scholarly journals Intermittency and Critical Scaling in Annular Couette Flow

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 988 ◽  
Author(s):  
Kazuki Takeda ◽  
Yohann Duguet ◽  
Takahiro Tsukahara
Keyword(s):  
Couette Flow ◽  
Finite Size ◽  
Radius Ratio ◽  
Small Radius ◽  
Plane Couette Flow ◽  
Confinement Effects ◽  
Finite Size Effects ◽  
One Dimensional ◽  
Onset Of Turbulence ◽  
Annular Geometry

The onset of turbulence in subcritical shear flows is one of the most puzzling manifestations of critical phenomena in fluid dynamics. The present study focuses on the Couette flow inside an infinitely long annular geometry where the inner rod moves with constant velocity and entrains fluid, by means of direct numerical simulation. Although for a radius ratio close to unity the system is similar to plane Couette flow, a qualitatively novel regime is identified for small radius ratio, featuring no oblique bands. An analysis of finite-size effects is carried out based on an artificial increase of the perimeter. Statistics of the turbulent fraction and of the laminar gap distributions are shown both with and without such confinement effects. For the wider domains, they display a cross-over from exponential to algebraic scaling. The data suggest that the onset of the original regime is consistent with the dynamics of one-dimensional directed percolation at onset, yet with additional frustration due to azimuthal confinement effects.

scholarly journals Homoclinic snaking in plane Couette flow: bending, skewing and finite-size effects

2016 ◽  
Vol 794 ◽  
pp. 530-551 ◽  
Author(s):  
J. F. Gibson ◽  
T. M. Schneider
Keyword(s):  
Couette Flow ◽  
Size Effects ◽  
Shear Flows ◽  
Numerical Study ◽  
Finite Size ◽  
Plane Couette Flow ◽  
Finite Size Effects ◽  
Localized Solutions ◽  
Viscous Shear ◽  
Homoclinic Snaking

Invariant solutions of shear flows have recently been extended from spatially periodic solutions in minimal flow units to spatially localized solutions on extended domains. One set of spanwise-localized solutions of plane Couette flow exhibits homoclinic snaking, a process by which steady-state solutions grow additional structure smoothly at their fronts when continued parametrically. Homoclinic snaking is well understood mathematically in the context of the one-dimensional Swift–Hohenberg equation. Consequently, the snaking solutions of plane Couette flow form a promising connection between the largely phenomenological study of laminar–turbulent patterns in viscous shear flows and the mathematically well-developed field of pattern-formation theory. In this paper we present a numerical study of the snaking solutions of plane Couette flow, generalizing beyond the fixed streamwise wavelength of previous studies. We find a number of new solution features, including bending, skewing and finite-size effects. We establish the parameter regions over which snaking occurs and show that the finite-size effects of the travelling wave solution are due to a coupling between its fronts and interior that results from its shift-reflect symmetry. A new winding solution of plane Couette flow is derived from a strongly skewed localized equilibrium.

scholarly journals Finite-size effects on topological interface states in one-dimensional scattering systems

2018 ◽  
Vol 98 (2) ◽  
Author(s):  
P. A. Kalozoumis ◽  
G. Theocharis ◽  
V. Achilleos ◽  
S. Félix ◽  
O. Richoux ◽  
...  
Keyword(s):  
Size Effects ◽  
Finite Size ◽  
Interface States ◽  
Finite Size Effects ◽  
One Dimensional ◽  
Scattering Systems

scholarly journals Suppression of finite-size effects in one-dimensional correlated systems

2011 ◽  
Vol 83 (5) ◽  
Author(s):  
A. Gendiar ◽  
M. Daniška ◽  
Y. Lee ◽  
T. Nishino
Keyword(s):  
Size Effects ◽  
Finite Size ◽  
Finite Size Effects ◽  
Correlated Systems ◽  
One Dimensional

scholarly journals Homogeneous one-dimensional Bose–Einstein condensate in the Bogoliubov’s regime

2016 ◽  
Vol 30 (22) ◽  
pp. 1650307 ◽  
Author(s):  
Elías Castellanos
Keyword(s):  
Ground State ◽  
Size Effects ◽  
Finite Size ◽  
Einstein Condensate ◽  
Finite Size Effects ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Ground State Properties ◽  
Low Dimensional ◽  
Bose Einstein

We analyze the corrections caused by finite size effects upon the ground state properties of a homogeneous one-dimensional (1D) Bose–Einstein condensate. We assume from the very beginning that the Bogoliubov’s formalism is valid and consequently, we show that in order to obtain a well-defined ground state properties, finite size effects of the system must be taken into account. Indeed, the formalism described in the present paper allows to recover the usual properties related to the ground state of a homogeneous 1D Bose–Einstein condensate but corrected by finite size effects of the system. Finally, this scenario allows us to analyze the sensitivity of the system when the Bogoliubov’s regime is valid and when finite size effects are present. These facts open the possibility to apply these ideas to more realistic scenarios, e.g. low-dimensional trapped Bose–Einstein condensates.

Fermi surface of the one-dimensional Hubbard model: Finite-size effects

1989 ◽  
Vol 162-164 ◽  
pp. 805-806
Author(s):  
C. Bourbonnais ◽  
H. Nelisse ◽  
A. Reid ◽  
A.-M.S. Tremblay
Keyword(s):  
Fermi Surface ◽  
Hubbard Model ◽  
Size Effects ◽  
Finite Size ◽  
Finite Size Effects ◽  
One Dimensional ◽  
The One
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