Forward-difference
From Atomix
For the forward-difference scheme
- start with [math]\displaystyle{ n }[/math] being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range should equal or exceed [math]\displaystyle{ n_{\text{rmax}} }[/math]) + 1
- start with [math]\displaystyle{ \delta = 1 }[/math]
- compute the second order forward-difference structure function [math]\displaystyle{ D(n,\delta) }[/math] as the segment mean of the square of the velocity difference between the bin [math]\displaystyle{ n }[/math] and bin [math]\displaystyle{ n + \delta }[/math]:
[math]\displaystyle{ D(n, \delta) = \Big\langle \big[b^\prime(n, t) - b^\prime(n+\delta,\ t)\big]^2 \Big\rangle }[/math]
where the angled brackets indicate the mean across all [math]\displaystyle{ t }[/math] for the data segment yielding a velocity difference after the application of the Level 1 QC criteria - increment [math]\displaystyle{ \delta }[/math] and repeat steps until [math]\displaystyle{ \delta = n_{\text{rmax}} }[/math] or [math]\displaystyle{ n + \delta }[/math] exceeds the last bin of the range over which the structure function is to be evaluated
- increment [math]\displaystyle{ n }[/math] and repeat steps until [math]\displaystyle{ n + 1 }[/math] is the last bin of the range over which the structure function is to be evaluated
See example forward-difference calculation for more detail regarding the calculation
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