scholarly journals Turbulence through the Spyglass of Bilocal Kinetics

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 539 ◽  
Author(s):  
Gregor Chliamovitch ◽  
Yann Thorimbert
Keyword(s):  
Turbulent Flows ◽  
Kinetic Scheme ◽  
Navier Stokes ◽  
Pressure Tensor ◽  
Kinetic Description ◽  
Balance Equations ◽  
Coupling Term ◽  
Navier Stokes Equation ◽  
Local Character ◽  
Non Local

In two recent papers we introduced a generalization of Boltzmann’s assumption of molecular chaos based on a criterion of maximum entropy, which allowed setting up a bilocal version of Boltzmann’s kinetic equation. The present paper aims to investigate how the essentially non-local character of turbulent flows can be addressed through this bilocal kinetic description, instead of the more standard approach through the local Euler/Navier–Stokes equation. Balance equations appropriate to this kinetic scheme are derived and closed so as to provide bilocal hydrodynamical equations at the non-viscous order. These equations essentially consist of two copies of the usual local equations, but coupled through a bilocal pressure tensor. Interestingly, our formalism automatically produces a closed transport equation for this coupling term.

scholarly journals GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO

2011 ◽  
Vol 21 (03) ◽  
pp. 421-457 ◽  
Author(s):  
RAPHAËL DANCHIN ◽  
MARIUS PAICU
Keyword(s):  
Global Existence ◽  
Turbulent Flows ◽  
Vertical Direction ◽  
Boussinesq System ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Incompressible Euler Equation ◽  
Navier Stokes Equation ◽  
Transport Diffusion ◽  
Anisotropic Viscosity

Models with a vanishing anisotropic viscosity in the vertical direction are of relevance for the study of turbulent flows in geophysics. This motivates us to study the two-dimensional Boussinesq system with horizontal viscosity in only one equation. In this paper, we focus on the global existence issue for possibly large initial data. We first examine the case where the Navier–Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transport–diffusion equation with diffusion in the horizontal direction only. For both systems, we construct global weak solutions à la Leray and strong unique solutions for more regular data. Our results rest on the fact that the diffusion acts perpendicularly to the buoyancy force.

ORIENTATION-INDUCED PATTERN FORMATION: SWARM DYNAMICS IN A LATTICE-GAS AUTOMATON MODEL

1996 ◽  
Vol 06 (09) ◽  
pp. 1735-1752 ◽  
Author(s):  
ANDREAS DEUTSCH
Keyword(s):  
Pattern Formation ◽  
Lattice Gas ◽  
Collective Motion ◽  
Particle Density ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Interaction Operator ◽  
Swarm Dynamics ◽  
Lattice Gas Models ◽  
Non Local

Swarming patterns might arise not just at organismic levels (bird and fishes exhibiting particularly striking examples) but even at cellular and intracellular scales whenever “collective motion” of biological or chemical entities is involved. Examples are the swarming of myxobacteria and ants, aggregation and slug pattern formation of the slime mold Dictyostelium discoideum, or intracellular network dynamics of actin filaments. Here a stochastic process — discrete in space and time — is developed, the “swarm lattice-gas automaton”. For some lattice-gas models (in physics and chemistry) it was demonstrated that the limit behavior resembles known master equations by means of expectation values of suitably chosen microscopic variables. In particular, for the Navier–Stokes equation the derivation of a continuous macroscopic description from discrete microdynamic equations was shown. The “swarm lattice-gas automaton” possesses a non-local integral-like interaction operator. Particles (cells, organisms) are assigned some orientation (and fixed absolute velocity) which might change by means of interaction with other members of the swarm within a given “region of perception”. The corresponding microdynamical equation is given and results of numerical experiments are shown. Simulations exhibit a variety of aggregation patterns which are distinguished by means of microscopic and macroscopic variables. The influence of a sensitivity parameter and particle density on pattern formation is examined systematically.

