By Tsinober, A. (1937-)

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Unfortunately, this is true of other theoretical approaches such as attempts to construct statistical and/or other theories. Another matter the technical tools, which are of purely experimental and observational nature. Unlike the theoretical issues/problems much essential progress has occurred in developing numerical, laboratory and field experimental approaches to turbulent flows (see Appendix E). It is noteworthy that in view of the state of the theoretical field, the experimental research in turbulence was and remains the main source of knowledge of turbulent flows.

In other words turbulent flows possess both predictable and unpredictable features. The well known problem of predictability from meteorology is essentially about the dynamics and statistics of an initial error, which is the measure of the differences between some two realizations of a turbulent flow under almost (hence the error) the same conditions. An important aspect is that the error also possesses stable statistical properties in the sense that errors corresponding to different pairs of realizations have the same statistical properties.

There exist ~ excited degrees of freedom7, many of which are strongly interacting. Hence extreme complexity of turbulence (along with its intrinsic randomness) means that description of turbulent flows should be of statistical nature. We emphasize that statistical description is not synonymous to statistical theorization. g. solitons in the systems described by the Korteveg de Vries and Shrödinger equations, and shocks in the Burgers equation and . Again most of the examples given in the previous section clearly show the multi-scale nature of turbulent flows in space.

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An informal introduction to turbulence by Tsinober, A. (1937-)

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