Conditional sampling and other measurements in a plane turbulent wake

1973 ◽  
Vol 57 (3) ◽  
pp. 549-582 ◽  
Author(s):  
R. M. Thomas
Keyword(s):  
Probability Density ◽  
Random Noise ◽  
Longitudinal Velocity ◽  
Time Derivative ◽  
Longitudinal Component ◽  
Longitudinal Velocity Component ◽  
Mean Velocity ◽  
Instantaneous Position ◽  
Probability Densities ◽  
Intermittency Factor

A series of hot-wire measurements has been carried out in a plane wake to investigate the structure of the turbulence boundary and the relation of its instantaneous position to the behaviour in the core of the flow. The principal measured quantities are as follows: mean velocity profile; intermittency factor; burst rate; mean of the longitudinal component of velocity conditioned upon various specified interface positions; autocorrelation of the intermittency signal; probability densities a t the half-intermittency point for the time between bursts and the duration of a burst; probability density for the longitudinal velocity component and its time derivative at various points across the wake; probability density a t the half-intermittency point for the same quantities in the turbulent and irrotational zones separately. In addition, the profile of the second moment of the probability density for the time between bursts has been obtained indirectly and part of the theory of Phillips (1955) has been shown to be applicable in the intermittent region.The present measurements appear to indicate that the turbulence boundary in the wake resembles that in other plane flows more closely than has been supposed hitherto. The theory of normally distributed random noise was found to explain many of the observed statistical properties of the turbulence boundary.

On the criteria for reverse transition in a two-dimensional boundary layer flow

1969 ◽  
Vol 35 (2) ◽  
pp. 225-241 ◽  
Author(s):  
M. A. Badri Narayanan ◽  
V. Ramjee
Keyword(s):  
Longitudinal Velocity ◽  
Outer Region ◽  
Transition Process ◽  
Velocity Profiles ◽  
Wall Region ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Reverse Transition ◽  
Turbulence Decay

Experiments on reverse transition were conducted in two-dimensional accelerated incompressible turbulent boundary layers. Mean velocity profiles, longitudinal velocity fluctuations $\tilde{u}^{\prime}(=(\overline{u^{\prime 2}})^{\frac{1}{2}})$ and the wall-shearing stress (TW) were measured. The mean velocity profiles show that the wall region adjusts itself to laminar conditions earlier than the outer region. During the reverse transition process, increases in the shape parameter (H) are accompanied by a decrease in the skin friction coefficient (Cf). Profiles of turbulent intensity (u’2) exhibit near similarity in the turbulence decay region. The breakdown of the law of the wall is characterized by the parameter \[ \Delta_p (=\nu[dP/dx]/\rho U^{*3}) = - 0.02, \] where U* is the friction velocity. Downstream of this region the decay of $\tilde{u}^{\prime}$ fluctuations occurred when the momentum thickness Reynolds number (R) decreased roughly below 400.

Static pressure distribution in the free turbulent jet

1957 ◽  
Vol 3 (1) ◽  
pp. 1-16 ◽  
Author(s):  
David R. Miller ◽  
Edward W. Comings
Keyword(s):  
Static Pressure ◽  
Longitudinal Velocity ◽  
Fluid Motion ◽  
Mean Velocity ◽  
Free Jet ◽  
Static Pressure Distribution ◽  
Two Dimensional Flow ◽  
The Common ◽  
Jet Theory ◽  
Made In

Measurements of mean velocity, turbulent stress and static pressure were made in the mixing region of a jet of air issuing from a slot nozzle into still air. The velocity was low and the two-dimensional flow was effectively incompressible. The results are examined in terms of the unsimplified equations of fluid motion, and comparisons are drawn with the common assumptions and simplifications of free jet theory. Appreciable deviations from isobaric conditions exist and the deviations are closely related to the local turbulent stresses. Negative static pressures were encountered everywhere in the mixing field except in the potential wedge region immediately adjacent to the nozzle. Lateral profiles of mean longitudinal velocity conformed closely to an error curve at all stations further than 7 slot widths from the nozzle mouth. An asymptotic approach to complete self-preservation of the flow was observed.

