# Physics of Turbulent Flows

This section on physics of turbulence introduces a brief history of turbulence and covers the theory behind turbulence generation, turbulence transition and energy cascade in fluid flows.

On a daily basis you encounter turbulent flows in many places including rivers, ocean currents, atmospheric turbulence, bush fires, flows over blunt bodies, for example, cars, aircraft, ships and buildings, cross flows of chimney plumes, internal flows in pipelines, turbines and engines and many other various forms. Despite the prevalence of turbulent flows in your daily life there is no consensus on the definition of turbulence.

The following are several definitions quoted from various sources of literature.

- Bradshaw (1971): “Turbulence is a three dimensional time dependent motion in which vortex stretching causes velocity fluctuations to spread to all wavelengths between a minimum determined by viscous forces and a maximum determined by the boundary conditions. It is the usual state of fluid motion except at low Reynolds numbers.”
- Hinze (1975): “Turbulent flow motion is an irregular condition of flow in which various quantities show a random variation with time and space coordinates, so that statistically distinct average values can be discerned.”
- Launder (1991): “At moderate Reynolds numbers the restraining effects of viscosity are too weak to prevent small, random disturbances in a shear flow from amplifying. The disturbances grow, become non linear and interact with neighboring disturbances. This mutual interaction leads to a tangling of vorticity filaments. Eventually the flow reaches a chaotic, non repeating form describable only in statistical terms. This is the turbulent flow.”
- Pope (2000): "An essential feature of turbulent flows is that the fluid velocity field varies significantly and irregularly in both position and time."

Considering these definitions you can arrive at the following set of characteristic
features of turbulent flows:

- Irregularity. Turbulent flow is highly chaotic and irregular in both space and time (Tennekes and Lumley, 1972; Hinze, 1975; Pope, 2000).
- Non-repetition. Turbulent flow is a non-repeating form (Launder, 1991).
- Three dimensional unsteady eddies with different scales. Turbulent flow is always three dimensional and unsteady. Turbulent flow contains eddies with different scales, which extract energy from shear stress of the mean flow and produce fluctuations in the velocity and pressure fields. The eddies also interact with one another and exchange momentum and energy (Bradshaw, 1971; Tennekes and Lumley, 1972).
- Diffusivity. Turbulent flow is diffusive (that is, the spreading of fluctuations) (Tennekes and Lumley, 1972; Pope, 2000). The chaotic eddies (vortices) within the turbulent flow increase the momentum exchange in boundary layers delaying separation on the surface of curved bodies and increasing the resistance (wall friction) and heat transfer.
- Dissipation. Turbulent flow is dissipative. This suggests that the kinetic energy within small eddies is transformed into thermal energy. The small eddies receive their energy from larger eddies, which receive their energy from even larger eddies, and so on. The largest eddies extract their energy from the mean flow. This process of transferring energy from the larger eddies to the smaller eddies is called the energy cascade process. Turbulence is not self sustainable without a source of energy input.
- Amplification. The flow disturbances amplify when the Reynolds number exceeds critical Reynolds numbers (~2300 for internal flows, ~500000 for external flows).
- Flow property. Turbulent flow is a property of flow, it is not a fluid property.
- Sensitivity. Turbulence is extremely sensitive to flow disturbances (Pope, 2000).