A unified view of Kolmogorov and Lorenz systems

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. (C) 2000 Elsevier Science B.V. All rights reserved.