The Hamiltonian dynamics of a two-degree-of-freedom system is shown to mimic the structure of an incompressible fluid if the fluid streamlines are considered instead of the pathlines used by many authors. This approach is formally equivalent to the determination of magnetic field lines, which satisfy the same mathematical equations. Turbulence in this case is seen as Hamiltonian chaotic dynamics perturbed by time, which plays the role of the codimension parameter of such chaos. Any spatial Lie symmetry leads to a laminar flow, whereas stationary flow could be considered chaotic but not turbulent. The transition from laminar to turbulent flow is associated with the destruction of KAM trajectories produced by time evolution.