scholarly journals Algebraic construction of a Nambu bracket for the two-dimensional vorticity equation

2011 ◽  
Vol 375 (37) ◽  
pp. 3310-3313 ◽  
Author(s):  
M. Sommer ◽  
K. Brazda ◽  
M. Hantel
Keyword(s):  
Vorticity Equation ◽  
Two Dimensional ◽  
Algebraic Construction ◽  
Nambu Bracket

Solution of Two-Dimensional Vorticity Equation on a Lagrangian Mesh

AIAA Journal ◽  
2000 ◽  
Vol 38 (5) ◽  
pp. 774-783 ◽  
Author(s):  
Stephen A. Huyer ◽  
John R. Grant
Keyword(s):  
Vorticity Equation ◽  
Two Dimensional

scholarly journals CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4769-4788 ◽  
Author(s):  
TEKİN DERELİ ◽  
ADNAN TEĞMEN ◽  
TUĞRUL HAKİOĞLU
Keyword(s):  
Phase Space ◽  
Canonical Transformation ◽  
Generating Functions ◽  
General Framework ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Nambu Bracket ◽  
Definition Of

Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

Solution of two-dimensional vorticity equation on a Lagrangian mesh

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 774-783
Author(s):  
Stephen A. Huyer ◽  
John R. Grant
Keyword(s):  
Vorticity Equation ◽  
Two Dimensional

scholarly journals Integrals of the Vorticity Equation. Part II: Special Two-Dimensional Flows

2006 ◽  
Vol 63 (2) ◽  
pp. 611-616 ◽  
Author(s):  
Robert Davies-Jones
Keyword(s):  
Shear Flow ◽  
Formal Solution ◽  
Inviscid Flow ◽  
Vorticity Equation ◽  
Two Dimensional ◽  
General Integral ◽  
2D Flow ◽  
Stratified Shear Flow ◽  
Two Dimensional Flows

Abstract In Part I, a general integral of the 2D vorticity equation was obtained. This is a formal solution for the vorticity of a moving tube of air in a 2D unsteady stratified shear flow with friction. This formula is specialized here to various types of 2D flow. For steady inviscid flow, the integral reduces to an integral found by Moncrieff and Green if the flow is Boussinesq and to one obtained by Lilly if the flow is isentropic. For steady isentropic frictionless motion of clear air, several quantities that are invariant along streamlines are found. These invariants provide another way to obtain Lilly’s integral from the general integral.

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