On the two-dimensional mixing region

1976 ◽  
Vol 74 (2) ◽  
pp. 209-250 ◽  
Author(s):  
F. H. Champagne ◽  
Y. H. Pao ◽  
I. J. Wygnanski
Keyword(s):  
Initial Conditions ◽  
Longitudinal Velocity ◽  
Higher Order ◽  
Digital Data ◽  
Statistical Characteristics ◽  
Wave Number ◽  
Two Dimensional ◽  
Eighth Order ◽  
Lateral Velocity ◽  
Velocity Fluctuations

An experimental investigation of the two-dimensional incompressible mixing layer was carried out. The measurements provide new information on the development of the mean and turbulent fields towards a self-preserving state and on the higher-order statistical characteristics of the turbulent field. The relevance of initial conditions to the development of the flow is discussed in the light of both present and previous data. Measurements of spectra, probability densities and moments to eighth order of all three velocity-component fluctuations at various transverse positions across the flow were carried out using an on-line digital data acquisition system. The probability density distributions of the derivative and the squared derivative of the longitudinal and lateral velocity fluctuations were also determined. Direct measurements of moments to eighth order of the velocity derivatives were attempted and are discussed in the light of the simultaneously measured histograms. The problems in obtaining higher-order statistical data are considered in some detail. Estimates of the integral time scale of many of the higher-order statistics are presented. The high wave-number structure was found to be locally anisotropic according to both spectral and turbulent velocity-gradient moment requirements. Higher-order spectra to fourth order of the longitudinal velocity fluctuations were measured and are discussed. Finally the lognormality of the squared longitudinal and lateral velocity-derivative fluctuations was investigated and the universal lognormal constant μ was evaluated.

Exponential Compact Higher Order Scheme for Nonlinear Steady Convection-Diffusion Equations

2011 ◽  
Vol 9 (4) ◽  
pp. 897-916 ◽  
Author(s):  
Y. V. S. S. Sanyasiraju ◽  
Nachiketa Mishra
Keyword(s):  
Coefficient Matrix ◽  
Higher Order ◽  
Diffusion Equations ◽  
Wave Number ◽  
Two Dimensional ◽  
Thomas Algorithm ◽  
Convection Diffusion ◽  
Numerous Model ◽  
Order Scheme ◽  
Higher Order Scheme

AbstractThis paper presents an exponential compact higher order scheme for Convection-Diffusion Equations (CDE) with variable and nonlinear convection coefficients. The scheme is for one-dimensional problems and produces a tri-diagonal system of equations which can be solved efficiently using Thomas algorithm. For two-dimensional problems, the scheme produces an accuracy over a compact nine point stencil which can be solved using any line iterative approach with alternate direction implicit procedure. The convergence of the iterative procedure is guaranteed as the coefficient matrix of the developed scheme satisfies the conditions required to be positive. Wave number analysis has been carried out to establish that the scheme is comparable in accuracy with spectral methods. The higher order accuracy and better rate of convergence of the developed scheme have been demonstrated by solving numerous model problems for one and two-dimensional CDE, where the solutions have the sharp gradient at the solution boundary.

scholarly journals The Zeldovich & Adhesion approximations and applications to the local universe

2014 ◽  
Vol 11 (S308) ◽  
pp. 69-76 ◽  
Author(s):  
Johan Hidding ◽  
Rien van de Weygaert ◽  
Sergei Shandarin
Keyword(s):  
Initial Conditions ◽  
Higher Order ◽  
Deformation Tensor ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Local Universe ◽  
Web Based ◽  
Two Dimensional Model ◽  
Novel Method ◽  
Adhesion Model

AbstractThe Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A3 lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe.

Correlation measurements in grid turbulence using digital harmonic analysis

1968 ◽  
Vol 34 (3) ◽  
pp. 497-515 ◽  
Author(s):  
C. W. Van Atta ◽  
W. Y. Chen
Keyword(s):  
Probability Density ◽  
High Speed ◽  
Longitudinal Velocity ◽  
Joint Probability ◽  
Grid Turbulence ◽  
Eighth Order ◽  
Transform Method ◽  
Velocity Fluctuations ◽  
Odd Order ◽  
Joint Probability Density

Two-point time correlations up to eighth order of longitudinal velocity fluctuations in grid-generated turbulence have been measured using linearized hot-wire anemometry, digital sampling, and a high-speed digital computer. A novel feature of the present measurements is the adoption of digital Fourier analysis, using the recently developed fast-Fourier transform method. The joint probability density function for the velocity fluctuations at two points separated in time is found to be significantly non-Gaussian. All measured even-order correlations are nearly identical with those reported by Frenkiel & Klebanoff (1967 a, b), and higher-order correlations may be accurately predicted from the second-order correlation by assuming a Gaussian joint probability density. All individual odd-order correlations are substantially different from those reported by Frenkiel & Klebanoff. In particular, all mean values of odd powers of the fluctuating velocity are nearly zero, and the correlations are nearly antisymmetrical functions of the time delay as would be the case for purely isotropic homogeneous turbulence. In spite of the large difference between the individual measured odd-order correlations and previous measurements, quantities such as the skewness and skewness factor derived from certain combinations of the correlations are found to be quite insensitive to observed differences in the form of the correlations and are very similar to previous measurements.

