Flow of drilling fluids can be classified into one of three phases which are laminar, transition and turbulent flow.
Laminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow the motion of the particles of fluid is very orderly with all particles moving in straight lines parallel to the pipe walls.
Transitional flow exhibits characteristics of both laminar and turbulent flow. The edges of the fluid flow in a laminar state, while the center of the flow remains turbulent. Like turbulent flows, transitional flows are difficult, if not impossible, to accurately measure.
Turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. As you can see, the flow profile show disorganized flow pattern. From the study, It usually happened when the Reynolds Number is over 4,000.
Reference: Drilling Hydraulic Books