EFFECTS OF THE SCALE OF SPATIAL AVERAGING ON THE KINETIC ENERGIES OF SMALL-SCALE TURBULENT MOTION

Several recent investigations in geophysics and astrophysics have involved a consideration of the hydrodynamics of a fluid which is a good electrical conductor. In this paper one of the problems which seem likely to arise in such investigations is discussed. The fluid is assumed to be incompressible and in homogeneous turbulent motion, and externally imposed electric and magnetic fields are assumed to be absent. The equations governing the interaction of the electromagnetic field and the turbulent motion are set up with the same assumptions as are used to obtain the Maxwell and current flow equations for a metallic conductor. It is shown that the equation for the magnetic field is identical in form with that for the vorticity in a non-conducting fluid; immediate deductions are that lines of magnetic force move with the fluid when the conductivity is infinite, and that the small-scale components of the turbulence have the more powerful effect on the magnetic field. The first question considered is the stability of a purely hydrodynamical system to small disturbing magnetic fields, and it is shown that the magnetic energy of the disturbance will increase provided the conductivity is greater than a critical value determined by the viscosity of the fluid. The rate of growth of magnetic energy is approximately exponential, with a doubling time which can be simply related to the properties of the turbulence. General mechanical considerations suggest that a steady state is reached when the magnetic field has as much energy as is contained in the small-scale components of the turbulence. Estimates of this amount of energy and of the region of the spectrum in which it will lie are given in terms of observable properties of the turbulence.

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Filtering of Background Error Variances and Correlations by Local Spatial Averaging: A Review

Monthly Weather Review ◽

10.1175/2010mwr3111.1 ◽

2010 ◽

Vol 138 (10) ◽

pp. 3693-3720 ◽

Cited By ~ 57

Author(s):

Loïk Berre ◽

Gérald Desroziers

Keyword(s):

Correlation Functions ◽

Weather Prediction ◽

Spatial Filter ◽

Small Scale ◽

Spatial Structures ◽

Spatial Averaging ◽

Probabilistic Forecasting ◽

Ensemble Kalman Filters ◽

Background Error ◽

Averaging Techniques

Abstract The use of local spatial averaging to estimate and validate background error covariances has received increasing attention recently, in particular in the context of variational data assimilation for global numerical weather prediction. First, theoretical and experimental results are presented to examine spatial structures of sampling noise and signal in ensemble-based variance fields in this context. They indicate that sampling noise tends to be relatively small scale, compared to the signal of interest. This difference in spatial structure motivates the use of spatial averaging techniques. Based on the usual linear estimation theory, it is shown how this information can be taken into account in order to calculate and apply an objective spatial filter. This kind of approach can also be used to compare and validate ensemble-based variances with innovation-based variances. The use of spatial averaging is even more important for innovation-based variances because local innovations correspond to single error realizations. Similar ideas can be considered for the estimation of correlation functions. The spatial structures of sampling noise and signal in correlation length scale fields suggest that space-averaging techniques could also be applied to correlation functions. The use of wavelets for this purpose is presented in particular. Connections with related approaches in different contexts such as ensemble Kalman filters and probabilistic forecasting are also discussed.

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Small-scale Turbulent Motion of the Plasma in a Solar Filament as the Precursor of Eruption

The Astrophysical Journal ◽

10.3847/1538-4357/ac0d51 ◽

2021 ◽

Vol 918 (1) ◽

pp. 38

Author(s):

Daikichi Seki ◽

Kenichi Otsuji ◽

Hiroaki Isobe ◽

Giulio Del Zanna ◽

Takako T. Ishii ◽

...

Keyword(s):

Turbulent Motion ◽

Small Scale ◽

Solar Filament

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Long open path measurements of greenhouse gases in air using near infrared Fourier transform spectroscopy

10.5194/amt-2017-272 ◽

2017 ◽

Author(s):

David W. T. Griffith ◽

Denis Pöhler ◽

Stefan Schmitt ◽

Samuel Hammer ◽

Sanam N. Vardag ◽

...

