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Pasini, Antonello; Pelino, Vinicio

A unified view of Kolmogorov and Lorenz systems. (English) Zbl 1115.76320

Phys. Lett., A 275, No. 5-6, 435-446 (2000).
Summary: The discussion on the relation between the Kolmogorov system, considered as low-order approximation of Navier-Stokes equations, and the well-known Lorenz equations is still not completely understood. In this Letter, referring to the mathematical theory of motion on Lie groups, a particular class of Kolmogorov systems, largely studied in low-dimensional models of geophysical fluid dynamics, is extended and analysed in its geometric and dynamical features. The dynamical behaviour of this extended and unifying system generally shows chaos, contrarily to the original Kolmogorov one, and actually two well known Lorenz models, useful as toy-models in geophysical fluid dynamics, are included in it.

Cited in 30 Documents

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76E20 Stability and instability of geophysical and astrophysical flows
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
86A10 Meteorology and atmospheric physics

Keywords:

Kolmogorov system; Lorenz attractors
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References:

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