TITLE:
A Seven-Dimensional System of the Navier-Stokes Equations for a Two-Dimensional Incompressible Fluid on a Torus
AUTHORS:
Heyuan Wang, Yan Gao
KEYWORDS:
The Navier-Stokes Equations, Strange Attractor, Lyapunov Function, Bifurcation, Chaos
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.4 No.4,
November
17,
2014
ABSTRACT: A seven-mode truncation system of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is considered. Its stationary solutions and stability are presented; the existence of the attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through instability of invariant tori, is simulated numerically by computers with the changing of Reynolds number. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, some basic dynamical behaviors of the new chaos system are revealed.