Bin-centred difference scheme

For a bin-centred difference scheme:

1. start at bin n = (n_max / 2) + 1
   1. start with <math>\delta</math> = 1
   2. if <math>\delta</math> is even compute the second order structure function D(n,<math>\delta</math>) as the segment mean of the square of the velocity difference between the bins separated by distance <math>\delta</math>r₀ centered around bin n:
      
      D(n, <math>\delta</math>) = <math>\langle</math> [v’(n+(<math>\delta</math>/2), t) - v’(n-(<math>\delta</math>/2), t)]² <math>\rangle</math>
      
      where the angled brackets indicate the mean across all t for the data segment yielding a velocity difference after the application of the Level 1 QC criteria
   3. if <math>\delta</math> is odd compute the second order structure function D(n,<math>\delta</math>) as the segment mean of the mean of the square of the velocity difference between the bins separated by distance <math>\delta</math>r₀ centered on the upper and lower extent of bin n:
      
      dv'_lo(n, <math>\delta</math>, t) = v’(n+floor(<math>\delta</math>/2), t) - v’(n-ceil(<math>\delta</math>/2), t)
      dv'_hi(n, <math>\delta</math>, t) = v’(n+ceil(<math>\delta</math>/2), t) - v’(n-floor(<math>\delta</math>/2), t)
      
      where ceil and floor indicate the upper and lower integer value respectively, then
      
      D(n, <math>\delta</math>) = <math>\langle</math> [dv'_lo(n, <math>\delta</math>, t)² + dv'_hi(n, <math>\delta</math>, t)²] / 2 <math>\rangle</math>
      
      the angled brackets again indicating the mean across all t in the data segment yielding a velocity difference after the application of the Level 1 QC criteria
   4. increment <math>\delta</math> and repeat steps until <math>\delta</math> = n_max
2. increment n and repeat steps until n + (n_max / 2) exceeds the bin number for which valid v’ are available