Exploring Self-Correlation in Flux–Gradient Relationships for Stably Stratified Conditions

2006 ◽  
Vol 63 (11) ◽  
pp. 3045-3054 ◽  
Author(s):  
P. Baas ◽  
G. J. Steeneveld ◽  
B. J. H. van de Wiel ◽  
A. A. M. Holtslag
Keyword(s):  
Heat Flux ◽  
Stability Parameter ◽  
Lapse Rate ◽  
Physical Processes ◽  
Obukhov Length ◽  
Flux Gradient ◽  
Stable Conditions ◽  
Measurement Uncertainties ◽  
Relative Errors ◽  
The Stability

Abstract In this paper, the degree of scatter in flux–gradient relationships for stably stratified conditions is analyzed. It is generally found that scatter in the dimensionless lapse rate ϕh is larger than in the dimensionless shear ϕm when plotted versus the stability parameter z/Λ (where Λ is the local Obukhov length). Here, this phenomenon is explained to be a result of self-correlation due to the occurrence of the momentum and the heat flux on both axes, measurement uncertainties, and other possibly relevant physical processes left aside. It is shown that the ratio between relative errors in the turbulent fluxes influences the orientation of self-correlation in the flux–gradient relationships. In stable conditions, the scatter in ϕm is largely suppressed by self-correlation while for ϕh this is not the case (vice versa for unstable stratification). An alternative way of plotting is discussed for determining the slope of the linear ϕm function.

scholarly journals Characteristics of the Heat Flux in the Unstable Atmospheric Surface Layer

2016 ◽  
Vol 73 (11) ◽  
pp. 4519-4529 ◽  
Author(s):  
Maithili Sharan ◽  
Piyush Srivastava
Keyword(s):  
Heat Flux ◽  
Surface Layer ◽  
Temperature Gradient ◽  
Power Law ◽  
Atmospheric Surface Layer ◽  
Potential Temperature ◽  
Stability Parameter ◽  
Layer Potential ◽  
Power Law Function ◽  
The Stability

Abstract The behavior of the heat flux H with respect to the stability parameter (=z/L, where z is the height above the ground, and L is the Obukhov length) in the unstable atmospheric surface layer is analyzed within the framework of Monin–Obukhov similarity (MOS) theory. Using MOS equations, H is expressed as a function of and vertical surface-layer potential temperature gradient . A mathematical analysis is carried out to analyze the theoretical nature of heat flux with the stability parameter by considering the vertical potential temperature gradient as (i) a constant and (ii) a power-law function of heat flux. For a given value of H, two values of associated with different stability regimes are found to occur in both the conditions, suggesting the nonuniqueness of MOS equations. Turbulent data over three different sites—(i) Ranchi, India; (ii) the Met Office’s Cardington, United Kingdom, monitoring facility; and (iii) 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99; United States—are analyzed to compare the observed nature of H with that predicted by MOS. The analysis of observational data over these three sites reveals that the observed variation of H with is consistent with that obtained theoretically from MOS equations when considering the vertical temperature gradient as a power-law function of heat flux having the exponent larger than 2/3. The existence of two different values of the stability parameter for a given value of heat flux suggests that the application of heat flux as a boundary condition involves some intricacies, and it should be applied with caution in convective conditions.

scholarly journals The Role of Atmospheric Stability and Turbulence in Offshore Wind-Farm Wakes in the German Bight

2021 ◽  
Author(s):  
Andreas Platis ◽  
Marie Hundhausen ◽  
Astrid Lampert ◽  
Stefan Emeis ◽  
Jens Bange
Keyword(s):  
German Bight ◽  
Wind Farm ◽  
Atmospheric Stability ◽  
Wind Farms ◽  
Offshore Wind ◽  
Lapse Rate ◽  
Offshore Wind Farm ◽  
Near Surface ◽  
Stable Conditions ◽  
The Stability

