• Turbulence is a science itself
• In this section^23.1 we discuss turbulence in general.
• Most fluid flows in the nature and in technical applications are turbulent.
• Turbulence appears in all fluids and at all speeds from low speeds in the sea or in the atmosphere to supersonic speeds in technical applications.
• Turbulence appears in every fluid, when inertial or volume forces in the fluid are large enough in comparison with viscous forces that damp accidental disorders or non-stabilities of flow.
• If critical Reynolds number exceeded, laminar flow regime turns into turbulent.
• Turbulence is considered to be always three dimensional.
• Turbulence is three-dimensional non-stationary motion of viscous fluid, that has four major attributes:

• Turbulent flow consists of spectrum of turbulent eddies, whose size differs from the smallest ones, where turbulent kinetic energy dissipates in heat, to greatest ones, whose size equals to geometry of flow.
• Turbulence shows non-deterministic changes in time (chaotic behavior).
• Over accidental character of turbulence, the good news is: the same boundary conditions lead to the same flow characteristics.
• As a result, the turbulence can be considered as a quasi-deterministic processes in flowing fluid.
• The mean flow of the fluid can be described with the help of statistic laws.

Subsections

• Reynolds number
• Laminar vs. Turbulent Flow
• Turbulence Fluctuations
• Mean Velocity Profile
• Developed Boundary Layer
• Boundary Layer Thickness
• Momentum Thickness
• Reynolds number
• Reynolds number
• Turbulent Boundary Layer
• Friction Coefficient
• Pressure Coefficient