Statistical Theory of Rubber‐Like Elasticity. IV. (Two‐Dimensional Stretching)

1951 ◽  
Vol 19 (12) ◽  
pp. 1508-1512 ◽  
Author(s):  
Akira Isihara ◽  
Natsuki Hashitsume ◽  
Masao Tatibana
Keyword(s):  
Statistical Theory ◽  
Two Dimensional

scholarly journals Statistical theory of reversals in two-dimensional confined turbulent flows

2016 ◽  
Vol 94 (6) ◽  
Author(s):  
Vishwanath Shukla ◽  
Stephan Fauve ◽  
Marc Brachet
Keyword(s):  
Statistical Theory ◽  
Turbulent Flows ◽  
Two Dimensional

Classification of robust isolated vortices in two-dimensional hydrodynamics

1998 ◽  
Vol 356 ◽  
pp. 259-296 ◽  
Author(s):  
P. H. CHAVANIS ◽  
J. SOMMERIA
Keyword(s):  
Statistical Theory ◽  
Linear Relationship ◽  
Stream Function ◽  
Control Parameter ◽  
Additional Restriction ◽  
Strong Mixing ◽  
Two Dimensional ◽  
Stability Criteria ◽  
Infinite Domain

We determine solutions of the Euler equation representing isolated vortices (monopoles, dipoles) in an infinite domain, for arbitrary values of energy, circulation, angular momentum and impulse. A linear relationship between vorticity and stream function is assumed inside the vortex (while the flow is irrotational outside). The emergence of these solutions in a turbulent flow is justified by the statistical mechanics of continuous vorticity fields. The additional restriction of mixing to a ‘maximum-entropy bubble’, due to kinetic constraints, is assumed. The linear relationship between vorticity and stream function is obtained from the statistical theory in the limit of strong mixing (when constraints are weak). In this limit, maximizing entropy becomes equivalent to a kind of enstrophy minimization. New stability criteria are investigated and imply in particular that, in most cases, the vorticity must be continuous (or slightly discontinuous) at the vortex boundary. Then, the vortex radius is automatically determined by the integral constraints and we can obtain a classification of isolated vortices such as monopoles and dipoles (rotating or translating) in terms of a single control parameter. This article generalizes the classification obtained in a bounded domain by Chavanis & Sommeria (1996).

scholarly journals A STATISTICAL THEORY OF THE TWO-DIMENSIONAL ALTERNATIVE BINARY SYSTEM

1983 ◽  
Vol 32 (7) ◽  
pp. 917
Author(s):  
DU YI-JING ◽  
YAN ZU-TONG ◽  
CHEN LI-RONG
Keyword(s):  
Statistical Theory ◽  
Binary System ◽  
Two Dimensional

Statistical theory of vortex merger in the two-dimensional mixing layer

1978 ◽  
Vol 21 (2) ◽  
pp. 153 ◽  
Author(s):  
Ryuji Takaki ◽  
Leslie S. G. Kovasznay
Keyword(s):  
Statistical Theory ◽  
Mixing Layer ◽  
Two Dimensional ◽  
Vortex Merger
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