AbstractAirborne meteorological in situ measurements as well as stationary measurements at the offshore masts FINO1 and FINO3 in the German Bight are evaluated in order to examine the hypothesis that the wake dissipation downstream of large offshore wind farms depends on atmospheric stability. A long-term study of the mast data for the years 2016 and 2017 demonstrates a clear dependence of stability on the wind direction. Stable conditions are predominantly expected during southerly winds coming from the land. The analysis of various stability and turbulence criteria shows that the lapse rate is the most robust parameter for stability classification in the German Bight, but further implies that stability depends on the measurement height. A near-surface (0 to 30 m), predominantly convective, layer is present and more stable conditions are found aloft (55 to 95 m). Combing the stability data with the airborne measurements of the offshore wind-farm wakes reveals the trend of a correlation between longer wake lengths and an increase in the initial wind-speed deficit downwind of a wind farm with stronger thermal stability. However, the stability correlation criteria with the wake length downstream of the four investigated wind farms, Godewind, Amrumbank West, Meerwind Süd/Ost, and Nordsee Ost, contain large variance. It is assumed that the observed scattering is due to the influence of the wind-farm architecture and temperature inversions around hub height. These, however, are crucial for the classification of stability and illustrate the complexity of a clear stability metric.

scholarly journals An Analysis for the Applicability of Monin–Obukhov Similarity Theory in Stable Conditions

2012 ◽  
Vol 69 (6) ◽  
pp. 1910-1915 ◽  
Author(s):  
Pramod Kumar ◽  
Maithili Sharan
Keyword(s):  
Similarity Theory ◽  
Ground Surface ◽  
Surface Fluxes ◽  
Stability Parameters ◽  
Surface Exchange ◽  
Obukhov Length ◽  
Stable Conditions ◽  
Data Points ◽  
The Stability ◽  
Few Data

Abstract An analysis in a plane of the stability parameters ζ = z/L (where z is a height above the ground surface and L is the Obukhov length) and bulk Richardson number RiB is proposed to examine the applicability of Monin–Obukhov similarity (MOS) theory in stable conditions. In this analysis, the data available from two different experimental datasets [(i) Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) and (ii) Cardington] are divided into four quadrants. An unexpected behavior of decreasing ζ with increasing RiB was observed with both datasets in quadrant II characterized by ζ < 1 and RiB > 0.2 and in quadrant IV with ζ > 1 and RiB < 0.2. This is in contrast to a commonly expected monotonically increasing behavior between ζ and RiB. It is shown that the MOS theory is consistent for computing the surface fluxes corresponding to the data points lying in quadrants I (with ζ > 1 and RiB > 0.2) and III (with ζ < 1 and RiB < 0.2), whereas it may not be applicable for the points in quadrants II and IV. Thus, a breakdown of the relationship between observed ζ and RiB with growing stability in these quadrants may limit the applicability of MOS theory in stable conditions. Since quadrant IV has very few data points, the applicability of MOS theory needs to be substantiated further with the availability of sufficient data points in this regime.

Performance of Electronic Structure Methods for the Description of Hückel-Möbius Interconversions in Extended π-Systems

2019 ◽  
Author(s):  
Tatiana Woller ◽  
Ambar Banerjee ◽  
Nitai Sylvetsky ◽  
Xavier Deraet ◽  
Frank De Proft ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Basis Set ◽  
Dft Methods ◽  
Molecular Switching ◽  
Wide Range ◽  
Electronic Structure Methods ◽  
Explicitly Correlated ◽  
Relative Errors ◽  
The Stability ◽  
Basis Set Expansion

