On the realizability of pressure–strain closures

2014 ◽  
Vol 755 ◽  
pp. 535-560 ◽  
Author(s):  
Aashwin A. Mishra ◽  
Sharath S. Girimaji
Keyword(s):  
Statistical Models ◽  
Flow Stability ◽  
Mean Flow ◽  
Model Formulation ◽  
Closure Model ◽  
Two Component ◽  
The Mean ◽  
The Relationship ◽  
Rapid Pressure ◽  
Domain Of Validity

AbstractThe realizability condition for statistical models of turbulence is augmented to ensure that not only is the Reynolds stress tensor positive semi-definite, but the process of its evolution is physically attainable as well. The mathematical constraints due to this process realizability requirement on the rapid pressure strain correlation are derived. The resulting constraints reveal important limits on the inter-component energy transfer and the consequent flow stability characteristics, as a function of the mean flow. For planar mean flows, the realizability constraints are most stringent for the case of purely sheared flows rather than elliptic flows. The relationship between the constraints and flow stability is explained. Process realizability leads to closure model guidance not only at the two-component (2C) limit of turbulence (as in the classical realizability approach) but throughout the anisotropy space. Consequently, the domain of validity and applicability of current models can be clearly identified for different mean flows. A simple framework for incorporating these process realizability constraints in model formulation is outlined.

scholarly journals Mean flow of turbulent–laminar patterns in plane Couette flow

2007 ◽  
Vol 576 ◽  
pp. 109-137 ◽  
Author(s):  
DWIGHT BARKLEY ◽  
LAURETTE S. TUCKERMAN
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Full Range ◽  
Force Balance ◽  
Computational Domain ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
The Mean ◽  
The Relationship ◽  
And Diffusion

A turbulent–laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow, averaged in time and in the homogeneous direction, is analysed. The flow in the quasi-laminar region is not the linear Couette profile, but results from a non-trivial balance between advection and diffusion. This force balance yields a first approximation to the relationship between the Reynolds number, angle, and wavelength of the pattern. Remarkably, the variation of the mean flow along the pattern wavevector is found to be almost exactly harmonic: the flow can be represented via only three cross-channel profiles as U(x, y, z) ≈ U0(y) + Uc(y) cos(kz) + Us(y) sin(kz). A model is formulated which relates the cross-channel profiles of the mean flow and of the Reynolds stress. Regimes computed for a full range of angle and Reynolds number in a tilted rectangular periodic computational domain are presented. Observations of regular turbulent–laminar patterns in other shear flows – Taylor–Couette, rotor–stator, and plane Poiseuille – are compared.

Emotional Response to Testing in Gifted and Highly Gifted Children

2021 ◽  
Author(s):  
Cesare Cornoldi ◽  
David Giofrè ◽  
Irene Mammarella ◽  
Enrico Toffalini
Keyword(s):  
Statistical Models ◽  
Emotional Response ◽  
Fifth Graders ◽  
Gifted Children ◽  
Intellectually Gifted ◽  
The Mean ◽  
Standard Deviations ◽  
National Test ◽  
The Relationship ◽  
Practical Implications

Whether intellectually gifted children have a greater emotional response when tested is still unclear. This may be due to the marked heterogeneity of this particular population, and the fact that most studies lack the power to reduce the noise associated with this heterogeneity. The present study examined the relationship between performance and emotional response in 468,423 Italian fifth-graders taking a national test on mathematics and language. Analyses were performed using statistical models with polynomial terms. Special attention was paid to estimating the mean emotional response of the children who were gifted (1.5-2.5 standard deviations above the mean) or highly gifted (more than 2.5 standard deviations above the mean). The results showed that, although a lower emotional response correlated with a higher achievement, this relationship is nonlinear, and the estimates for gifted and highly gifted children were virtually the same. Girls showed a greater emotional response than boys on all levels of performance. The theoretical and practical implications of these findings are discussed.

scholarly journals Observational Analysis of the 27 May 1997 Central Texas Tornadic Event. Part I: Prestorm Environment and Storm Maintenance/Propagation

2007 ◽  
Vol 135 (3) ◽  
pp. 701-726 ◽  
Author(s):  
Adam L. Houston ◽  
Robert B. Wilhelmson
Keyword(s):  
Cold Front ◽  
Extreme Values ◽  
Vertical Shear ◽  
State Variables ◽  
Mean Flow ◽  
Level Ii ◽  
Central Texas ◽  
The Mean ◽  
Cell Motion ◽  
The Relationship

