Turbulent flow is flow characterized by recirculation, eddies, and randomness. Flow in which turbulence is not exhibited is called laminar flow. It should be noted that the presence of eddies or recirculation alone does not necessarily indicate turbulent flow these phenomena may be present in laminar flow as well. Mathematically, turbulent flow is often represented via a Reynolds decomposition using Reynolds number, in which the flow is broken down into the sum of an average component and a perturbation component. In fluid dynamics, potential flow describes the velocity gradient as the gradient of a scalar function called asthe velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications and the irrotationality of a potential flow is due to the curl of a gradient always being equal to zero.
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