<p>Expanded porphyrins provide a versatile route to molecular switching devices due to their ability to shift between several π-conjugation topologies encoding distinct properties. Taking into account its size and huge conformational flexibility, DFT remains the workhorse for modeling such extended macrocycles. Nevertheless, the stability of Hückel and Möbius conformers depends on a complex interplay of different factors, such as hydrogen bonding, p···p stacking, steric effects, ring strain and electron delocalization. As a consequence, the selection of an exchange-correlation functional for describing the energy profile of topological switches is very difficult. For these reasons, we have examined the performance of a variety of wavefunction methods and density functionals for describing the thermochemistry and kinetics of topology interconversions across a wide range of macrocycles. Especially for hexa- and heptaphyrins, the Möbius structures have a pronouncedly stronger degree of static correlation than the Hückel and figure-eight structures, and as a result the relative energies of singly-twisted structures are a challenging test for electronic structure methods. Comparison of limited orbital space full CI calculations with CCSD(T) calculations within the same active spaces shows that post-CCSD(T) correlation contributions to relative energies are very minor. At the same time, relative energies are weakly sensitive to further basis set expansion, as proven by the minor energy differences between MP2/cc-pVDZ and explicitly correlated MP2-F12/cc-pVDZ-F12 calculations. Hence, our CCSD(T) reference values are reasonably well-converged in both 1-particle and n-particle spaces. While conventional MP2 and MP3 yield very poor results, SCS-MP2 and particularly SOS-MP2 and SCS-MP3 agree to better than 1 kcal mol<sup>-1</sup> with the CCSD(T) relative energies. Regarding DFT methods, only M06-2X provides relative errors close to chemical accuracy with a RMSD of 1.2 kcal mol<sup>-1</sup>. While the original DSD-PBEP86 double hybrid performs fairly poorly for these extended p-systems, the errors drop down to 2 kcal mol<sup>-1</sup> for the revised revDSD-PBEP86-NL, again showing that same-spin MP2-like correlation has a detrimental impact on performance like the SOS-MP2 results. </p>

scholarly journals Lettau’s Contribution to the Obukhov Length Scale: A Scientific Historical Study

2021 ◽  
Author(s):  
Thomas Foken ◽  
Michael Börngen
Keyword(s):  
Characteristic Length ◽  
Stability Parameter ◽  
Historical Study ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Obukhov Length ◽  
The Future

AbstractIt has been repeatedly assumed that Heinz Lettau found the Obukhov length in 1949 independently of Obukhov in 1946. However, it was not the characteristic length scale, the Obukhov length L, but the ratio of height and the Obukhov length (z/L), the Obukhov stability parameter, that he analyzed. Whether Lettau described the parameter z/L independently of Obukhov is investigated herein. Regardless of speculation about this, the significant contributions made by Lettau in the application of z/L merit this term being called the Obukhov–Lettau stability parameter in the future.

scholarly journals Thermodynamic feedback processes in a single-column sea-ice-ocean model

1997 ◽  
Vol 25 ◽  
pp. 327-332 ◽  
Author(s):  
Marika M. Holland ◽  
Julie L. Schramm ◽  
Judith A. Curry
Keyword(s):  
Heat Flux ◽  
Sea Ice ◽  
Surface Heat Flux ◽  
General Circulation ◽  
Accurate Determination ◽  
Circulation Model ◽  
Surface Heat ◽  
Physical Processes ◽  
Feedback Mechanisms ◽  
Albedo Feedback

Due to large uncertainties in many of the parameters used to model sea ice, it is possible that models with significantly different physical processes can be tuned to obtain realistic present-day simulations. However, in studies of climate change, it is the response of the model it various perturbations that is important, in studies response can be significantly different in sea-ice models that include or exclude various physical feedback mechanisms. Because simplifications in sea-ice physics are necessary for general circulation model experiments, it is important to assess which physical processes are essential for the accurate determination of the sensitivity of the ice pack to climate perturbations. We have attempted to address these issues using a new coupled ice-thickness distribution ocean mixed-layer model. The sensitivity of the model to surface heat-flux perturbations is examined and the importance of the ice ocean and ice-albedo feedback mechanisms in determining this sensitivity is analyzed. We find that the ice ocean and ice-albedo feedback processes are not mutually exclusive, and that they both significantly alter the model response to surface heat flux perturbations.