Abstract A detailed analysis of the 27 May 1997 central Texas tornadic storm complex is undertaken in an attempt to document the prestorm environment and identify the roles played by preexisting boundaries on storm maintenance/propagation and rotation. Analysis is carried out using a broad suite of synoptic and subsynoptic data but focuses on the level-II and -III Weather Surveillance Radar-1988 Doppler (WSR-88D) data from three Texas radars. The 27 May 1997 event was characterized by a back-building (propagation against the mean flow) storm complex that produced at least 12 tornadoes including the F5 Jarrell, Texas, tornado. Furthermore, five of the eight longest-lived cells during the analysis period are shown to contain midlevel mesocyclones. However, one-dimensional metrics calculated using representative vertical profiles of state variables reveal that, despite the extreme values of CAPE in place (>6500 J kg−1), the (1D) environment associated with this event is best classified as only marginally favorable for supercells and unfavorable for significant, supercellular tornadoes. Furthermore, the observed wind shear values are shown to be more in line with the vertical shear values typically associated with nonsevere back-building storms. Examples of propagation controlled by quasi-continuous maintenance of a single cell as well as successive discrete cell redevelopment are found. In all situations, two preexisting boundaries in place during this event (a cold front and a dryline) are found to have been necessary for the maintenance/propagation of the storm complex. Specifically, it is argued that the “zippering” of the cold front and dryline (the collision of the dryline and cold front that allowed the cold front to overtake the dryline and penetrate into the most unstable air to the east) was essential for the back-building of the storm complex in this event since it resulted in new cell development at points farther south. While midlevel mesocyclones were present in five of the eight longest-lived and well-sampled cells, analysis of the relationship between observed cell motion, expected cell motion, expected supercellular deviation, and boundary motion for the longest-lived and well-sampled cells reveals little evidence that deviate motions generated through supercellular dynamics governed cell motions. Instead, it is shown that boundary motions largely controlled the propagation of individual cells.

scholarly journals Mean flow stability analysis of oscillating jet experiments

2014 ◽  
Vol 757 ◽  
pp. 1-32 ◽  
Author(s):  
Kilian Oberleithner ◽  
Lothar Rukes ◽  
Julio Soria
Keyword(s):  
Stability Analysis ◽  
Wave Model ◽  
Flow Stability ◽  
Mean Flow ◽  
Axisymmetric Mode ◽  
Wide Range ◽  
Flow Oscillations ◽  
The Mean ◽  
Wave Models ◽  
The Stability

AbstractLinear stability analysis (LSA) is applied to the mean flow of an oscillating round jet with the aim of investigating the robustness and accuracy of mean flow stability wave models. The jet’s axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry (PIV) and decomposed into a mean and periodic part utilizing proper orthogonal decomposition (POD). Local LSA is applied to the measured mean flow adopting a weakly non-parallel flow approach. The resulting global perturbation field is carefully compared with the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{>}40\, \%$), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows. The high accuracy of mean flow stability wave models as demonstrated here is of great importance for the analysis of coherent structures in turbulent shear flows.

scholarly journals Optimization of the Cross-Correlation Algorithm for Two-Component Wind Field Estimation from Single Aerosol Lidar Data and Comparison with Doppler Lidar

2016 ◽  
Vol 33 (1) ◽  
pp. 81-101 ◽  
Author(s):  
Masaki Hamada ◽  
Pierre Dérian ◽  
Christopher F. Mauzey ◽  
Shane D. Mayor
Keyword(s):  
Cross Correlation ◽  
Field Experiments ◽  
Flow Direction ◽  
Interrogation Window ◽  
Lidar Data ◽  
Doppler Lidar ◽  
Mean Flow ◽  
Correlation Algorithm ◽  
Two Component ◽  
The Mean

AbstractNumerical and field experiments were conducted to test an optimized cross-correlation algorithm (CCA) for the remote sensing of two-component wind vectors from horizontally scanning elastic backscatter lidar data. Each vector is the result of applying the algorithm to a square and contiguous subset of pixels (an interrogation window) in the lidar scan area. Synthetic aerosol distributions and flow fields were used to investigate the accuracy and precision of the technique. Results indicate that in neutral static stability, when the mean flow direction over the interrogation window is relatively uniform, the random error of the estimates increases as the mean wind speed and turbulence intensity increases. In convective conditions, larger errors may occur as a result of the cellular nature of convection and the dramatic changes in wind direction that may span the interrogation window. Synthetic fields were also used to determine the significance of various image processing and numerical steps used in the CCA. Results show that an iterative approach that dynamically reduces the block size provides the largest performance gains. Finally, data from a field experiment conducted in 2013 in Chico, California, are presented. Comparisons with Doppler lidar data indicate excellent agreement for the 10-min mean wind velocity computed over a set of 150 h: the root-mean-square deviations (and slopes) for the u and υ components are 0.36 m s−1 (0.974) and 0.37 m s−1 (0.991), respectively, with correlation coefficients > 0.99.

