Stochastic estimation of organized turbulent structure: homogeneous shear flow

1988 ◽  
Vol 190 ◽  
pp. 531-559 ◽  
Author(s):  
Ronald J. Adrian ◽  
Parviz Moin
Keyword(s):  
Probability Density Function ◽  
Shear Flow ◽  
Probability Density ◽  
Density Function ◽  
Deformation Tensor ◽  
Stochastic Estimation ◽  
Correlation Tensor ◽  
Homogeneous Shear ◽  
Wide Range ◽  
Homogeneous Shear Flow

The large-scale organized structures of turbulent flow can be characterized quantitatively by a conditional eddy, given the local kinematic state of the flow as specified by the conditional average of u(x’, t) given the velocity and the deformation tensor at a point x: 〈u(x’, t)|u(x, t), d(x, t)〉. By means of linear mean-square stochastic estimation, 〈u’|u, d〉 is approximated in terms of the two-point spatial correlation tensor, and the conditional eddy is evaluated for arbitrary values of u(x, t) and d(x, t), permitting study of the turbulent field for a wide range of local kinematic states. The linear estimate is applied to homogeneous turbulent shear flow data generated by direct numerical simulation. The joint velocity-deformation probability density function is used to obtain conditions corresponding to those events that contribute most to the Reynolds shear stress. The primary contributions to the second-quadrant and fourth-quadrant Reynolds-stress events in homogeneous shear flow come from flow induced through the ‘legs’ and close to the ‘heads’ of upright and inverted ‘hairpins’, respectively.The equation governing the joint probability density function of fu,d (u, d) is derived. It is shown that this equation contains 〈u’/u, d〉 and that the equations for second-order closure can be derived from it. Closure requires approximation of 〈u’/u, d〉.

scholarly journals Mean velocity and suspended sediment concentration profile model of turbulent shear flow with probability density function

2017 ◽  
Vol 21 (3) ◽  
pp. 129-134
Author(s):  
Guanglin Wu ◽  
Liangsheng Zhu ◽  
Fangcheng Li
Keyword(s):  
Probability Density Function ◽  
Shear Flow ◽  
Probability Density ◽  
Density Function ◽  
Suspended Sediment Concentration ◽  
Sediment Concentration ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Velocity ◽  
Profile Model

This work purposes a general mean velocity and a suspended sediment concentration (SSC) model to express distribution at every point of the cross section of turbulent shear flow by using a probability density function method. The probability density function method was used to describe the velocity and concentration profiles interacted on directly by fluid particles in the turbulent shear flow to solve turbulent flow and avoid different dynamical mechanics. The velocity profile model was obtained by solving for the profile integral with the product of the laminar velocity and probability density, through adopting an exponential probability density function to express probability distribution of velocity alteration of a fluid particle in turbulent shear flow. An SSC profile model was also created following a method similar to the above and based on the Schmidt diffusion equation. Different velocity and SSC profiles were created while changing the parameters of the models. The models were verified by comparing the calculated results with traditional models. It was shown that the probability density function model was superior to log-law in predicting stream-wise velocity profiles in coastal currents, and the probability density function SSC profile model was superior to the Rouse equation for predicting average SSC profiles in rivers and estuaries. Outlooks for precision investigation are stated at the end of this article.

scholarly journals A numerical study of entropy and residual entropy estimators based on smooth density estimators for non-negative random variables

2021 ◽  
Vol 54 (2) ◽  
pp. 99-121
Author(s):  
Yogendra P. Chaubey ◽  
Nhat Linh Vu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Numerical Study ◽  
Random Variables ◽  
Random Variable ◽  
Residual Entropy ◽  
Density Estimator ◽  
Wide Range ◽  
Smooth Density

In this paper, we are interested in estimating the entropy of a non-negative random variable. Since the underlying probability density function is unknown, we propose the use of the Poisson smoothed histogram density estimator to estimate the entropy. To study the per- formance of our estimator, we run simulations on a wide range of densities and compare our entropy estimators with the existing estimators based on different approaches such as spacing estimators. Furthermore, we extend our study to residual entropy estimators which is the entropy of a random variable given that it has been survived up to time $t$.

scholarly journals Mechanical Integrity of 3D Rough Surfaces during Contact

Coatings ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 15
Author(s):  
Maxence Bigerelle ◽  
Franck Plouraboue ◽  
Frederic Robache ◽  
Abdeljalil Jourani ◽  
Agnes Fabre
Keyword(s):  
Plastic Deformation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Contact Pressure ◽  
Rough Surfaces ◽  
Morphological Structure ◽  
Random Variable ◽  
Wide Range ◽  
Weierstrass Functions