Determining modes and fractal dimension of turbulent flows

1985 ◽  
Vol 150 ◽  
pp. 427-440 ◽  
Author(s):  
P. Constantin ◽  
C. Foias ◽  
O. P. Manley ◽  
R. Temam
Keyword(s):  
Fractal Dimension ◽  
Turbulent Flows ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Approximate Solutions ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Rigorous Results ◽  
Navier Stokes Equations

Research on the abstract properties of the Navier–Stokes equations in three dimensions has cast a new light on the time-asymptotic approximate solutions of those equations. Here heuristic arguments, based on the rigorous results of that research, are used to show the intimate relationship between the sufficient number of degrees of freedom describing fluid flow and the bound on the fractal dimension of the Navier–Stokes attractor. In particular it is demonstrated how the conventional estimate of the number of degrees of freedom, based on purely physical and dimensional arguments, can be obtained from the properties of the Navier–Stokes equation. Also the Reynolds-number dependence of the sufficient number of degrees of freedom and of the dimension of the attractor in function space is elucidated.

scholarly journals Unstable periodic motion in turbulent flows

2006 ◽  
Vol 13 (5) ◽  
pp. 499-507 ◽  
Author(s):  
G. Kawahara ◽  
S. Kida ◽  
L. van Veen
Keyword(s):  
Phase Space ◽  
Periodic Orbit ◽  
Turbulent Flows ◽  
Periodic Motion ◽  
Isotropic Turbulence ◽  
Space Structure ◽  
Navier Stokes ◽  
Low Velocity ◽  
Navier Stokes Equation ◽  
Phase Space Structure

Abstract. Recently found unstable time-periodic solutions to the incompressible Navier-Stokes equation are reviewed to discuss their relevance to plane Couette turbulence and isotropic turbulence. It is shown that the periodic motion embedded in the Couette turbulence exhibits a regeneration cycle of near-wall coherent structures, which consists of formation and breakdown of streamwise vortices and low-velocity streaks. In phase space a turbulent state wanders around the corresponding periodic orbit for most of the time, so that the root-mean-squares of velocity fluctuations of the Couette turbulence agree very well with the temporal averages of those along the periodic orbit. The Kolmogorov universal-range energy spectrum is observed for the periodic motion embedded in high-symmetric turbulence at the Taylor-microscale Reynolds number Reλ=67. A laminarization strategy inspired by investigation of the phase-space structure in the vicinity of the unstable periodic orbit is presented for the Couette turbulence.

scholarly journals Numerical Solution of Three-Dimensional Turbulent Flows for Modern Gas Turbine Components

1987 ◽  
Author(s):  
C. Hah ◽  
J. H. Leylek
Keyword(s):  
Gas Turbine ◽  
Turbulent Flows ◽  
Gas Turbines ◽  
Solid Wall ◽  
Control Volume ◽  
Three Dimensional ◽  
Computer Code ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Aerodynamic Loss

This paper describes the development and assessment of a computer code for three-dimensional compressible turbulent flows in modern gas turbine components. The code is based on a high-order upwinding relaxation scheme with fully conservative control volume. A three-dimensional Reynolds-averaged Navier-Stokes equation is solved with a two-equation turbulence model that has a low Reynolds number modification near the solid wall. The code is applied to the study of compressible flow inside turbine blade rows of modern gas turbines. Measured data and calculations are carefully compared for the production and convection of aerodynamic loss to evaluate the code as an advanced design technique. The predicted aerodynamic performance is further compared with predictions based on current design techniques.

Overview of Particle Transport and Deposition in Environmental and Industrial Applications

2012 ◽  
Author(s):  
Goodarz Ahmadi
Keyword(s):  
Computational Modeling ◽  
Turbulent Flows ◽  
Particle Transport ◽  
Particle Deposition ◽  
Industrial Applications ◽  
Navier Stokes ◽  
Upper Airways ◽  
Navier Stokes Equation ◽  
Wall Flow ◽  
Alternative Scenarios

Overview of particle transport and deposition in flows in environmental and industrial applications was presented. Aerosol transport including particle deposition, removal and re-entrainment in turbulent flows were discussed. The numerical simulation airflow through the Reynolds averaged Navier-Stokes equation was described. The approximate stochastic models for simulation of instantaneous flow were discussed. The Lagrangian particle equation of motion was presented. It was shown that the particle deposition and removal processes in turbulent flows are strongly affected by the near wall flow structures. Wind tunnel studies of particle transport and deposition were also discussed. Examples of computational modeling of gas-solid flows in indoor and out door air were described. It was shown that computational modeling was an efficient tool for studying alternative scenarios. A simulation procedure for pollutant transport through human upper airways was discussed and sample results were presented.