scholarly journals ENTRAINMENT DUE TO MEAN FLOW IN TWO-LAYERED FLUID

1988 ◽  
Vol 1 (21) ◽  
pp. 189
Author(s):  
Masaru Ura ◽  
Nobuhiro Matsunaga
Keyword(s):  
Grid Turbulence ◽  
Mean Flow ◽  
Mean Velocity ◽  
Entrainment Velocity ◽  
Turbulent Entrainment ◽  
The Mean ◽  
Flow Turbulence ◽  
Turbulence Factor ◽  
Relationship Of ◽  
The Relationship

The entrainment phenomena have been investigated across an interface between two-layered stratified flow induced by wind shear stress. The velocities of mean flow, turbulence and entrainment have been measured under three different conditions of water surface by using a wind-wave tank. When the entrainment velocity ue is expressed on the basis of the turbulent quantities at the interface, the turbulent entrainment coefficient E ( = ue/u) is given by E = A-(egl/u2)-3I1 ( A = 0.7). Here Eg, u and 1 are the effective buoyancy, the turbulence intensity and the integral lengthscale of turbulence at the interface, respectively. This result coincides with the relationship of entrainment due to oscillating grid turbulence, in which the mean flow does not exist. When, for the practical purpose, the estimation of ue is made by using the mean velocity Um and the depth h of mixed layer, Em ( - Ue/Um ) = Am•(egh/Um 2)"3/2 is derived from the transformation of E = A-(egl/u2)-3/2. There holds Am = A-Tf between Am and Tf, Tf being a turbulence factor given by (u/Um)4•(1/h)-3/2. It has been found that this relationship is also valid in various types of two-layered stratified flows as well as the wind-induced two-layered flows.

Emotional Response to Testing in Gifted and Highly Gifted Children

2021 ◽  
pp. 001698622110429
Author(s):  
Cesare Cornoldi ◽  
David Giofrè ◽  
Irene Cristina Mammarella ◽  
Enrico Toffalini
Keyword(s):  
Statistical Models ◽  
Emotional Response ◽  
Fifth Graders ◽  
Gifted Children ◽  
Intellectually Gifted ◽  
The Mean ◽  
Standard Deviations ◽  
National Test ◽  
The Relationship ◽  
Practical Implications

Whether intellectually gifted children have a greater emotional response when tested is still unclear. This may be due to the marked heterogeneity of this particular population, and the fact that most studies lack the power to reduce the noise associated with this heterogeneity. The present study examined the relationship between performance and emotional response in 468,423 Italian fifth-graders taking a national test on mathematics and language. Analyses were performed using statistical models with polynomial terms. Special attention was paid to estimating the mean emotional response of the children who were gifted (1.5-2.5 standard deviations above the mean) or highly gifted (more than 2.5 standard deviations above the mean). The results showed that, although a lower emotional response correlated with a higher achievement, this relationship is nonlinear, and the estimates for gifted and highly gifted children were virtually the same. Girls showed a greater emotional response than boys on all levels of performance. The theoretical and practical implications of these findings are discussed.

Multi-Center Calibration of the Second Reference Material for Thromboplastin, Rabbit, Plain, Coded CRM 149R

1991 ◽  
Vol 65 (03) ◽  
pp. 263-267 ◽  
Author(s):  
A M H P van den Besselaar ◽  
R M Bertina
Keyword(s):  
Reference Material ◽  
Standard Error ◽  
Standard Errors ◽  
Sensitivity Index ◽  
Long Term Stability ◽  
Significant Bias ◽  
The Mean ◽  
The Relationship ◽  
International Sensitivity Index

SummaryIn a collaborative trial of eleven laboratories which was performed mainly within the framework of the European Community Bureau of Reference (BCR), a second reference material for thromboplastin, rabbit, plain, was calibrated against its predecessor RBT/79. This second reference material (coded CRM 149R) has a mean International Sensitivity Index (ISI) of 1.343 with a standard error of the mean of 0.035. The standard error of the ISI was determined by combination of the standard errors of the ISI of RBT/79 and the slope of the calibration line in this trial.The BCR reference material for thromboplastin, human, plain (coded BCT/099) was also included in this trial for assessment of the long-term stability of the relationship with RBT/79. The results indicated that this relationship has not changed over a period of 8 years. The interlaboratory variation of the slope of the relationship between CRM 149R and RBT/79 was significantly lower than the variation of the slope of the relationship between BCT/099 and RBT/79. In addition to the manual technique, a semi-automatic coagulometer according to Schnitger & Gross was used to determine prothrombin times with CRM 149R. The mean ISI of CRM 149R was not affected by replacement of the manual technique by this particular coagulometer.Two lyophilized plasmas were included in this trial. The mean slope of relationship between RBT/79 and CRM 149R based on the two lyophilized plasmas was the same as the corresponding slope based on fresh plasmas. Tlowever, the mean slope of relationship between RBT/79 and BCT/099 based on the two lyophilized plasmas was 4.9% higher than the mean slope based on fresh plasmas. Thus, the use of these lyophilized plasmas induced a small but significant bias in the slope of relationship between these thromboplastins of different species.

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