ManchesterCFD Amin

# Why are ‘Turbulent Flows’ so difficult to understand?

**Introduction**

Turbulence is composed of eddies of various length-scales. Energy is extracted from the mean flow and is cascaded down to the smallest eddies by essentially inviscid mechanism. Turbulence is a phenomenon of great complexity and has exercised many eminent scientists including Osborne Reynolds, the finest professor of engineering at the University of Manchester, and after who the ‘Reynolds number’ is named. Reynolds identified the parameter *UD*/n as a dimensionless group that could be used to characterize whether the flow would be laminar or turbulent. The Reynolds number is defined as

Turbulent flows occur at large Reynolds numbers:

Note that other factors such as freestream turbulence, surface conditions, blowing, suction and other disturbances etc. may cause transition to turbulence at lower Reynolds numbers.

**Some characteristics of Turbulent Flows**

· One characteristic of turbulent flows is their *irregularity* or randomness. A full deterministic approach is very difficult. Turbulent flows are usually described statistically. Turbulent flows are always *chaotic*. But not all chaotic flows are turbulent. Waves in the ocean, for example, can be chaotic but are not necessarily turbulent.

· The *diffusivity* of turbulence causes rapid mixing and increased rates of momentum, heat and mass transfer. A flow that looks random but does not exhibit the spreading of velocity fluctuations through the surrounding fluid is not turbulent. If a flow is chaotic, but not diffusive, it is not turbulent. The trail left behind a jet plane that seems chaotic, but does not diffuse for miles is then not turbulent.

· Turbulent flows always occur at *high Reynolds numbers*. They are caused by the complex interaction between the viscous terms and the inertia terms in the momentum equations.

· Turbulent flows are *rotational*; that is, they have non-zero vorticity. Mechanisms such as the stretching of three-dimensional vortices play a key role in turbulence.

· Turbulent flows are *dissipative*. Kinetic energy gets converted into heat due to viscous shear stresses. Turbulent flows die out quickly when no energy is supplied. Random motions that have insignificant viscous losses, such as random sound waves, are not turbulent.

· Turbulence is a *continuum* phenomenon. Even the smallest eddies are significantly larger than the molecular scales. Turbulence is therefore governed by the equations of fluid mechanics.

· Turbulent flows are flows. Turbulence is a *feature of fluid flow*, not of the fluid. When the Reynolds number is high enough, most of the dynamics of turbulence are the same whether the fluid is an actual fluid or a gas. Most of the dynamics are then independent of the properties of the fluid.