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

scholarly journals Evaluation of single and multiple Doppler lidar techniques to measure complex flow during the XPIA field campaign

2017 ◽  
Vol 10 (1) ◽  
pp. 247-264 ◽  
Author(s):  
Aditya Choukulkar ◽  
W. Alan Brewer ◽  
Scott P. Sandberg ◽  
Ann Weickmann ◽  
Timothy A. Bonin ◽  
...  
Keyword(s):  
Measurement Uncertainty ◽  
Measurement Techniques ◽  
Vertical Plane ◽  
Complex Flow ◽  
Field Campaign ◽  
Velocity Statistics ◽  
Spatial Coverage ◽  
Stable Conditions ◽  
Sonic Anemometers ◽  
Measurement Uncertainties

Abstract. Accurate three-dimensional information of wind flow fields can be an important tool in not only visualizing complex flow but also understanding the underlying physical processes and improving flow modeling. However, a thorough analysis of the measurement uncertainties is required to properly interpret results. The XPIA (eXperimental Planetary boundary layer Instrumentation Assessment) field campaign conducted at the Boulder Atmospheric Observatory (BAO) in Erie, CO, from 2 March to 31 May 2015 brought together a large suite of in situ and remote sensing measurement platforms to evaluate complex flow measurement strategies. In this paper, measurement uncertainties for different single and multi-Doppler strategies using simple scan geometries (conical, vertical plane and staring) are investigated. The tradeoffs (such as time–space resolution vs. spatial coverage) among the different measurement techniques are evaluated using co-located measurements made near the BAO tower. Sensitivity of the single-/multi-Doppler measurement uncertainties to averaging period are investigated using the sonic anemometers installed on the BAO tower as the standard reference. Finally, the radiometer measurements are used to partition the measurement periods as a function of atmospheric stability to determine their effect on measurement uncertainty. It was found that with an increase in spatial coverage and measurement complexity, the uncertainty in the wind measurement also increased. For multi-Doppler techniques, the increase in uncertainty for temporally uncoordinated measurements is possibly due to requiring additional assumptions of stationarity along with horizontal homogeneity and less representative line-of-sight velocity statistics. It was also found that wind speed measurement uncertainty was lower during stable conditions compared to unstable conditions.

scholarly journals Numerical Simulation of Coherent Structures in the Turbulent Boundary Layer under Different Stability Conditions

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1068
Author(s):  
Shujin Laima ◽  
Hehe Ren ◽  
Hui Li ◽  
Jinping Ou
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Correlation Coefficient ◽  
Wind Velocity ◽  
Coherent Structures ◽  
Stability Conditions ◽  
Velocity Spectrum ◽  
Turbulent Eddy ◽  
Stable Conditions ◽  
The Stability

Coherent structures in the turbulent boundary layer were investigated under different stability conditions. Qualitative analyses of the flow field, spatial correlation coefficient field and pre-multiplied wind velocity spectrum showed that the dominant turbulent eddy structure changed from small-scale motions to large- and very-large-scale motions and then to thermal plumes as the stability changed from strong stable to neutral and then to strong unstable. A quantitative analysis of the size characteristics of the three-dimensional turbulent eddy structure based on the spatial correlation coefficient field showed that under near-neutral stability, the streamwise, wall-normal and spanwise extents remained constant at approximately 0.3 δ , 0.1 δ and 0.2 δ ( δ , boundary layer height), respectively, while for other conditions, the extent in each direction varied in a log-linear manner with stability; only the spanwise extent under stable conditions was also independent of stability. The peak wavenumber of the pre-multiplied wind velocity spectrum moves towards small values from stable conditions to neutral condition and then to unstable conditions; thus, for the wind velocity spectrum, another form is needed that takes account the effects of the stability condition.

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