scholarly journals About Universality and Thermodynamics of Turbulence

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 326 ◽  
Author(s):  
Damien Geneste ◽  
Hugues Faller ◽  
Florian Nguyen ◽  
Vishwanath Shukla ◽  
Jean-Philippe Laval ◽  
...  
Keyword(s):  
Phase Transition ◽  
Velocity Structure ◽  
Stokes Equations ◽  
Structure Functions ◽  
Velocity Fields ◽  
Stereoscopic Particle Image Velocimetry ◽  
Navier Stokes ◽  
Universal Curve ◽  
Navier Stokes Equations ◽  
Hölder Exponents

This paper investigates the universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and direct numerical simulations (DNS) of the Navier-Stokes equations. It shows that the numerical and experimental velocity structure functions up to order 9 follow a log-universality (Castaing et al. Phys. D Nonlinear Phenom. 1993); this leads to a collapse on a universal curve, when units including a logarithmic dependence on the Reynolds number are used. This paper then investigates the meaning and consequences of such log-universality, and shows that it is connected with the properties of a “multifractal free energy”, based on an analogy between multifractal and thermodynamics. It shows that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different Hölder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data.

Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition

2010 ◽  
Vol 656 ◽  
pp. 189-204 ◽  
Author(s):  
ILIA V. ROISMAN
Keyword(s):  
Heat Transfer ◽  
Phase Transition ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Reynolds Numbers ◽  
Drop Impact ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Viscous Drop

This theoretical study is devoted to description of fluid flow and heat transfer in a spreading viscous drop with phase transition. A similarity solution for the combined full Navier–Stokes equations and energy equation for the expanding lamella generated by drop impact is obtained for a general case of oblique drop impact with high Weber and Reynolds numbers. The theory is applicable to the analysis of the phenomena of drop solidification, target melting and film boiling. The theoretical predictions for the contact temperature at the substrate surface agree well with the existing experimental data.

scholarly journals A DISPERSIVE APPROACH TO THE ARTIFICIAL COMPRESSIBILITY APPROXIMATIONS OF THE NAVIER–STOKES EQUATIONS IN 3D

2006 ◽  
Vol 03 (03) ◽  
pp. 575-588 ◽  
Author(s):  
DONATELLA DONATELLI ◽  
PIERANGELO MARCATI
Keyword(s):  
Weak Solution ◽  
Stokes Equations ◽  
Velocity Fields ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method ◽  
Dispersive Approach ◽  
Incompressible Navier Stokes Equation

In this paper we study how to approximate the Leray weak solutions of the incompressible Navier–Stokes equations. In particular we describe an hyperbolic version of the so-called artificial compressibility method investigated by J. L. Lions and Temam. By exploiting the wave equation structure of the pressure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimates of Strichartz type. We prove that the projection of the approximating velocity fields on the divergence free vectors is relatively compact and converges to a Leray weak solution of the incompressible Navier–Stokes equation.

scholarly journals Renormalisation Group Analysis of Turbulent Hydrodynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Dirk Barbi ◽  
Gernot Münster
Keyword(s):  
Stokes Equations ◽  
Group Analysis ◽  
Structure Functions ◽  
Renormalisation Group ◽  
Theoretical Physics ◽  
Navier Stokes ◽  
Scaling Exponents ◽  
Navier Stokes Equations ◽  
Scaling Properties ◽  
Promising Tool

Turbulent hydrodynamics is characterised by universal scaling properties of its structure functions. The basic framework for investigations of these functions has been set by Kolmogorov in 1941. His predictions for the scaling exponents, however, deviate from the numbers found in experiments and numerical simulations. It is a challenge for theoretical physics to derive these deviations on the basis of the Navier-Stokes equations. The renormalization group is believed to be a very promising tool for the analysis of turbulent systems, but a derivation of the scaling properties of the structure functions has so far not been achieved. In this work, we recall the problems involved, present an approach in the framework of the exact renormalisation group to overcome them, and present first numerical results.