The structure of internal intermittency in turbulent flows at large Reynolds number: experiments on scale similarity

1973 ◽  
Vol 59 (3) ◽  
pp. 537-559 ◽  
Author(s):  
C. W. Van Atta ◽  
T. T. Yeh
Keyword(s):  
Reynolds Number ◽  
Probability Density ◽  
Streamwise Velocity ◽  
Statistical Characteristics ◽  
Large Reynolds Number ◽  
Higher Moments ◽  
Scale Similarity ◽  
Probability Densities ◽  
Scale Ratio ◽  
Velocity Derivative

Some of the statistical characteristics of the breakdown coefficient, defined as the ratio of averages over different spatial regions of positive variables characterizing the fine structure and internal intermittency in high Reynolds number turbulence, have been investigated using experimental data for the streamwise velocity derivative ∂u/∂tmeasured in an atmospheric boundary layer. The assumptions and predictions of the hypothesis of scale similarity developed by Novikov and by Gurvich & Yaglom do not adequately describe or predict the statistical characteristics of the breakdown coefficientqr,lof the square of the streamwise velocity derivative. Systematic variations in the measured probability densities and consistent variations in the measured moments show that the assumption that the probability density of the breakdown coefficient is a function only of the scale ratio is not satisfied. The small positive correlation between adjoint values ofqr,land measurements of higher moments indicate that the assumption that the probability densities for adjoint values ofqr,lare statistically independent is also not satisfied. The moments ofqr,ldo not have the simple power-law character that is a consequence of scale similarity.As the scale ratiol/rchanges, the probability density ofqr,levolves from a sharply peaked, highly negatively skewed density for large values of the scale ratio to a very symmetrical distribution when the scale ratio is equal to two, and then to a highly positively skewed density as the scale ratio approaches one. There is a considerable effect of heterogeneity on the values of the higher moments, and a small but measurable effect on the mean value. The moments are roughly symmetrical functions of the displacement of the shorter segment from the centre of the larger one, with a minimum value when the shorter segment is centrally located within the larger one.

scholarly journals Computation of Power Loss in Likelihood Ratio Tests for Probability Densities Extended by Lehmann Alternatives

2018 ◽  
Author(s):  
Lucas Gallindo
Keyword(s):  
Probability Density ◽  
Likelihood Ratio ◽  
Power Loss ◽  
Likelihood Ratio Tests ◽  
Probability Densities ◽  
Lehmann Alternative

We compute the loss of power in likelihood ratio tests when we test the original parameter of a probability density extended by the first Lehmann alternative.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Quantum Process ◽  
Hidden Variable ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years, Man’ko and coauthors have successfully reconciled quantum and classic probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely, that mathematically, the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables, and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classic probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic hidden variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. Uncovering this variable confirms the possibility that it could be the stochastic archetype of quantum probability.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Classical Probability ◽  
Quantum Process ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years Man’ko and co-authors have successfully reconciled quantum and classical probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely that mathematically the interference term in the squared amplitude of superposed wavefunctions has the form of a variance of a sum of correlated random variables and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classical probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. This hidden generic variable appears to be such an archetype.

scholarly journals PROBABILITIES OF BREAKING WAVE CHARACTERISTICS

1970 ◽  
Vol 1 (12) ◽  
pp. 25 ◽  
Author(s):  
J. Ian Collins
Keyword(s):  
Shallow Water ◽  
Probability Density ◽  
Deep Water ◽  
Surf Zone ◽  
Probability Distributions ◽  
Rayleigh Distribution ◽  
Breaking Wave ◽  
Wave Characteristics ◽  
Probability Densities ◽  
Wave Heights

Utilizing the hydrodynamic relationships for shoaling and refraction of waves approaching a shoreline over parallel bottom contours a procedure is developed to transform an arbitrary probability density of wave characteristics in deep water into the corresponding breaking characteristics in shallow Water A number of probability distributions for breaking wave characteristics are derived m terms of assumed deep water probability densities of wave heights wave lengths and angles of approach Some probability densities for wave heights at specific locations in the surf zone are computed for a Rayleigh distribution in deep water The probability computations are used to derive the expectation of energy flux and its distribution.

