# Measurements of High-Froude Number Boat Wakes near a Seawall
## 3 Results
### Supervised Boat Passes  
Most of the wakes recorded in this study were undocumented, with no information on the boat size, speed, direction, or location that generated the wave signals. Supervised boat passes allowed a direct association between recorded wakes at a particular time and vessel activity, as well as testing and calibration of the AWD. Ten passes over a variety of paths, speeds, and distances from the gauge were conducted over 1 h using a single boat (Figure 7, Table 1). The odd-numbered passes were from the west or northwest, and the even-numbered were from the east or southeast. The mean water depth at the gauge changed from 1.28 m to 1.16 m from the first to final transit. Passes 5, 7, and 8 were farthest from the gauge, about 330 m, and 2, 4, and 10 were the closest, about 5, 5, and 1 m, respectively. Passes 7-10 were the fastest, and 6 the slowest. Values of \(F_{L}\) ranged from 0.4 to about 2, and \(F_{h}\) ranged from 0.8 to 4.2, assuming a mean depth of 1.2 m. The water depth over each path varied, with several being between 2 and 3 m deep, but \(F_{h}\) remained > 1. The start of the generated wakes at the gauge were all identifiable as rapid increases in the amplitude of \(h^{\prime}\), followed by a decline over many oscillations to near background levels (Figure 8). The signal strength of each wake varied, and their maxima were taken as representative of the wake amplitude. All wakes were composed of a single wave form, except for wakes 4 and 10, both of which generated two distinct wave packets separated by about 15 and 30 s, respectively. The largest wake was from pass 1, with an amplitude of 51 mm. This wake also had a waveform distinct from the others, likely due to the boat motor being trimmed up, pushing the bow higher, the stern lower, and increasing the effective \(F_{L}\) and \(F_{h}\). All other passes were with vertical trim. The second largest was from pass 4 at 32 mm. The weakest wakes were from passes 7-9, with amplitudes 8-9.5 mm (Table 1). These low-amplitude wakes were also the highest \(F_{L}\), except for pass 10 that had \(F_{L}=1.9\) but generated a higher wake amplitude, 23 mm. This was due to the proximity of the travel line to the gauge, a minimum of \(\sim\)1 m, so there was little time for the initial disturbance to disperse. Figure 6: Paths of boat wakes generated by boat passing (heavy arrow) at an angle \(\theta\) with respect to straight seawall. The angle of propagation relative to the shipline is \(\phi\). The gauge-intersecting paths of reflected wake (L\({}_{1}\) + L\({}_{2}\)) and directly impacting wake (L\({}_{\alpha}\)) are indicated. Figure 8: Wakes from supervised boat passes (Figure 7) on 29 November 2022: (**a**) high-passed water level (\(h^{\prime}\)) from sensor 1 (orange). Objectively identified wake times (cyan); (**b**) the natural logarithm of the wavelet amplitude. K-lines of identified primary wakes (solid black) are indicated; (**c**) Wake-detection function (\(M\), orange), smoothed (\(\overline{M}\), yellow), and rectified (\(M^{\prime}\), purple). The wake between pass 7 and 8 was not part of this study. See Table 1 for details of each pass. Figure 7: Boat passes 29 November 2022 (green) near the wave gauge (red). Start, middle, and end boat positions indicated with circles. Pass number is indicated near the starting point. The gauge position was (82.677326\({}^{\circ}\) W, 28.009944\({}^{\circ}\) N). Mean bathymetry (contours) from [73] was adjusted to match the mean gauge depth. See Table 1 for boat speed. One other boat traveled through the study area between passes 7 and 8. This was identified as a Carolina skiff about 5 m in length on a path such that its wake was recorded by the gauge. No other boats were in the vicinity of the gauge during this time. The AWD correctly identified the presence of 11 wakes in the supervised period (Figure 8a). The times of maximum \(M^{\prime}\) and their associated \(K\)-lines showed a close correspondence with the primary wakes revealed in \(\|Wh^{\prime}\|\) (Figure 8b).