Processing your ADCP data using structure function techniques

Structure Function Processing Steps

1. Extract or compute the along-beam distance of the center of each bin [z_b] and bin center separation [r0]
2. Calculate the along-beam velocity fluctuations in each bin [v’(z_b)]
   1. If using burst sampling, calculations are done over the length of the burst if stationary
   2. If using continuous sampling, a time interval must be selected in which the flow can assumed to be stationary
   3. You can calculate the fluctuations around:
      1. The mean of the time interval
      2. A linear detrend of the time interval
      3. A low pass filtered signal
3. Select the maximum distance over which to compute the structure function based on conditions of the flow (e.g., expected max overturn) [r_max]
4. Start at the first bin where z_b >= r_max/2
5. Compute the centered difference of v’ along the beam for the first pair of bins on either side: v’(z+r₀)-v’(z-r₀)
6. Compute the second order structure function D(z,r) = mean-square of the velocity fluctuation difference: D(z,2*r0) = mean(v’(z+r₀)-v’(z-r₀))2
7. Repeat steps 5-6 for all pairs of bins where the separation distance between bins r <= r_max
8. With these data points, fit a line to the form D(z,r) = N + Ar²/3 to estimate values for A and N where A = Cv²ε²/3 and N is an estimate of the uncertainty due to noise.
9. Solve for ε using Cv² = 2.1
10. Repeat the steps in (5) – (9) for each bin until z_b + r_max/2 >= end of profile

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