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The '''integral length scale''' measures the correlation distance of a [[Process theory|process]] in terms of space or time.<ref>{{cite journal|last1=O’Neill|first1=P. L.|last2=Nicolaides|first2=D.|last3=Honnery|first3=D.|last4=Soria|first4=J.|title=Autocorrelation Functions and the Determination of Integral Length with Reference to Experimental and Numerical Data|journal=15th Australasian Fluid Mechanics Conference|date=13-17 December 2004}}</ref> |
The '''integral length scale''' measures the correlation distance of a [[Process theory|process]] in terms of space or time.<ref>{{cite journal|last1=O’Neill|first1=P. L.|last2=Nicolaides|first2=D.|last3=Honnery|first3=D.|last4=Soria|first4=J.|title=Autocorrelation Functions and the Determination of Integral Length with Reference to Experimental and Numerical Data|journal=15th Australasian Fluid Mechanics Conference|date=13-17 December 2004}}</ref> |
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In essence, it looks at the overall memory of the process and how it is influenced by previous positions and [[parameter]]s. 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. |
In essence, it looks at the overall memory of the process and how it is influenced by previous positions and [[parameter]]s. 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. |
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The time dependence of field quantities changes the way that they behave. |
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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". |
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In the static case, the displacement current density is simply equal to zero. |
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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. |
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See Thomas Young's Double Slit Diffraction Experiment for more information on the conditionality of this phenomenon. |
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The mathematical expressions for integral scales are: |
The mathematical expressions for integral scales are: |
Revision as of 14:55, 5 October 2017
The integral length scale measures the correlation distance of a process in terms of space or time.[1] 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 mathematical expressions for integral scales are:
Where is the integral time scale, L is the integral length scale, and and are the autocorrelation with respect to time and space respectively.
In isotropic homogeneous turbulence, the integral length scale is defined as the weighted average of the inverse wavenumber, i.e.,
where is the energy spectrum.
References
- ^ O’Neill, P. L.; Nicolaides, D.; Honnery, D.; Soria, J. (13–17 December 2004). "Autocorrelation Functions and the Determination of Integral Length with Reference to Experimental and Numerical Data". 15th Australasian Fluid Mechanics Conference.
{{cite journal}}
: CS1 maint: date format (link)