ABSTRACT
A remarkable feature of two-dimensional (2D) flows is the spontaneous emergence of large-scale coherent structures. The 2D flows are modeled by 2D Navier–Stokes equations (2D NSE), which can be solved numerically with the spectral method by transforming the equations to Fourier space, and truncating the Fourier series to a finite number of modes for numerical implementation. Systematic study of the transition to chaos in the 2D NSE was presented by Feudel and Seehafer. Braun et al. compared numerical simulations of the 2D NSE using stress-free and no-slip boundary conditions in the vertical direction, and periodic boundary conditions in the horizontal direction. The chapter discusses a crisis-like transition to hyperchaos in the 2D NSE with periodic boundary conditions and an external force. Quasiperiodic doubling bifurcations have been observed in numerical studies of low-dimensional models of the 2D NSE and in simulations of three-dimensional highly symmetric flows.
