Energy dissipation and dynamical complexity in a truncated two-dimensionalNavier-Stokes dynamics

The five-mode truncated version of the planar incompressible Navier-Stokes equations developed by Franceschini and co-authors is analyzed from the sta ndpoint of irreversible thermodynamics. The entropy production is expressed in terms of the model variables and its dependence on the control paramete r (driving force) is determined. Its variability patterns as the system run s over the periodic and the chaotic attractors encountered at different par ameter values are subsequently compared with various indicators of the intr insic complexity of the dynamics, such as the local Lyapunov exponents and a local generalization of the Kolmogorov entropy. The analysis reveals some unexpected correlations. In particular, it appears that the largest span o f values of entropy production occurs during stages dominated by stability, while the maximum value occurs during stages dominated by instability. (C) 2001 Elsevier Science B.V. All rights reserved.