Keyword(s):

Near Infrared ◽

Measurement Techniques ◽

Trace Gas ◽

Small Scale ◽

Gas Composition ◽

Spatial Averaging ◽

Mid Infrared ◽

Open Path ◽

Atmospheric Trace Gas

Abstract. In complex and urban environments, atmospheric trace gas composition is highly variable in time and space. Point measurement techniques for trace gases with in situ instruments are well established and accurate, but do not provide spatial averaging to compare against developing high resolution atmospheric models of composition and small scale meteorology with resolutions of the order of a kilometre. Open path measurement techniques provide path average concentrations and spatial averaging which, if sufficiently accurate, may be better suited to assessment and interpretation with such models. Open path Fourier Transform Spectroscopy (FTS) in the mid infrared region, and Differential Optical Absorption Spectroscopy (DOAS) in the UV and visible, have been used for many years for open path spectroscopic measurements of selected species in both clean air and in polluted environments. Compared to the mid infrared, near infrared instrumentation allows measurements over longer paths than mid IR FTS, for species such as greenhouse gases which are not easily accessible to DOAS. In this pilot study we present the first open path near infrared (4000–10 000 cm−1, 1.0–2.5 μm) FTS measurements of CO2, CH4, O2, H2O and HDO over a 1.5 km path in urban Heidelberg, Germany. We describe the construction of the open path FTS system, the analysis of the collected spectra, precision and accuracy of the measurements, and the results from a four-month trial measurement period in July–November 2014. The open path measurements are compared to calibrated in situ measurements made at one end of the open path. There are small but significant differences between in situ and open path measurements coincident in time which reflect local sources and sinks and the way in which they are sampled by the point and path-averaged measurements. Open path FTS may provide a valuable new tool for investigations of atmospheric trace gas composition in complex, small scale environments such as cities.

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The Impact of Length-Scale Variation When Diagnosing the Standard Deviations of Background Error in a 4D-Var System and Filtering Method Investigation

Advances in Meteorology ◽

10.1155/2020/8885607 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Xiang Xing ◽

Bainian Liu ◽

Weimin Zhang ◽

Xiaoqun Cao ◽

Hongze Leng

Keyword(s):

Standard Deviation ◽

Data Assimilation ◽

Variational Data Assimilation ◽

Small Scale ◽

Model Parameters ◽

Spatial Averaging ◽

Background Error ◽

Operational System ◽

Filtering Method ◽

Standard Deviations

The four-dimensional variational data assimilation (4D-Var) method has been widely employed as an operational scheme in mainstream numerical weather prediction (NWP) centers. In addition to the ensemble data assimilation method, the randomization technique is still used to diagnose the standard deviations of background error in variational data assimilation (VAR) systems; however, such randomization techniques induce sampling noise, which may contaminate the quality of the standard deviations. First, this paper studies the properties of the sampling noise induced by the randomization technique. The results show that the sampling noise is on a small scale displaying high-frequency oscillations around the estimate compared with the estimate and this difference motivates the use of filtering techniques to eliminate the sampling noise effects. The characteristics of the standard deviation field of the control variables are also investigated, and the standard deviation fields of different model parameters have different scales and vary with the vertical model levels. To eliminate such sampling noise, the spectral filtering method used widely in the operational system and a modified spatial averaging approach are investigated. Although both methods have splendid performance in eliminating sampling noise, the spatial averaging approach is more efficient and easier to implement in operational systems. In addition, the optimal filtered results from the spatial averaging approach are dependent on model parameters and vertical levels, which is consistent with the variation in the standard deviation field. Finally, the spatial averaging approach is tested on the operational system at the global scale based on the YH4DVAR and the global NWP system, and the results indicate that the spatial averaging approach has positive effects on both analysis and forecast quality.

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Reasons to strike first

Behavioral and Brain Sciences ◽

10.1017/s0140525x19000840 ◽

2019 ◽

Vol 42 ◽

Author(s):

William Buckner ◽

Luke Glowacki

Keyword(s):

Intergroup Conflict ◽

Small Scale

Abstract De Dreu and Gross predict that attackers will have more difficulty winning conflicts than defenders. As their analysis is presumed to capture the dynamics of decentralized conflict, we consider how their framework compares with ethnographic evidence from small-scale societies, as well as chimpanzee patterns of intergroup conflict. In these contexts, attackers have significantly more success in conflict than predicted by De Dreu and Gross's model. We discuss the possible reasons for this disparity.

