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Long-range correlation: Difference between revisions
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More interesting is the typical behaviour of the correlation function for turbulent states. | More interesting is the typical behaviour of the correlation function for turbulent states. | ||
In this case, the correlation function typically decays exponentially as a function of Δ and can be characterized by a single number: the 'decorrelation time' (or length) Δ<sub>corr</sub>, calculated as the distance at which the correlation has dropped from its maximum value by a factor ''1/e''. | In this case, the correlation function typically decays exponentially as a function of Δ and can be characterized by a single number: the 'decorrelation time' (or length) Δ<sub>corr</sub>, calculated as the distance at which the correlation has dropped from its maximum value by a factor ''1/e''. | ||
Δ<sub>corr</sub> consitutes the typical ''scale length'' for turbulent dynamics (turbulent transport). | |||
== Long range effects == | == Long range effects == | ||
However, often it is observed that the correlation exhibits a slower decay for large values of the delay (or distance) Δ, namely an algebraic decay proportional to 1/Δ<sup>α</sup> (α > 0 but not too large, < 2). | |||
In this case, the correlations at large delay may be quite important to understand the global system behaviour (contrasting sharply with the exponential decay case). | |||
Particularly, an algebraic decay of the mentioned type implies that no particular ''scale length'' can be assigned to the turbulent dynamics, and all scales (up to the system size) will participate in the global description of system behaviour. | |||
This unusual, slow decay of the correlation function has important consequences, implying that the system exhibits 'memory effects' or 'non-local behaviour' (self-similarity). | This unusual, slow decay of the correlation function has important consequences, implying that the system exhibits 'memory effects' or 'non-local behaviour' (self-similarity). | ||