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A simple one‐dimensional model for the three‐dimensional vorticity equation
Author(s) -
Constantin P.,
Lax P. D.,
Majda A.
Publication year - 1985
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160380605
Subject(s) - vorticity , euler equations , vorticity equation , simple (philosophy) , mathematics , simplicity , computation , vortex , compressibility , flow (mathematics) , mathematical analysis , semi implicit euler method , euler's formula , backward euler method , geometry , physics , mechanics , philosophy , epistemology , algorithm , quantum mechanics
A simple qualitative one‐dimensional model for the 3‐D vorticity equation of incompressible fluid flow is developed. This simple model is solved exactly; despite its simplicity, this equation retains several of the most important structural features in the vorticity equations and its solutions exhibit some of the phenomena observed in numerical computations for breakdown for the 3‐D Euler equations.