scholarly journals Diameter structure of the stands of poplar clones

2010 ◽  
Vol 56 (No. 4) ◽  
pp. 165-170 ◽  
Author(s):  
R. Petráš ◽  
J. Mecko ◽  
V. Nociar
Keyword(s):  
Probability Density ◽  
Small Variation ◽  
Skewed Distribution ◽  
Likelihood Method ◽  
Weibull Function ◽  
Frequency Distributions ◽  
Poplar Clones ◽  
Mean Diameter ◽  
Probability Densities ◽  
Diameter Structure

The construction of a continuous mathematical model of frequency distributions of the diameters of trees of poplar clones Robusta and I-214 in dependence on tree diameter and mean diameter of stand is presented. Empirical material consists of diameter measurements on research plots from poplar regions in Slovakia. There were 90 plots for I-214 clone and 142 plots for Robusta clone. There were about 10–250 trees with mean diameter 2–70 cm on the research plots. The model was derived according to the three-parameter Weibull function. Its parameters were estimated by maximum likelihood method of the logarithm of the probability density function. Smoothed sample probability densities were processed in continuous mathematical models where the probability density of trees in stands is a function of their diameters and mean diameter of the stand. The method of regression smoothing of the parameters of Weibull function from sample sets in dependence on their mean diameter was used. In the whole range of mean diameters both clones have slightly left-skewed distribution with a relatively small variation range.

scholarly journals Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues

2018 ◽  
Vol 50 (2) ◽  
pp. 373-395 ◽  
Author(s):  
Dmitri Finkelshtein ◽  
Pasha Tkachov
Keyword(s):  
Fundamental Solution ◽  
Heat Equation ◽  
Probability Density ◽  
Real Line ◽  
The Real ◽  
Probability Densities ◽  
Tail Asymptotic

Abstract We study the tail asymptotic of subexponential probability densities on the real line. Namely, we show that the n-fold convolution of a subexponential probability density on the real line is asymptotically equivalent to this density multiplied by n. We prove Kesten's bound, which gives a uniform in n estimate of the n-fold convolution by the tail of the density. We also introduce a class of regular subexponential functions and use it to find an analogue of Kesten's bound for functions on ℝd. The results are applied to the study of the fundamental solution to a nonlocal heat equation.

Probability Density Functions of Vorticities in Turbulent Channels with Effects of Blowing and Suction

2016 ◽  
Vol 17 (2) ◽  
pp. 127-135
Author(s):  
Can Liu ◽  
Xi Chen
Keyword(s):  
New York ◽  
Probability Density ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Generalized Hyperbolic Distribution ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Channel Flows ◽  
Probability Density Function Pdf

AbstractThis paper presents direct numerical simulation (DNS) result of the Navier–Stokes equations for turbulent channel flows with blowing and suction effects. The friction Reynolds number is ${\rm{R}}{{\rm{e}}_\tau} = 394$ and a range of blowing and suction conditions is covered with different perturbation strengths, i. e. $A = 0.05, $ 0.1, 0.2. While the mean velocity profile has been severely altered, the probability density function (PDF) for (spanwise) vorticity – depending on wall distance $({y^ +})$ and blowing/suction strength (A) – satisfies the generalized hyperbolic distribution (GHD) of Birnir [The Kolmogorov-Obukhov statistical theory of turbulence, J. Nonlinear Sci. (2013a), doi: 10.1007/s00332-012-9164–z; The Kolmogorov-Obukhov theory of turbulence, Springer, New York, 2013b] in the bulk of the flow. The latter leads to accurate descriptions of all PDFs (at ${y^ +} = 40, $ 200, 390 and $A = 0.05, $ 0.2, for instance) with only four parameters. The result indicates that GHD is a general tool to quantify PDF for turbulent flows under various wall surface conditions.

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