Nominal wake measurement

• Steady straight towing condition

• Measurement location x/L = 0.935

• At point A, the number of data N = 1,720 (N_total =2,250) collected from 30 carriage runs.

• N < N_total due to the locally insufficient PIV particle density and by rejecting spurious vectors at the data reduction phase.

Mean axial velocity, U	Turbulent kinetic energy, k

1. Instantaneous velocity data and probability density function

• U, V, W data are apparently stationary, random, and normal.

  • Mean values, x = 0.534, -0.023, 0.059

  • Variance values, s² = 0.0075, 0.0035, 0.0024

Data	Probability density function

2. Running mean and variance

• Time histories of the mean x and variance s² values as increasing the number of sample N.

• For each N, s² is recalculated with the new x value using the following recursive equation:

   

• x converges fast, typically for N > 100.

• s² first fluctuates large and converges slowly for N > 500.

Mean	Variance

3. Statistical convergence error

• E and E_U exhibit similar curve shapes as the typical example cases shown earlier.
• At N = 1,720,

E (% U_C) = 0.4, 0.3, 0.3 for U, V, W, respectively.

E_U (% k) = 8, 4, 3 for uu, vv, ww, respectively.

Mean velocity	Reynolds normal stresses