A Stochastic Model for Small-scale Turbulence PDF Download

Author: Edward Carl Hylin
Publisher:
ISBN:
Category :
Languages : en
Pages : 290

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Author: Victor Yu Korolev
Publisher: Walter de Gruyter
ISBN: 9789067644495
Category : Plasma turbulence
Languages : en
Pages : 424

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The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Author: Grigory Sarnitsky
Publisher:
ISBN:
Category : Fluid mechanics
Languages : en
Pages : 174

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Lagrangian stochastic turbulence models offer a uniquely rich and intuitive framework for dealing with turbulence. By directly describing turbulent transport they capture the essential features of turbulence. Stochastic turbulence models are also in an immediate correspondence to the traditional modeling approaches and can be used for deriving realizable RANS and LES closures. At the same time stochastic Lagrangian models are closely related to the methods of modern nonequilibrium statistical mechanics and can draw inspiration from them. Yet the aforementioned virtues of the stochastic Lagrangian framework are underutilized, with no turbulent modeling approaches that would fully use the advantages of the statistical Lagrangian description. We attribute this to the relative difficulty of measuring the parameters (transport coefficients) of stochastic models from experiments and direct numerical simulations (DNS). For example, even for the most promising class of stochastic models, the generalized Langevin model (GLM), there are no methods to measure its parameters, the drift and diffusion tensors, that would work in general nonhomogeneous and nonstationary flows. It is challenging to develop any physical theory without an access to solid experimental data, even more so in the infamously unyieldly case of turbulence. In this work we develop inference methods that can be used to measure the drift and diffusion tensors of the GLM in general flows. These new inference techniques are extensively tested against DNS data for channel flow. Of particular interest are the Green--Kubo methods that originate in nonequilibrium statistical physics. With the newfound ability to measure the parameters of the GLM we investigated the validity of the GLM itself. We established that the GLM is a promising form for turbulence closure that is generally valid throughout the whole channel flow up to the very wall. We also argue how the inference methods based on the Lagrangian acceleration statistics, like the Green--Kubo formulas, can be used to find theoretical closures for the GLM. We show how the models for the drift and diffusion are linked to the small scale structure of turbulence. In the case of homogeneous isotropic turbulence we were able to close the GLM in terms of the dynamics of the velocity gradient tensor, a quantity currently subject to intense research.

Author: Oleg Mikha?lovich Belot?serkovski?
Publisher: World Scientific
ISBN: 9812833013
Category : Science
Languages : en
Pages : 489

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The book provides an original approach in the research of structural analysis of free developed shear compressible turbulence at high Reynolds number on the base of direct numerical simulation (DNS) and instability evolution for ideal medium (integral conservation laws) with approximate mechanism of dissipation (FLUX dissipative monotone ?upwind? difference schemes) and does not use any explicit sub-grid approximation and semi-empirical models of turbulence. Convective mixing is considered as a principal part of conservation law.Appropriate hydrodynamic instabilities (free developed shear turbulence) are investigated from unique point of view. It is based on the concept of large ordered structures with stochastic core of small scale developed turbulence (?turbulent spot?). Decay of ?turbulent spot? are simulated by Monte Carlo method. Proposed approach is based on two hypotheses: statistical independence of the characteristic of large ordered structures (LOS) and small-scale turbulence (ST) ?and? weak influence of molecular viscosity (or more generally, dissipative mechanism) on properties of large ordered structures.Two versions of instabilities, due to Rayleigh-Taylor and Richtmyer-Meshkov are studied detail by the three-dimensional calculations, extended to the large temporal intervals, up to turbulent stage and investigation turbulent mixing zone (TMZ).The book covers both the fundamental and practical aspects of turbulence and instability and summarizes the result of numerical experiments conducted over 30 years period with direct participation of the author.In the book are cited the opinions of the leading scientists in this area of research: Acad. A S Monin (Russia), Prof. Y Nakamura (Japan, Nagoya University) and Prof. F Harlow (USA, Los-Alamos).

