Instabilities in two‐dimensional spatially periodic flows. Part III: Inviscid triangular lattice

1993 ◽  
Vol 5 (2) ◽  
pp. 335-343 ◽  
Author(s):  
André Thess
Keyword(s):  
Triangular Lattice ◽  
Two Dimensional ◽  
Periodic Flows ◽  
Spatially Periodic

Mixing by chaotic advection in a class of spatially periodic flows

1992 ◽  
Vol 236 ◽  
pp. 1-26 ◽  
Author(s):  
Susan C. Ryrie
Keyword(s):  
Vortex Flow ◽  
Detailed Comparison ◽  
Laminar Flows ◽  
Basic Flow ◽  
Chaotic Advection ◽  
Taylor Vortex ◽  
Two Dimensional ◽  
Periodic Flows ◽  
Taylor Vortex Flow ◽  
Spatially Periodic

The paths followed by individual fluid particles can be extremely complicated even in smooth laminar flows. Such chaotic advection causes mixing of the fluid. This phenomenon is studied analytically for a class of spatially periodic flows comprising a basic flow of two-dimensional (or axisymmetric) counter-rotating vortices in a layer of fluid, and modulated by a perturbation which is periodic in time and/or space. Examples of this type of flow include Bénard convection just above the point of instability of two-dimensional roll cells, and Taylor vortex flow between concentric rotating cylinders. The transport of chaotically advected particles is modelled as a Markov process. This predicts diffusion-like mixing, and provides an expression for the diffusion coefficient. This expression explains some features of experimental results reported by Solomon & Gollub (1988): its accuracy is investigated through a detailed comparison with numerical results from a model of wavy Taylor vortex flow. The approximations used in the analysis are equivalent to those used to obtain the quasi-linear result for diffusion in the standard map.

scholarly journals Connecting Networks for Two-Dimensional Butler Matrices Generating a Triangular Lattice of Beams

2021 ◽  
Vol 1 (2) ◽  
pp. 646-658
Author(s):  
NELSON J. G. FONSECA ◽  
SOPHIE-ABIGAEL GOMANNE ◽  
PILAR CASTILLO-TAPIA ◽  
OSCAR QUEVEDO-TERUEL ◽  
TAKASHI TOMURA ◽  
...  
Keyword(s):  
Triangular Lattice ◽  
Two Dimensional

scholarly journals General up to next-nearest-neighbour elasticity of triangular lattices in three dimensions

2006 ◽  
Vol 462 (2073) ◽  
pp. 2695-2713 ◽  
Author(s):  
Cyril Dubus ◽  
Ken Sekimoto ◽  
Jean-Baptiste Fournier
Keyword(s):  
Blood Cell ◽  
Red Blood Cell ◽  
Triangular Lattice ◽  
Soft Matter ◽  
Rotational Symmetry ◽  
Three Dimensions ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Biological Physics ◽  
Crystalline System

We establish the most general form of the discrete elasticity of a two-dimensional triangular lattice embedded in three dimensions, taking into account up to next-nearest-neighbour interactions. Besides crystalline system, this is relevant to biological physics (e.g. red blood cell cytoskeleton) and soft matter (e.g. percolating gels, etc.). In order to correctly impose the rotational invariance of the bulk terms, it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice. We find that some terms that were suspected in the literature to violate rotational symmetry are, in fact, admissible.

Sign in / Sign up

Export Citation Format

Share Document