But when R becomes large turbulence sets in. Not much is known about the transition in general, and we will discuss this later. The type of chaos in turbulence is different from the chaos in Hamiltonian systems. In the latter trajectories diverged exponentially in time when initial conditions where slightly different, but the trajectories themselves where smooth. In turbulence, the trajectories are also wild and we have chaos in both time and space.
Tabor shows results of experimental observations of turbulence.
Chaos sets in at finite values of R. Note that R to infinity is the limit of no viscosity. In that limit the system shows chaotic behavior very similar to the one observed in Hamiltonian systems.