# Measurements of High-Froude Number Boat Wakes near a Seawall
## 3 Results
### Bulk Properties  
The AWD detected wakes by identifying peaks in the \(M^{\prime}\) function. False positives were found in cases of high wind-wave activity. These were characterized by values of \(||Wh^{\prime}||\) along the lower-frequency portion of the maximum K-line \(f\) less than about 0.178 Hz being \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Pass** & \(\mathbf{M^{\prime}}\) & \(\mathbf{\tau_{1}}\) & \(\mathbf{T_{2}}\) & \(\mathbf{T_{3}}\) & \(\mathbf{\tau_{1}}^{*}\) & \(\mathbf{\tau_{3}}^{*}\) \\
**\#** & **(\(\times 10^{-3}\))** & **(min)** & **(min)** & **(min)** & **(s)** & **(min)** \\ \hline
1 & 8.7 & 1.2 & 2.0 & 3.4 & 10 & 2.0 \\
2 & 7.9 & 0.9 & 1.1 & 1.7 & 25 & 2.5 \\
3 & 8 & 1.0 & 2.0 & 2.6 & 30 & 2.6 \\
4 & 4.4 & 0.2 & 1.6 & 2.0 & 5 & 1.9 \\
5 & 1.2 & 2.0 & 2.9 & 3.8 & 65 & 3.7 \\
6 & 0.6 & 1.4 & NA & 1.6 & 15 & 2.2 \\
7 & 1.1 & 2.8 & 3.6 & 4.5 & 90 & 4.4 \\
8 & 1.3 & 2.4 & 3.0 & 4.0 & 75 & 4.0 \\
9 & 3.2 & 0.8 & 2.0 & 2.8 & 25 & 2.5 \\
10 & 5.4 & 0.2 & 1.3 & 2.2 & 5 & 1.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of boat passes (Table 1). Shown are peak values of \(\mathbf{M^{\prime}}\), the duration of the primary wake (\(\mathbf{\tau_{1}}\)), the reflected wake (\(\mathbf{\tau_{2}}\)), and the full wake (\(\mathbf{\tau_{3}}\)) determined from Figure 9. Also shown are duration estimates from AWD of the primary wake (\(\mathbf{\tau_{1}}^{*}\)) and the full duration (\(\mathbf{\tau_{3}}^{*}\)). Figure 11: Duration of primary supervised wakes from AWD (\(\mathbf{\tau_{1}}^{*}\)) vs. measured duration of (**a**) primary wake (\(\mathbf{\tau_{1}}\)) from \(||Wh^{\prime}||\) (dots); (**b**) total wake (\(\mathbf{\tau_{3}}\)) from \(||Wh^{\prime}||\) (dots). Linear fit to all but Pass 1 and 6 is show (red) with the slopes and intercepts indicated. much lower than the high-frequency portion, indicating that the K-line was sampling wind waves. Instances with mean values in the lower frequency portion were \(<1/5\) of the mean in the higher-frequency portion were eliminated. After this quality control procedure, the AWD yielded 383 wakes, with a mean duration of 5.3 min. Vessel operations are generally determined by vessel type and function. Recreational boaters prefer to be on the water during times of high visibility. Most of the AWD-identified wakes were found during daylight hours (Figure 12), consistent with boat activity being comprised of recreational vessels. Wakes outside these times may have been law enforcement or from boats engaged in night fishing, but there was insufficient information to confirm this conjecture. As noted above, many wakes had no reflection. The occurrence of reflection was found to be tidally controlled. The water depth \(D(t)\) computed from \(h(t)\) determined the reflectivity of the seawall. All reflections, identified manually by the presence of a second dispersive wake in \(||Wh^{\prime}||\) immediately following an AWD-identified wake, occurred for \(D\geq 0.5\) (Figure 12). No reflected waves were identified during relatively shallow time periods. This was likely due to the shoaling of the shoreline which is exposed during low tide and submerged during high tide. In future studies, the effective reflectivity of the seawall might be estimated by examining the ratio of the reflected wave energy compared to that of the incoming wave. Figure 12: Statistics derived from AWD. (**a**) The hour of objectively identified wakes; (**b**) relative water depth (\(D\)) during reflection identified subjectively; (**c**) amplitude of all objectively identified wakes. The maximum amplitudes of each wake were determined using (4) with \(\mathcal{H}\) defined as a polygon around each AWD-identified wake. The beginning of each polygon was 1 min prior to the identified time and the end determined using the relation between \(\tau_{3}\) and \(\tau_{1}^{*}\) in the previous section. The polygon sides were curved to match the maximum K-line associated with each wake. The mean amplitude of the identified wakes was 1.1 cm with a median of 0.8 cm.