Turbulence

The turbulent flow (Latin: turbare = turn, disturb, confuse ) is the movement of liquids and gases, may occur with turbulence on all scales. This type of flow is characterized by mostly three-dimensional, seemingly random, unsteady movements of the fluid particles.

Properties

The enhanced diffusion due to the fluctuation of movement is one of the most important features of turbulent flows. It is several orders of magnitude over molecular diffusion. This turbulent cross- diffusion results, for example, that the losses increase in a pipe flow. While the pressure loss in a laminar flow tube is proportional to the average velocity, it is proportional to the square of the mean velocity of flow in a turbulent flow. Furthermore, the turbulent cross- diffusion favors the heat transport in flows with inhomogeneous temperature distribution. Turbulent boundary layers tend at high positive pressure gradient, for example, on the top of a highly salaried wing, later to be replaced as laminar boundary layers.

Turbulent flows are characterized in contrast to laminar flows by the following properties:

Example to (1): A hurricane is several kilometers in size, while the smallest eddies contained in it are smaller than one millimeter.

Example of ( 2): The wind strength at the location of a wind turbine is highly variable and difficult to predict.

Example to (3): If the wing of an aircraft iced up, the millimeter small ice crystals, the turbulent air flow influence so strong that the machine may crash.

Turbulence (in air masses, fluids ) can be defined in words as follows:

• Randomness ( the flow state, the velocities): not predictable ( or practically impossible to predict, statistically, but already see " deterministic chaos " )
• Diffusivity: strong and rapid mixing ( " convection ", " turbulence " ), in contrast to the influence of the slower molecular diffusion
• Dissipation: kinetic energy is continued on all scales converted to heat and is divided from the economies of scale of larger dimensions (larger " eddies " ) in a hierarchical manner into smaller elements ( " energy cascade "). Turbulent flow is thus obtained only when energy is supplied from the outside.
• Non-linearity: the laminar flow becomes unstable when the nonlinearities are gaining influence. With increasing nonlinearity of a sequence of different instabilities can occur before 'full turbulence ' is formed.

Formation

To illustrate the difference between laminar flow and turbulent flow of the physicists Osborne Reynolds has performed in a pipeline in 1883 a dyeing test water flow and found that the turbulence in the pipe can only be set from a speed limit. For this, the Reynolds number Re is used as a judgment criterion.

The linear stability theory is concerned with the envelope - even Transition - laminar flows in turbulent flows. It regards to the growth of wavy disturbances of small amplitude. The best-known instabilities are the Tollmien -Schlichting waves.

Description

To describe turbulent flows divided to the characteristic components, such as the speed and pressure in an averaged term, which is superimposed on a random spurious motion. We call this decomposition as Reynolds decomposition:

It is in the averaged size to the ensemble average. Substituting this decomposition into the Navier -Stokes equations, we obtain for the description of turbulent flows, the Reynolds equations, however, contain the Reynolds stresses as additional unknowns. It has now been more unknowns than equations, and therefore requires closure approaches to solve the system. Different closure approaches have led to different turbulence models.

The main closure approaches the approach of Boussinesq and Prandtl Mischungsweghypothese. The most important turbulence models are the turbulence models and the Large Eddy Simulation.

Turbulent flows can be homogeneous turbulence and shear turbulence in isotropic turbulence classify, which each have their own characteristics. In practice, usually occurs on the shear turbulence because it is idealized flow patterns in isotropic and homogeneous turbulence. Since turbulent flows are mathematically difficult to describe, one refers to their characterization often idealized flow patterns, since in such cases simplify the Reynolds equations further.

How little understood difficult, diverse, and is the turbulence, shows the following quote:

" If I were to go to heaven, I hope for enlightenment about two things: quantum electrodynamics and turbulence. As to the first request, I 'm pretty confident. "

Energy cascade

Lewis Fry Richardson laid in 1922 the foundation for further turbulence research by established today's selection of this phenomenon. After his groundbreaking interpretation, the energy is supplied on a larger scale in a turbulent flow, by the decay of vortices through all scales transported through (so-called Inertialbereich ) and dissipated at the smallest scales in heat. This is referred to as an energy cascade.

The theory of turbulence, considerable progress was Andrei Nikolaevich Kolmogorov of his works from 1941 and 1962, when he was able to statistically evaluate the scales argument of Richardson by a similarity hypothesis and thus derive the Kolmogorov-5/3-Gesetz for Inertialbereich, after the spectral thick with an exponent of -5 / 3 is dependent on the wavelength. Also, the dissipative range is named after him and is known as micro- scale of Kolmogorov.

Other examples

• Eddy and swirl in rivers
• The smoke of a cigarette in a resting environment is initially laminar ( layer ) flow, which is clearly visible turbulent after a certain height of rise then
• The milk in the coffee blends well with a turbulent flow, whereas the mixture of two colors usually corresponds to a laminar mixing by molecular diffusion
• The steam / water mixture in the holes of the metal block of evaporative cooling