scholarly journals Revisiting two-dimensional turbulence and mesoscale spectra

2021 ◽  
Author(s):  
Xiaoli Larsén ◽  
Søren Larsen ◽  
Erik Petersen ◽  
Torben Mikkelsen
Keyword(s):  
Boundary Layer ◽  
Stationary Time Series ◽  
Wave Number ◽  
Inertial Subrange ◽  
Spectral Structure ◽  
Two Dimensional ◽  
Spectral Slope ◽  
Lateral Velocity ◽  
2D Turbulence ◽  
Boundary Layer Meteorology

&lt;p&gt;Two-dimensional (2D) turbulence is not only a basic research topic that needs further investigations, it is also relevant for wind energy applications as today&amp;#8217;s wind farm clusters can be as large as thousands of kilometers squared and individual turbines hundreds of meters tall. This challenges the use of classical turbulence models applicable for scales smaller than ~1 h, or as denoted in H&amp;#246;gstr&amp;#246;m et al. (2002) the Kolmogoroff inertial subrange, the shear production range, and for ranges the spectral gap region.&lt;/p&gt;&lt;p&gt;This study revisits some key characteristics of 2D turbulence and interpretation of the physics behind it, including general literatures as well as a series of our studies in recent years (Lars&amp;#233;n et al. 2013, 2016, 2021). This includes&lt;/p&gt;&lt;ul&gt;&lt;li&gt;The respective frequency/wave number range and the spectral behaviours for the wind speed: the synoptic scales where the spectral slope is -3, the mesoscale where the spectral slope is typically -5/3, and the gap region. We analyze at what scales the spectra meet and merge, and how the spectra are affected by weather types, seasons and stability.&lt;/li&gt; &lt;li&gt;The 2D-isotropy characteristics. We analyze how the longitudinal and lateral velocities correlate across the scales.&lt;/li&gt; &lt;li&gt;The application of stationarity. The validity of an assumption of stationary time series decides to how large scales we can perform the analysis of the longitudinal and lateral velocity components, the Taylor frozen hypothesis and 2D-isotropy.&lt;/li&gt; &lt;/ul&gt;&lt;p&gt;The primary datasets are from several met stations over Denmark and the North Sea region, including both 10-min and sonic measurements from about 10 m up to 240 m.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;References:&lt;/p&gt;&lt;p&gt;H&amp;#246;gstr&amp;#246;m U, Hunt J, Smedman AS (2002) Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorol 103:101&amp;#8211;124&lt;/p&gt;&lt;p&gt;Lars&amp;#233;n, X. G., Larsen, S. E., Petersen, E. L., &amp; Mikkelsen, T. K. (2021). A Model for the Spectrum of the Lateral Velocity Component from Mesoscale to Microscale and Its Application to Wind-Direction Variation. Boundary-Layer Meteorology, 178, 415-434. https://doi.org/10.1007/s10546-020-00575-0&lt;/p&gt;&lt;p&gt;Lars&amp;#233;n X. Larsen S. and Petersen E. (2016): Full-scale spectrum of the boundary layer wind. Boundary-Layer Meteorology, Vol 159, p 349-371&lt;/p&gt;&lt;p&gt;Lars&amp;#233;n X., Vincent C. and Larsen S.E. (2013): Spectral structure of mesoscale winds over the water, Q. J. R. Meteorol. Soc., DOI:10.1002/qj.2003, 139, 685-700.&lt;/p&gt;

Two-Dimensional Local Deep-Level Transient Spectroscopy Imaging Using Super-Higher-Order Scanning Nonlinear Dielectric Microscopy

2016 ◽  
Author(s):  
N. Chinone ◽  
Y. Cho ◽  
R. Kosugi ◽  
Y. Tanaka ◽  
S. Harada ◽  
...  
Keyword(s):  
Deep Level Transient Spectroscopy ◽  
Deep Level ◽  
Higher Order ◽  
Trap Density ◽  
New Technique ◽  
Two Dimensional ◽  
Nonlinear Dielectric ◽  
Annealing Conditions ◽  
Transient Spectroscopy ◽  
A New Technique

Abstract A new technique for local deep level transient spectroscopy (DLTS) imaging using super-higher-order scanning nonlinear dielectric microscopy is proposed. Using this technique. SiCVSiC structure samples with different post oxidation annealing conditions were measured. We observed that the local DLTS signal decreases with post oxidation annealing (POA), which agrees with the well-known phenomena that POA reduces trap density. Furthermore, obtained local DLTS images had dark and bright areas, which is considered to show the trap distribution at/near SiCVSiC interface.

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