For values of C for which the sequence does not approach a periodic limit, the system is called chaotic . At low velocities, the flow of fluid is laminar. In other words, the fluid in the center, say of a hollow tube, is moving the fastest. As you approach the walls, the velocity decreases until the velocity is zero along the walls due to friction. As the velocity increases, turbulence begins to occur.
Turbulence is when eddies begin to occur at all different scales.
In 1843, Reynolds suggested that the transition from laminar flow to turbulent flow is due to the appearances of instability in the flow. At low velocities, these perturbations are damped out by the viscosity of the liquid, but this is not the case at higher velocities. Low R values indicate laminar flow while high R values indicate turbulence. Landau proposed that turbulence is a cascade of bifurcations in 1944. At a low velocity, laminar flow is a fixed point.