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Exploring Coronal Structures with SOHO

International Astronomical Union Colloquium ◽

10.1017/s0252921100064915 ◽

2000 ◽

Vol 179 ◽

pp. 403-406

Author(s):

M. Karovska ◽

B. Wood ◽

J. Chen ◽

J. Cook ◽

R. Howard

Keyword(s):

Solar Corona ◽

Image Enhancement ◽

Coronal Mass Ejections ◽

Dynamical Evolution ◽

Small Scale ◽

Low Contrast ◽

Contrast Structures ◽

Scale Structures ◽

Small Scale Structures ◽

Coronal Structures

AbstractWe applied advanced image enhancement techniques to explore in detail the characteristics of the small-scale structures and/or the low contrast structures in several Coronal Mass Ejections (CMEs) observed by SOHO. We highlight here the results from our studies of the morphology and dynamical evolution of CME structures in the solar corona using two instruments on board SOHO: LASCO and EIT.

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Scanning tunneling microscopy and atomic force microscopy: New tools for biology

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100155864 ◽

1989 ◽

Vol 47 ◽

pp. 778-779

Author(s):

CE Bracker ◽

P. K. Hansma

Keyword(s):

Physical Property ◽

Scanning Probe ◽

Scanning Tunneling ◽

Small Scale ◽

Tunneling Microscopy ◽

Force Microscopy ◽

New Family ◽

Small Probe ◽

Atomic Force ◽

Transmission Electron

A new family of scanning probe microscopes has emerged that is opening new horizons for investigating the fine structure of matter. The earliest and best known of these instruments is the scanning tunneling microscope (STM). First published in 1982, the STM earned the 1986 Nobel Prize in Physics for two of its inventors, G. Binnig and H. Rohrer. They shared the prize with E. Ruska for his work that had led to the development of the transmission electron microscope half a century earlier. It seems appropriate that the award embodied this particular blend of the old and the new because it demonstrated to the world a long overdue respect for the enormous contributions electron microscopy has made to the understanding of matter, and at the same time it signalled the dawn of a new age in microscopy. What we are seeing is a revolution in microscopy and a redefinition of the concept of a microscope.Several kinds of scanning probe microscopes now exist, and the number is increasing. What they share in common is a small probe that is scanned over the surface of a specimen and measures a physical property on a very small scale, at or near the surface. Scanning probes can measure temperature, magnetic fields, tunneling currents, voltage, force, and ion currents, among others.

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Superstructures and ordering phenomena in ceramic superconductors

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100166014 ◽

1996 ◽

Vol 54 ◽

pp. 710-711

Author(s):

R. Gronsky

Keyword(s):

Domain Growth ◽

Small Displacement ◽

Small Scale ◽

Ceramic Superconductors ◽

Oxygen Sublattices ◽

Tweed Contrast ◽

Diffraction Patterns ◽

Representative Image ◽

Static Lattice ◽

Modulation Wavelength

It is now well established that the phase transformation behavior of YBa2Cu3O6+δ is significantly influenced by matrix strain effects, as evidenced by the formation of accommodation twins, the occurrence of diffuse scattering in diffraction patterns, the appearance of tweed contrast in electron micrographs, and the generation of displacive modulation superstructures, all of which have been successfully modeled via simple Monte Carlo simulations. The model is based upon a static lattice formulation with two types of excitations, one of which is a change in oxygen occupancy, and the other a small displacement of both the copper and oxygen sublattices. Results of these simulations show that a displacive superstructure forms very rapidly in a morphology of finely textured domains, followed by domain growth and a more sharply defined modulation wavelength, ultimately evolving into a strong <110> tweed with 5 nm to 7 nm period. What is new about these findings is the revelation that both the small-scale deformation superstructures and coarser tweed morphologies can result from displacive modulations in ordered YBa2Cu3O6+δ and need not be restricted to domain coarsening of the disordered phase. Figures 1 and 2 show a representative image and diffraction pattern for fully-ordered (δ = 1) YBa2Cu3O6+δ associated with a long-period <110> modulation.

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