VORTICAL FLOW OF INCOMPRESSIBLE VISCOUS FLUID IN FINITE CYLINDER

2008 ◽  
Vol 13 (3) ◽  
pp. 371-381
Author(s):  
Harijs Kalis ◽  
Ilmārs Kangro
Keyword(s):  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Velocity Fields ◽  
Vortical Flow ◽  
Finite Cylinder ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vortex Lines ◽  
Smooth Pipe ◽  
Effective Use

The effective use of vortex energy in production of strong velocity fields by different devices is one of the modern areas of applications, developed during the last decade. In this paper the distribution of velocity field for viscous incompressible fluid in a pipe with a system of finite number of circular vortex lines, positioned on the inner surface of the finite cylinder is calculated. The approximation of the corresponding boundary value problem for the Navier‐Stokes equations is based on the finite difference method. This procedure allows us to reduce the 2D problem decribed by the system of Navier‐ Stokes PDEs to the monotonous difference equations. Calculations are done using the computer program Matlab and the following regimes are calculated: a) the flow in a smooth pipe; b) the flow, poured inside a pipe through the circle; c) the flow, poured inside a pipe through the ring. The model is investigated for different values of parameters Re (Reynolds number), G(swirl number) and A (vortex intensity).

scholarly journals A Note on the Vanishing Viscosity Limit in the Yudovich Class

2020 ◽  
pp. 1-11
Author(s):  
Christian Seis
Keyword(s):  
Stokes Equations ◽  
Velocity Fields ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Vanishing Viscosity ◽  
Navier Stokes Equations ◽  
Vanishing Viscosity Limit ◽  
Viscosity Limit ◽  
The Difference

Abstract We consider the inviscid limit for the two-dimensional Navier–Stokes equations in the class of integrable and bounded vorticity fields. It is expected that the difference between the Navier–Stokes and Euler velocity fields vanishes in $L^2$ with an order proportional to the square root of the viscosity constant $\nu $ . Here, we provide an order $ (\nu /|\log \nu | )^{\frac 12\exp (-Ct)}$ bound, which slightly improves upon earlier results by Chemin.

scholarly journals Phase transition in time-reversible Navier-Stokes equations

2019 ◽  
Vol 100 (4) ◽  
Author(s):  
Vishwanath Shukla ◽  
Bérengère Dubrulle ◽  
Sergey Nazarenko ◽  
Giorgio Krstulovic ◽  
Simon Thalabard
Keyword(s):  
Phase Transition ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Viscosity in air-gun bubble modeling

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. T1-T9 ◽  
Author(s):  
Jack King
Keyword(s):  
Velocity Structure ◽  
Stokes Equations ◽  
Bubble Surface ◽  
Slip Condition ◽  
Navier Stokes ◽  
Friction Drag ◽  
Navier Stokes Equations ◽  
Collapse Pressure ◽  
Air Gun ◽  
Rise Rate

I have presented finite volume simulations of an air-gun bubble in which the compressible Navier-Stokes equations were solved numerically. These equations included viscosity. My simulation also applied the no-slip condition at the bubble surface. The effects of the viscous terms were small; however, the effect of the no-slip condition was significant, causing a reduction in the bubble rise rate of 18.1% and an increase in the collapse pressure of 17.9%. The no-slip condition caused boundary layers at the bubble surface and changes in the velocity structure throughout the bubble. The no-slip condition allowed the effect of skin-friction drag on the bubble to be captured, along with Kelvin-Helmholtz instabilities at the surface, which caused a change in the shape of the bubble during collapse. The influence of the no-slip condition suggests that it is important and should be included in air-gun bubble models.

Melting Powder Particles in a Low-Pressure Plasma Jet

1987 ◽  
Vol 109 (4) ◽  
pp. 971-976 ◽  
Author(s):  
D. Y. C. Wei ◽  
B. Farouk ◽  
D. Apelian
Keyword(s):  
Stokes Equations ◽  
Plasma Jet ◽  
Low Pressure ◽  
Velocity Fields ◽  
Temperature History ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
History Of ◽  
Powder Particles ◽  
Temperature And Velocity Fields

A numerical model has been developed to predict the temperature history of metal particles injected in a low-pressure (supersonic) d-c plasma jet. The temperature and velocity fields of the plasma jet are predicted by solving the parabolized compressible Navier–Stokes equations using a spatial marching scheme. Particle trajectories and heat transfer characteristics are calculated using the predicted plasma jet temperature and velocity fields. Correction factors have been introduced to take into account the noncontinuum effects encountered in the low-pressure environment. The plasma jet profiles as well as the particle/plasma interactions under different jet pressure ratios (from underexpanded to overexpanded cases) have been investigated.

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