The effect of velocity sensitivity on temperature derivative statistics in isotropic turbulence

1971 ◽  
Vol 48 (4) ◽  
pp. 763-769 ◽  
Author(s):  
J. C. Wyngaard
Keyword(s):  
Temperature Gradient ◽  
Temperature Sensor ◽  
Isotropic Turbulence ◽  
Mean Square ◽  
Temperature Derivative ◽  
Spectral Form ◽  
Temperature Spectrum ◽  
Velocity Sensitivity ◽  
The Mean ◽  
Third Moment

The velocity sensitivity of a resistance-wire temperature sensor is expressed in terms of sensor parameters, and the resulting errors in temperature derivative moments in isotropic turbulence are evaluated. It is shown that velocity sensitivity of a degree completely negligible for most purposes causes severe contamination of the measured third moment. The contamination terms are shown to be production rates of the mean square temperature gradient and vorticity, respectively, and therefore create positive values of measured derivative skewness. The dominant contamination term is related to the temperature spectrum through the balance equation for the mean-square temperature gradient, and calculations based on an assumed spectral form show that under typical conditions the measured skewness is large. This mechanism could provide an alternative to anisotropy as an explanation of the positive skewnesses recently measured in the atmosphere.

scholarly journals On the strength of the nonlinearity in isotropic turbulence

2013 ◽  
Vol 733 ◽  
pp. 158-170 ◽  
Author(s):  
W. J. T. Bos ◽  
R. Rubinstein
Keyword(s):  
Nonlinear Term ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Direct Interaction ◽  
Inertial Range ◽  
Gaussian Field ◽  
Mean Square ◽  
Closed Expression ◽  
Gaussian Estimate ◽  
The Mean

AbstractTurbulence governed by the Navier–Stokes equations shows a tendency to evolve towards a state in which the nonlinearity is diminished. In fully developed turbulence, this tendency can be measured by comparing the variance of the nonlinear term to the variance of the same quantity measured in a Gaussian field with the same energy distribution. In order to study this phenomenon at high Reynolds numbers, a version of the direct interaction approximation is used to obtain a closed expression for the statistical average of the mean-square nonlinearity. The wavenumber spectrum of the mean-square nonlinear term is evaluated and its scaling in the inertial range is investigated as a function of the Reynolds number. Its scaling is dominated by the sweeping by the energetic scales, but this sweeping is weaker than predicted by a random sweeping estimate. At inertial range scales, the depletion of nonlinearity as a function of the wavenumber is observed to be constant. At large scales it is observed that the mean-square nonlinearity is larger than its Gaussian estimate, which is shown to be related to the non-Gaussianity of the Reynolds-stress fluctuations at these scales.

scholarly journals Remarks on the Motility and Thermotactic Response of Fibroblasts

1983 ◽  
Vol 36 (5) ◽  
pp. 707
Author(s):  
WC Parkinson
Keyword(s):  
Temperature Gradient ◽  
Mean Square Displacement ◽  
Time Lapse ◽  
Mean Square ◽  
Centre Of Gravity ◽  
Statistical Fluctuations ◽  
The Mean ◽  
Number Of Cells ◽  
Time Lapse Photography

The motion of mouse L cells (fibroblast) in vitro is studied by means of time-lapse photography. In particular, the response of the cells to a temperature gradient of7� 22�Ccm-1 is studied for several temperatures from 32� 6�C to 39� 7�C. Three measures of the thermotactic response are used: (1) the motility, defined in terms of the mean-square displacement of an ensemble of cells, (2) the displacement of the centre of gravity of an ensemble of cells versus time, and (3) the distribution in the number of cells in an ensemble moving up the gradient compared with the number moving down the gradient. There is no evidence of a thermotactic response as determined by these three measures. The variance in the data can be understood in terms of statistical fluctuations.

The mean value of the fluctuations in pressure and pressure gradient in a turbulent fluid

1938 ◽  
Vol 34 (4) ◽  
pp. 534-539
Author(s):  
A. E. Green
Keyword(s):  
Unit Volume ◽  
Isotropic Turbulence ◽  
Fluid Motion ◽  
Mean Value ◽  
Mean Square ◽  
Turbulent Fluid ◽  
Dissipation Of Energy ◽  
The Mean ◽  
Rate Of Dissipation ◽  
Image Position

1. Taylor has shown (1) that two characteristic lengthsλ and λη may be defined for turbulent fluid motion. The length λ, which is connected with the dissipation of energy, is, for isotropic turbulence, given bywhere is the mean rate of dissipation of energy per unit volume and represents the mean square value of any component of velocity. The length λη can be defined in terms of thuswhere For isotropic turbulence Taylor assumed thatwhere B is a constant. Since the turbulence is isotropic,and so, from (1), (2), (3) and (4) we have

Pressure fluctuations in isotropic turbulence

1951 ◽  
Vol 47 (2) ◽  
pp. 359-374 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Pressure Gradient ◽  
Isotropic Turbulence ◽  
Alternative Hypothesis ◽  
Pressure Fluctuations ◽  
Reynolds Numbers ◽  
Fourth Moment ◽  
Mean Square ◽  
Important Special Case ◽  
Odd Order ◽  
The Mean

