top to the side wall as the parameter increases. The adaptive DES model is quite accurate in this regard. It is found to predict the mean velocity accurately, but the pressure coefficient is underpredicted. The latter is due to the onset of separation being slightly earlier in the DES than in the LES.

Development of the female flower and gynecandrous partial inflorescence of Myrica californica

1979 ◽  
Vol 57 (2) ◽  
pp. 141-151 ◽  
Author(s):  
Alastair D. Macdonald
Keyword(s):  
Fourth Order ◽  
Female Flower ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Unique Structure ◽  
Inflorescence Axis ◽  
Definition Of ◽  
Fifth Order ◽  
Partial Inflorescence

Organogenesis of the female flower and gynecandrous partial inflorescence is described. Approximately 25 first-order inflorescence bracts are formed in an acropetal sequence. A second-order inflorescence axis, the partial inflorescence, develops in the axil of each bract. Third-, fourth-, and fifth-order axes arise in the axils of second-, third-, and fourth-order bracts. A gynoecium terminates a second-order axis and sometimes a distal third-order axis. A gynoecium consists of two stigmas and one basal, unitegmic, orthotropous ovule. The wall enclosing the ovule, the circumlocular wall, is comprised distally of gynoecial tissue and proximally of tissue of the inflorescence axis and its appendages. The latter portion of the wall is formed by zonal growth. Androecial members, formed proximal to the gynoecium on the partial inflorescence, are carried onto the circumlocular wall by zonal growth. A stamen may develop from the last-formed primordium before gynoecial inception or from a potentially stigmatic primordium. The papillae of the flower and fruit arise as emergences and from potentially bracteate, axial, and staminate primorida during the development of the circumlocular wall. The term circumlocular wall is used in a neutral sense to describe this unique structure. Since the gynoecium is composed of gynoecial appendages and inflorescence axis and appendages, a functional definition of gynoecium must be expanded to include any tissue, including an inflorescence, that surrounds the ovule(s) and forms the fruit(s).

Large Eddy Simulation of Gas - Second Order Moment of Particle Approach for Riser

2013 ◽  
Vol 274 ◽  
pp. 596-599 ◽  
Author(s):  
Ju Hui Chen ◽  
Ting Hu ◽  
Jiu Ru Li
Keyword(s):  
Large Eddy Simulation ◽  
Fluid Model ◽  
Flow Behavior ◽  
Second Order ◽  
Order Moment ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Particle Approach

Flow behavior of gas and particles is performed by means of gas–solid two-fluid model with the large eddy simulation for gas and the second order moment for particles in the riser. This study shows that the computed solids volume fractions of two cases are compared with the experimental data using a two-dimensional model. The gas and solid velocity is computed.

Sign in / Sign up

Export Citation Format

Share Document