Integral length scale

The integral length scale measures the amount of time a process is correlated with itself. In essence, it looks at the overall memory of the process and how it is influenced by previous positions and parameters. An intuitive example would be the case in which you have very low Reynolds number flows (e.g., a Stokes flow), where the flow is fully reversible and thus fully correlated with previous particle positions. This concept may be extended to turbulence, where it may be thought of as the time during which a particle is influenced by its previous position.

The time dependence of field quantities changes the way that they behave.

For example, the time dependent form of Maxwell's equations give extra information about the previous state of the fields in the form of the "displacement current density".

In the static case, the displacement current density is simply equal to zero.

The principle of Orthogonality is present in nature and especially in co-field relationships such as the phenomenon of the Electromagnetic, Z-axis oriented wave (transverse AND longitudinal, it has been proven), a.k.a. TEMZ waves, also known as LIGHT has the hidden dimension of also constraining the system's energy quanta to behave in certain fashions under certain conditions.

See Thomas Young's Double Slit Diffraction Experiment for more information on the conditionality of this phenomenon.

T = ∫ 0 ∞ ρ ( τ ) d τ

Where τ is the time and ρ the autocorrelation.

In isotropic homogeneous turbulence, the integral length scale ℓ is defined as the weighted average of the inverse wavenumber, i.e.,

ℓ = ∫ 0 ∞ k − 1 E ( k ) d k / ∫ 0 ∞ E ( k ) d k

where E ( k ) is the energy spectrum.