Rough surfaces are in contact locally by the peaks of roughness. At this local scale, the pressure of contact can be sharply superior to the macroscopic pressure. If the roughness is assumed to be a random morphology, a well-established observation in many practical cases, mechanical indicators built from the contact zone are then also random variables. Consequently, the probability density function (PDF) of any mechanical random variable obviously depends upon the morphological structure of the surface. The contact pressure PDF, or the probability of damage of this surface can be determined for example when plastic deformation occurs. In this study, the contact pressure PDF is modeled using a particular probability density function, the generalized Lambda distributions (GLD). The GLD are generic and polymorphic. They approach a large number of known distributions (Weibull, Normal, and Lognormal). The later were successfully used to model damage in materials. A semi-analytical model of elastic contact which takes into account the morphology of real surfaces is used to compute the contact pressure. In a first step, surfaces are simulated by Weierstrass functions which have been previously used to model a wide range of surfaces met in tribology. The Lambda distributions adequacy is qualified to model contact pressure. Using these functions, a statistical analysis allows us to extract the probability density of the maximal pressure. It turns out that this density can be described by a GLD. It is then possible to determine the probability that the contact pressure generates plastic deformation.

scholarly journals A note on an extreme left skewed unit distribution: Theory, modelling and data fitting

2021 ◽  
Vol 2 (1) ◽  
pp. 1-23
Author(s):  
Christophe Chesneau
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Power Distribution ◽  
Stochastic Order ◽  
Cumulative Distribution ◽  
Closed Form Expression ◽  
Survival Times ◽  
Data Set ◽  
Wide Range

Abstract In probability and statistics, unit distributions are used to model proportions, rates, and percentages, among other things. This paper is about a new one-parameter unit distribution, whose probability density function is defined by an original ratio of power and logarithmic functions. This function has a wide range of J shapes, some of which are more angular than others. In this sense, the proposed distribution can be thought of as an “extremely left skewed alternative” to the traditional power distribution. We discuss its main characteristics, including other features of the probability density function, some stochastic order results, the closed-form expression of the cumulative distribution function involving special integral functions, the quantile and hazard rate functions, simple expressions for the ordinary moments, skewness, kurtosis, moments generating function, incomplete moments, logarithmic moments and logarithmically weighted moments. Subsequently, a simple example of an application is given by the use of simulated data, with fair comparison to the power model supported by numerical and graphical illustrations. A new modelling strategy beyond the unit domain is also proposed and developed, with an application to a survival times data set.

scholarly journals On the theory of advective effects on biological dynamics in the sea. III. The role of turbulence in biological–physical interactions

2007 ◽  
Vol 464 (2091) ◽  
pp. 555-572 ◽  
Author(s):  
Louis Goodman ◽  
Allan R Robinson
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Euphotic Zone ◽  
Biological Interaction ◽  
State Variables ◽  
Turbulent Layer ◽  
Wide Range ◽  
The Mean ◽  
Interaction Term

A nonlinear model for biological and physical dynamical interactions in a laminar upwelling flow field in parts I and II of this study is extended to turbulent flow. In the previous studies, a prescription for obtaining quadrature solutions to the fundamental biodynamical equations was developed. In this study, we use a probability density function approach on these solutions to obtain statistics of the biodynamical state variables and their self-interaction for the case of turbulent advection. To illustrate the theory, a simple nutrient ( N ), phytoplankton ( P ) problem is considered, that of upwelling into a surface turbulent layer. Biological interaction is modelled as bilinear, representing the uptake of N by P in a uniform light euphotic zone. A random walk model is used to obtain the appropriate probability density function for the advective turbulent field. The mean quantities, , , as well as the biological interaction term are calculated. The term has two contributions, , and the turbulence-induced interaction term, . It is shown that the often neglected turbulence-induced coupling term is of the order and opposite in sign. This results in, over a wide range of Peclet numbers, the mean interaction term being significantly smaller than either of its constituent terms, and .

Experimental Investigation for Flow Regime Identification Using Probability Density Function of Void Fraction Signals

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Min-Song Lin ◽  
Shao-Wen Chen ◽  
Feng-Jiun Kuo ◽  
Yen-Shih Cheng ◽  
Pei-Syuan Ruan ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Flow Regime ◽  
Void Fraction ◽  
Flow Conditions ◽  
Two Phase ◽  
Specific Flow ◽  
Wide Range ◽  
Flow Regime Identification

Abstract In this study, upward air–water two-phase flow tests were carried out in a 3 cm diameter pipe under atmospheric pressure, and over 3000 data points were collected from a wide range of superficial gas and liquid velocities (⟨jg⟩ ≈ 0.02–30 m/s and ⟨jf⟩ ≈ 0.02–2 m/s) for the investigation of flow regime identification. The probability density function (PDF) of transient void fraction signals and its full-width at half-maximum (FWHM) were obtained and used for analysis and data classification. Considering the features of PDF profiles, the flow conditions can be classified into four regions, which show a fair agreement with the existing flow regime maps in general trends. Furthermore, by examining the FWHM distributions, two more regions with high-FWHM (HF) values were identified as the transitions of higher-flow bubbly-to-slug and slug-to-churn flows as well as most portion of churn flow, and a valley region next to the HF regions can express the transition of churn-to-annular flows. Overall, six groups of flow conditions can be classified based on the present methodology, and each group can be corresponding to specific flow regimes or transition regions. This study can provide a simple and efficient way for flow regime identification.

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