∑ (cos *X *- cos *X *)(cos *Y *- cos *Y *)

=

(12)

∑ ( *X *- cos *X *) ∑ (*Y *- cos *Y *)

2

2

∑ (sin *X *- sin *X *)(sin *Y *- sin *Y *)

(13)

∑ ( *X *- sin *X *) ∑ (*Y *- sin *Y *)

2

2

1

(*R*U 2 + *R*V 2 )

(14)

2

Figure 37 contains scatterplots of wave directions near the spectral peak for

collocated CIIS and ADV observations. Only CIIS observations meeting the

coherence cutoff criterion were selected for comparison. Table 6 summarizes the

scatterplots. The statistics show good correlation between the two measurement

techniques, with low scatter indices. Where the CIIS coherence cutoff criterion

is met, wave directions are typically within the reported margin of error for the

ADV probe measurements.

σθ

a

Structure 1

2.64

4.57

4.58

8

0.89

Structure 2

1.98

7.02

6.99

12

0.79

b

Structure 3

-5.16

13.08

13.14

24

0.77

c

Structure 4

-1.27

7.78

7.66

14

0.93

a

Structure 1: Only experiments X4, X5, X6 analyzed.

b

Structure 3: X1c and X2c did not meet coherence cutoff criterion.

c

Structure 4: X2 did not meet coherence cutoff criterion.

Analysis of pixel array timestacks resulted in estimates of mean spectral

density *S*( *f *) and vector-mean wave direction θm( *f *). To demonstrate the video

system application, peak vector-mean wave direction for Structure 1, Experiment

2 (random wave, *f*peak = 1.25 Hz) is indicated by arrows (scaled by wave celerity)

superimposed on a rectified snapshot of the wave field in Figure 38. Arrows

with a circled tail represent directions obtained from analyses meeting the strict

coherence cutoff criterion. Some arrows without circled tails are spurious in

direction and magnitude in the diffraction area behind the breakwater.

52

Chapter 5 Video-Based Wave Direction Measurement

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