Qualitative and quantitative stabilized behavior of truncated two-dimensional naver-stokes equations

N-mode truncations of the Navier-Stokes equations on a two-dimensional torus are investigated for increasing N, up to a maximum of N=1000. A parameter range is considered in which the behavior is first quasi-periodic and then chaotic. A Poincare map analysis shows features which clearly stabilize as N increases, from both a qualitative and quantitative point of view. Concerning the onset of chaos, it is found that the appearance of bumps and foldings in the section curve is the cause of the breaking of the torus. A detailed description of the transition is given for N=502.