ABSTRACTThis paper considers the correlation P(r) between the fluctuating pressures at two different points distance r apart in a field of homogeneous isotropic turbulence. P(r) can be expressed in terms of the fourth moment of the velocity fluctuation, which is evaluated with the aid of the hypothesis that fourth moments are related to second moments in the same way as for a normal joint distribution of the velocities at any two points. The experimental evidence relevant to this hypothesis (which cannot be exactly true since it gives zero odd-order moments) is examined. The alternative hypothesis made by Heisenberg, that the Fourier coefficients of the velocity distribution are statistically independent, has identical consequences for the fourth moments of the velocity, although it does not lead to such convenient results.The pressure correlation is worked out in detail for the important special case of very large Reynolds numbers of turbulence; the mean-square pressure fluctuation is found to be . The mean-square pressure gradient is evaluated, from the available data concerning the doublevelocity correlation, for the cases of very small and very large Reynolds numbers, and a simple interpolation between these results is suggested for the general case. Finally, the relation between the mean-square pressure gradient and rate of diffusion of marked fluid particles from a fixed source is established without the neglect of the viscosity effect, and the available observations of diffusion are used to obtain estimates of which are compared with the theoretical values.

A statistical theory of turbulent relative dispersion

2007 ◽  
Vol 571 ◽  
pp. 391-417 ◽  
Author(s):  
P. FRANZESE ◽  
M. CASSIANI
Keyword(s):  
Laboratory Experiments ◽  
Isotropic Turbulence ◽  
Diffusion Theory ◽  
Relative Dispersion ◽  
Inertial Subrange ◽  
Mean Square ◽  
Homogeneous Isotropic Turbulence ◽  
Relative Kinetic ◽  
The Mean ◽  
Closure Assumption

The laws governing the spread of a cluster of particles in homogeneous isotropic turbulence are derived using a theoretical approach based on inertial subrange scaling and statistical diffusion theory. The equations for the mean square dispersion of a puff admit an analytical solution in the inertial subrange and at large scales. The solution is consistent with Taylor's theory of absolute dispersion. An analytical derivation of the Richardson–Obukhov constant of relative dispersion is presented. A time scale for relative dispersion is identified, as well as relations between Lagrangian and Eulerian structure functions. The results are extended to turbulence at finite Reynolds number. A closure assumption for the relative kinetic energy, based on Taylor's theory, is presented. Comparisons with direct numerical simulations and laboratory experiments are reported.

Direct simulation of particle dispersion in a decaying isotropic turbulence

1992 ◽  
Vol 242 ◽  
pp. 655-700 ◽  
Author(s):  
S. Elghobashi ◽  
G. C. Truesdell
Keyword(s):  
Particle Motion ◽  
Isotropic Turbulence ◽  
Particle Dispersion ◽  
Time Development ◽  
Solid Particles ◽  
Mean Square ◽  
Lagrangian Velocity ◽  
The Mean ◽  
Simulation Results ◽  
Surrounding Fluid

Dispersion of solid particles in decaying isotropic turbulence is studied numerically. The three-dimensional, time-dependent velocity field of a homogeneous, non-stationary turbulence was computed using the method of direct numerical simulation (DNS). A numerical grid containing 963 points was sufficient to resolve the turbulent motion at the Kolmogorov lengthscale for a range of microscale Reynolds numbers starting from Rλ = 25 and decaying to Rλ = 16. The dispersion characteristics of three different solid particles (corn, copper and glass) injected in the flow, were obtained by integrating the complete equation of particle motion along the instantaneous trajectories of 223 particles for each particle type, and then performing ensemble averaging. The three different particles are those used by Snyder & Lumley (1971), referred to throughout the paper as SL, in their pioneering wind-tunnel experiment. Good agreement was achieved between our DNS results and the measured time development of the mean-square displacement of the particles.The simulation results also include the time development of the mean-square relative velocity of the particles, the Lagrangian velocity autocorrelation and the turbulent diffusivity of the particles and fluid points. The Lagrangian velocity frequency spectra of the particles and their surrounding fluid, as well as the time development of all the forces acting on one particle are also presented. In order to distinguish between the effects of inertia and gravity on the dispersion statistics we compare the results of simulations made with and without the buoyancy force included in the particle motion equation. A summary of the significant results is provided in §7 of the paper.The main objective of the paper is to enhance the understanding of the physics of particle dispersion in a simple turbulent flow by examining the simulation results described above and answering the questions of how and why the dispersion statistics of a solid particle differ from those of its corresponding fluid point and surrounding fluid and what influences inertia and gravity have on these statistics.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

The mean-square generalized delayed decision feedback sequence detector

2003 ◽  
Vol 14 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Maurizio Magarini ◽  
Arnaldo Spalvieri ◽  
Guido Tartara
Keyword(s):  
Decision Feedback ◽  
Mean Square ◽  
The Mean

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

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