In measurement of a physical observable A(x) one encounters two essentially distinct types or phenomenological behavior: deterministic or stochastic. The deterministic form displays a regular dependence on x whereas the stochastic form contains a randomly fluctuating component superimposed on a regular behavior. In the real world, all physical measurements display some degree of stochastic behavior but the level of fluctuations is usually small. Stochastic systems in which the fluctuating component has a quantum or thermal origin usually have low levels of fluctuations and are not regarded as turbulent. In the presence of appropriate causative factors, the level of fluctuations can greatly exceed the quantum or thermal levels. In these cases one characterizes them as turbulent, and depending on whether turbulent levels are much or somewhat greater than thermal, as "strong" or "weak" turbulence respectively.

Systems displaying turbulence may occur in the solid, liquid, or gaseous states of matter, usually subsumed under the general heading of many-particle systems and describable with decreasing detail: at microscopic, kinetic, or macroscopic (fluid) levels. The particles that comprise these systems may be neutral or carry electric charges whose collective effects are important. In this latter case the system is said to be a plasma. Plasma systems occur on different laboratory scales: geophysical and astronomical. On a laboratory scale they appear in metal, semi-conductor, ionized gas, and ionized liquid structures in such varied devices as solid state oscillators, plasma amplifiers, energy converters, fusion reactors, etc. Geophysically, one encounters plasma in regions that surround the earth’s atmosphere such as the ionosphere and exosphere. On an astronomical scale, many interplanetary space phenomena are traceable to the presence of plasma.

Turbulent phenomena occur with different scales in neutral and plasma systems. A neutral fluid flowing in a pipe, or surrounding an object, will display turbulence in certain regions when the flow speed exceeds a critical value determined by the dimensions of the pipe and the object. Conversely, at a certain speeds depending on object size and viscosity of the fluid, an object moving through a fluid exhibits turbulent phenomena in its wake region.. An electron beam injected into an ionized gas plasma will give rise to turbulent conditions depending on the beam speed, size, and electron density. A high power microwave impinging on plasma will initiate turbulence when the microwave amplitude exceeds a certain level. In the presence of a static magnetic field, plasma excited within a tube by an electric current will suddenly exhibit turbulence when the magnetic field is increased beyond a critical value.

In all of the above examples one observes, because of non-linearity, that turbulence appears when some physical parameter exceeds a certain level. The onset of turbulence may be gradual or it may occur with explosive suddenness; it may occur with relative spatial homogeneity or in local and periodic bursts. These different characteristics reveal different non-linear causative factors underlying the appearance of turbulence. One suspects, and this is confirmed in many cases, that the origins of turbulence lie in latent instabilities that are called into p1ay at appropriate levels of excitation. Since there are numerous types of’ instabilities, both microscopic and macroscopic, it is to be anticipated that there will be different types of’ turbulence. Another distinctive feature, also traceable to the nature of the underlying instabilities, is associated with the relative suddenness of the transition to turbulence; if it occurs gradually the turbulent excitation process is said to be "soft", whereas if it develops discontinuously it is "hard". The onset of turbulence may also give rise to certain anomalies in macroscopic transport properties such as diffusion, electrical conduction, and heat conduction.

Weak vs Strong Turbulent Systems

Plasma Fluctuations