TITLE:
A Five-Mode System of the Navier-Stokes Equations on a Torus
AUTHORS:
Heyuan Wang
KEYWORDS:
The Navier-Stokes Equations, Strange Attractor, Lyapunov Function, Bifurcation, Chaos
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.7,
July
22,
2016
ABSTRACT: A five-mode
truncation of the Navier-Stokes equations for a two-dimensional incompressible
fluid on a torus is studied. Its stationary solutions and stability are presented;
the existence of attractor and the global stability of the system are
discussed. The whole process, which shows a chaos behavior approached through
an involved sequence of bifurcations with the changing of Reynolds number, is
simulated numerically. Based on numerical simulation results of bifurcation
diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and
return map of the system, some basic dynamical behavior of the new chaos system
are revealed.