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.

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.

Evolution of localized disturbances in the elliptic instability

2014 ◽  
Vol 755 ◽  
pp. 603-627 ◽  
Author(s):  
Yuji Hattori ◽  
Mohd Syafiq bin Marzuki
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Energy Spectrum ◽  
Short Wavelength ◽  
Isotropic Turbulence ◽  
Inertial Range ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Elliptical Flow ◽  
The Mean

AbstractThe time evolution of localized disturbances in an elliptical flow confined in an elliptical cylinder is studied by direct numerical simulation (DNS). The base flow is subject to the elliptic instability. The unstable growth of localized disturbances predicted by the short-wavelength stability analysis is captured. The time evolution can be divided into four stages: linear, weakly nonlinear, nonlinear and turbulent. In the linear stage a single wavepacket grows exponentially without changing its shape. The exponential growth is accompanied by large oscillations which have time period half that of the fluid particles in the elliptical flow. An averaged wavepacket, which is a train of bending waves that has a finite spatial extent, also grows exponentially, while the oscillations of the growth rate are small. The averaged growth rate increases as the kinematic viscosity decreases; the inviscid limit is close to the value predicted by the short-wavelength stability analysis. In the weakly nonlinear stage the energy stops growing. The vortical structure of the initial disturbances is deformed into wavy patterns. The energy spectrum loses the peak at the initial wavenumber, developing a broad spectrum, and the flow goes into the next stage. In the nonlinear stage weak vorticity is scattered in the whole domain although strong vorticity is still localized. The probability density functions (p.d.f.) of a velocity component and its longitudinal derivative are similar to those of isotropic turbulence; however, the energy spectrum does not have an inertial range showing the Kolmogorov spectrum. Finally in the turbulent stage fine-scale structures appear in the vorticity field. The p.d.f. of the longitudinal derivative of velocity shows the strong intermittency known for isotropic turbulence. The energy spectrum attains an inertial range showing the Kolmogorov spectrum. The turbulence is not symmetric because of rotation and strain; the component of vorticity in the compressing direction is smaller than the other two components. The energy of the mean flow as well as the total energy decreases. The ratio of the lost energy to the initial energy of the mean flow is large in the core region.

scholarly journals Coding of Time-Varying Signals in Spike Trains of Integrate-and-Fire Neurons with Random Threshold

1996 ◽  
Vol 8 (1) ◽  
pp. 44-66 ◽  
Author(s):  
Fabrizio Gabbiani ◽  
Christof Koch
Keyword(s):  
Experimental Data ◽  
Information Transmission ◽  
Firing Rate ◽  
Mean Square Error ◽  
Model Neuron ◽  
Correlation Technique ◽  
Time Varying ◽  
Mean Square ◽  
Closed Expression ◽  
The Mean

Recently, methods of statistical estimation theory have been applied by Bialek and collaborators (1991) to reconstruct time-varying velocity signals and to investigate the processing of visual information by a directionally selective motion detector in the fly's visual system, the H1 cell. We summarize here our theoretical results obtained by studying these reconstructions starting from a simple model of H1 based on experimental data. Under additional technical assumptions, we derive a closed expression for the Fourier transform of the optimal reconstruction filter in terms of the statistics of the stimulus and the characteristics of the model neuron, such as its firing rate. It is shown that linear reconstruction filters will change in a nontrivial way if the statistics of the signal or the mean firing rate of the cell changes. Analytical expressions are then derived for the mean square error in the reconstructions and the lower bound on the rate of information transmission that was estimated experimentally by Bialek et al. (1991). For plausible values of the parameters, the model is in qualitative agreement with experimental data. We show that the rate of information transmission and mean square error represent different measures of the reconstructions: in particular, satisfactory reconstructions in terms of the mean square error can be achieved only using stimuli that are matched to the properties of the recorded cell. Finally, it is shown that at least for the class of models presented here, reconstruction methods can be understood as a generalization of the more familiar reverse-correlation technique.

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.

Liouvillian theory of magnetic fluctuations

1995 ◽  
Vol 54 (2) ◽  
pp. 185-199 ◽  
Author(s):  
E. Vanden Eijnden ◽  
R. Balescu
Keyword(s):  
Liouville Equation ◽  
Equations Of Motion ◽  
Direct Interaction ◽  
Mean Square ◽  
Magnetic Fluctuations ◽  
System A ◽  
The Status ◽  
Direct Interaction Approximation ◽  
The Mean ◽  
Field Lines

The study of the diffusion of magnetic field lines is based on a stochastic model with a Hamiltonian structure. A Liouville equation can then be associated with Hamilton's equations representing the magnetic line. This allows a statistical description of all observable quantities. In particular, the mean-square displacements (MSD) of a field line and the mean-square relative distance (MSRD) of two lines are considered. Equations for these quantities are obtained by applying the direct-interaction approximation (DIA) to the stochastic Liouville equation. The running diffusion coefficient is derived from the MSD equation. The status of the temporal and spatial Markovian approximations in the DIA is discussed. The MSRD's evolution establishes the existence of a clumping effect between two lines, which eventually leads to gyrotropization of the system. A clump life length is defined. In both cases the equations of motion are shown to be identical to the equations obtained within the Langevin treatment of magnetic fluctuations. This shows the equivalence between the DIA and the Corrsin approximation performed in the Langevin approach.

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
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