A Navier-Stokes Analysis of Three-Dimensional Turbulent Flows Inside Turbine Blade Rows at Design and Off-Design Conditions

1984 ◽  
Vol 106 (2) ◽  
pp. 421-429 ◽  
Author(s):  
C. Hah
Keyword(s):  
Turbulent Flows ◽  
Turbine Blade ◽  
Numerical Scheme ◽  
Control Volume ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equation

A numerical scheme based on the compressible Navier-Stokes equation has been developed for three-dimensional turbulent flows inside turbine blade rows. The numerical scheme is based on a fully conservative control volume formulation and solves the governing equations in fully elliptic form. Higher order discretizations are used for the convection term to reduce the numerical diffusion. An algebraic Reynolds stress model modified for the effects of the streamline curvature and the rotation is used for the closure of the governing equations. General coordinate transformations are used to represent the complex blade geometry accurately, and a grid generation technique based on elliptic partial differential equations is employed. Comparisons with the experimental data show that various complex three-dimensional viscous flow phenomena (three-dimensional flow separation near the leading edge, formation of the horseshoe vortex, etc.) are well predicted with the present method.

Two-Dimensional "Poor Man's Navier-Stokes Equation" Model of Turbulent Flows

AIAA Journal ◽  
2003 ◽  
Vol 41 (9) ◽  
pp. 1690-1696 ◽  
Author(s):  
Tianliang Yang ◽  
J. M. McDonough ◽  
J. D. Jacob
Keyword(s):  
Turbulent Flows ◽  
Stokes Equation ◽  
Equation Model ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation

NEW DEVELOPMENTS AND CLASSICAL THEORIES OF TURBULENCE

1996 ◽  
Vol 10 (18n19) ◽  
pp. 2325-2392 ◽  
Author(s):  
E. LEVICH
Keyword(s):  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Physical Space ◽  
Phase Coherence ◽  
Navier Stokes ◽  
Homogeneous Isotropic Turbulence ◽  
Navier Stokes Equation ◽  
Inviscid Flows ◽  
Turbulence Control ◽  
Developed Turbulence

In this paper we review certain classical and modern concepts pertinent for the theory of developed turbulent flows. We begin by introducing basic facts concerning the properties of the Navier-Stokes equation with the emphasis on invariant properties of the vorticity field. Then we discuss classical semiempirical approaches to developed turbulence which for a long time have constituted a basis for engineering solutions of turbulent flows problems. We do it for two examples, homogeneous isotropic turbulence and flat channel turbulent flow. Next we discuss the insufficiency of classical semi-empirical approaches. We show that intermittency is an intrinsic feature of all turbulent flows and hence it should be accounted for in any reasonable theoretical approach to turbulence. We argue that intermittency in physical space is in one to one correspondence with certain phase coherence of turbulence in an appropriate dual space, e.g. Fourier space for the case of homogeneous isotropic turbulence. In the same time the phase coherence has its origin in invariant topological properties of vortex lines in inviscid flows, modified by the presence of small molecular viscosity. This viewpoint is expounded again using the examples of homogeneous isotropic turbulence and channel flow turbulence. Finally we briefly discuss the significance of phase coherence and intermittency in turbulence for the fundamental engineering challenge of turbulence control.

scholarly journals Turbulence in the View of Wavelets: Abdominal Aortic Aneurysm’s ECG Signal Analysis as an Illustrative Example

2018 ◽  
Vol 11 (2) ◽  
pp. 907-915
Author(s):  
Ruchi Agarwal ◽  
C.S. Salimath ◽  
Khursheed Alam
Keyword(s):  
Wavelet Analysis ◽  
Turbulent Flows ◽  
Human Body ◽  
Stokes Equations ◽  
Body Part ◽  
Navier Stokes ◽  
Ecg Signal ◽  
Navier Stokes Equation ◽  
Adaptive Wavelet ◽  
Abdominal Aortic

Turbulence can occur anywhere including our human body, some phenomenon describe it well. One of them is Abdominal Aortic Aneurysm. Therefore, as an illustration in this article, wavelet analysis of electrocardiographic (ECG) signal of a subject is performed to study the effect of complex phenomenon turbulence in human body part. This article deals with different perspective of turbulence, main emphasis is on wavelet analysis. Therefore, different wavelet family members are employed to get various views of analysis at different decomposition levels. Turbulent flows are generally modeled with the help of Navier-Stokes equation. Different numerical techniques for solving Navier-Stokes equations using adaptive wavelet bases are also pondered.

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