scholarly journals A statistical mechanical phase transition to turbulence in a model shear flow

2017 ◽  
Vol 830 ◽  
pp. 1-4
Author(s):  
Nigel Goldenfeld
Keyword(s):  
Phase Transition ◽  
Shear Flow ◽  
Stokes Equations ◽  
Equilibrium Phase ◽  
Transition To Turbulence ◽  
Crystalline Lattice ◽  
Navier Stokes ◽  
Directed Percolation ◽  
Statistical Mechanical ◽  
Non Equilibrium

It is becoming increasingly clear that the strong spatial and temporal fluctuations observed in a narrow Reynolds number regime around the laminar–turbulent transition in shear flows can best be understood using the concepts and techniques from a seemingly unrelated discipline – statistical mechanics. During the last few years, a consensus has begun to emerge that these phenomena reflect an underlying non-equilibrium phase transition exhibited by a model of interacting particles on a crystalline lattice, directed percolation, that seems very far from fluid mechanics. Now, Chantry et al. (J. Fluid Mech., vol. 824, 2017, R1) have developed a truncated-mode computation of a model shear flow, capable of simulating systems far larger and longer than any previous study and have for the first time generated enough statistical data that a high-precision test of theory is feasible. The results broadly confirm the theory, extending the class of flows for which the directed percolation scenario holds and removing any remaining doubts that non-equilibrium statistical mechanical critical phenomena can be exhibited by the Navier–Stokes equations.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

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.

A new roll-type instability in an oscillating fluid plane

1994 ◽  
Vol 268 ◽  
pp. 293-313 ◽  
Author(s):  
Edward W. Bolton ◽  
J. Maurer
Keyword(s):  
Shear Flow ◽  
Stokes Equation ◽  
Maximum Amplitude ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Secondary Wave ◽  
Initial Increase ◽  
Parallel Plates ◽  
Navier Stokes Equation ◽  
Roll Type

A new roll-type instability has been discovered experimentally. When fluid between two closely spaced, parallel plates is oscillated about an axis midway between the plates, it exhibits an instability that takes the form of longitudinal rolls aligned perpendicular to the axis of rotation. The basic-state oscillatory shear flow, before the onset of rolls, may be viewed as driven by the $\dot{\bm \Omega}\times \hat{\bm r}$ term of the Navier–Stokes equation in the oscillatory reference frame. A regime diagram is presented in a parameter space defined by the maximum amplitude of angular oscillation, α, and the non-dimensional frequency, Φ = ωd2/ν. The equilibrium wavelength of the rolls scales with d, the gap spacing between the plates, and it increases as Φ increases. Supercritical to a weak-roll onset, an abrupt transition to stronger roll amplitude occurs. Photographs of the cell after an impulsive start show the roll development and initial increase in roll wavelength. A variety of phenomena are observed, including wavelength selection via defect creation and elimination, front propagation, secondary wave instabilities, and the transition to turbulence. We also present solutions of the Navier–Stokes equation for the basic-state shear flow in a near-axis approximation. We develop a simple resonance model which shows some promise in understanding the low-α, high-Φ behaviour of strong rolls. A theoretical analysis of this instability is presented by Hall (1994).

Impurity-tuned non-equilibrium phase transition in a bacterial carpet

2016 ◽  
Vol 108 (18) ◽  
pp. 183701 ◽  
Author(s):  
Yi-Teng Hsiao ◽  
Kuan-Ting Wu ◽  
Nariya Uchida ◽  
Wei-Yen Woon
Keyword(s):  
Phase Transition ◽  
Equilibrium Phase ◽  
Equilibrium Phase Transition ◽  
Non Equilibrium

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.

Quantitative Elucidation of the Non-Equilibrium Phase Transition in LiFePO4 via the Intermediate Phase

2019 ◽  
Vol 31 (18) ◽  
pp. 7160-7166 ◽  
Author(s):  
Takahiro Yoshinari ◽  
Takuya Mori ◽  
Kazufumi Otani ◽  
Toshiyuki Munesada ◽  
Kentaro Yamamoto ◽  
...  
Keyword(s):  
Phase Transition ◽  
Intermediate Phase ◽  
Equilibrium Phase ◽  
Equilibrium Phase Transition ◽  
Non Equilibrium
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