Author: Stefan Heinz
Publisher: Springer Science & Business Media
ISBN: 3662100223
Category : Science
Languages : en
Pages : 232

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The simulation of technological and environmental flows is very important for many industrial developments. A major challenge related to their modeling is to involve the characteristic turbulence that appears in most of these flows. The traditional way to tackle this question is to use deterministic equations where the effects of turbulence are directly parametrized, i. e. , assumed as functions of the variables considered. However, this approach often becomes problematic, in particular if reacting flows have to be simulated. In many cases, it turns out that appropriate approximations for the closure of deterministic equations are simply unavailable. The alternative to the traditional way of modeling turbulence is to construct stochastic models which explain the random nature of turbulence. The application of such models is very attractive: one can overcome the closure problems that are inherent to deterministic methods on the basis of relatively simple and physically consistent models. Thus, from a general point of view, the use of stochastic methods for turbulence simulations seems to be the optimal way to solve most of the problems related to industrial flow simulations. However, it turns out that this is not as simple as it looks at first glance. The first question concerns the numerical solution of stochastic equations for flows of environmental and technological interest. To calculate industrial flows, 3 one often has to consider a number of grid cells that is of the order of 100 .

Author: John L. Lumley
Publisher: Courier Corporation
ISBN: 0486462706
Category : Science
Languages : en
Pages : 210

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This accessible treatment offers the mathematical tools for describing and solving problems related to stochastic vector fields. Advanced undergraduates and graduate students will find its use of generalized functions a relatively simple method of resolving mathematical questions. It will prove a valuable reference for applied mathematicians and professionals in the fields of aerospace, chemical, civil, and nuclear engineering. The author, Professor Emeritus of Engineering at Cornell University, starts with a survey of probability distributions and densities and proceeds to examinations of moments, characteristic functions, and the Gaussian distribution; random functions; and random processes in more dimensions. Extensive appendixes—which include information on Fourier transforms, tensors, generalized functions, and invariant theory—contribute toward making this volume mathematically self-contained.

Author: National Research Council
Publisher: National Academies Press
ISBN: 0309046483
Category : Technology & Engineering
Languages : en
Pages : 145

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Computational mechanics is a scientific discipline that marries physics, computers, and mathematics to emulate natural physical phenomena. It is a technology that allows scientists to study and predict the performance of various productsâ€"important for research and development in the industrialized world. This book describes current trends and future research directions in computational mechanics in areas where gaps exist in current knowledge and where major advances are crucial to continued technological developments in the United States.

Author: Stanislav A. Molchanov
Publisher: Springer Science & Business Media
ISBN: 1461385008
Category : Science
Languages : en
Pages : 496

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This IMA Volume in Mathematics and its Applications STOCHASTIC MODELS IN GEOSYSTEMS is based on the proceedings of a workshop with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Stanislav A. Molchanov and Wojbor A. Woyczynski for their hard work in organizing this meeting and in edit ing the proceedings. We also take this opportunity to thank the National Science Foundation, the Office of N aval Research, the Army Research Of fice, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE A workshop on Stochastic Models in Geosystems was held during the week of May 16, 1994 at the Institute for Mathematics and Its Applica tions at the University of Minnesota. It was part of the Special Year on Emerging Applications of Prob ability program put together by an organiz ing committee chaired by J. Michael Steele. The invited speakers represented a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmo spheric physics, fluid mechanics, seismology, and oceanography. The com mon underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.

Author: Franco Flandoli
Publisher: Springer Nature
ISBN: 9819903858
Category : Mathematics
Languages : en
Pages : 206

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This book is devoted to stochastic Navier–Stokes equations and more generally to stochasticity in fluid mechanics. The two opening chapters describe basic material about the existence and uniqueness of solutions: first in the case of additive noise treated pathwise and then in the case of state-dependent noise. The main mathematical techniques of these two chapters are known and given in detail for using the book as a reference for advanced courses. By contrast, the third and fourth chapters describe new material that has been developed in very recent years or in works now in preparation. The new material deals with transport-type noise, its origin, and its consequences on dissipation and well-posedness properties. Finally, the last chapter is devoted to the physical intuition behind the stochastic modeling presented in the book, giving great attention to the question of the origin of noise in connection with small-scale turbulence, its mathematical form, and its consequences on large-scale properties of a fluid.

Author: J. M. McDonough
Publisher:
ISBN:
Category : Mathematical models
Languages : en
Pages : 40

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