# Measurements of High-Froude Number Boat Wakes near a Seawall
## 1 Introduction  
Boat-driven waves [1, 2], generally known as \"wakes\" or \"wash\", along with wind-driven waves are primary mechanisms of coastal erosion and bank retreat [3, 4, 5, 6, 7]. Seawalls are a common form of hardening built to protect shorelines from wave energies, but these reflect waves back into the environment and can generate scouring at their base [8, 9]. In regions of frequent boat activity, wakes can potentially compromise the stability of protective structures, such as seawalls, levees and reventments [10, 11], archaeological sites [11], and other nearshore structures. Wakes can also create a broad range of negative impacts on aquatic ecosystems. For example, wakes can enhance sediment resuspension and turbidity, inundate nesting shorebirds, and displace invertebrates, fish eggs, and larvae [12, 13, 14]. Understanding wake properties is therefore essential for resiliency planning of many coastal regions [15]. Boat wake form, amplitude, and propagation vary with vessel shape, speed, and size, along with water depth and dimensions of the water body [16, 17, 18]. The multivariate dependence of wake properties has motivated the use of in situ measurements of wakes in order to determine wake characteristics in specific locations and vessel traffic patterns. We present results from a field study of wind waves and recreational boat wakes in a sheltered sub-embayment of Tampa Bay, FL, that employed novel methods for assessing wave reflection and identifying and measuring ship wakes. Ship wakes are wave packets generated by objects moving on or near the water surface. They form their distinctive \"V'-shape due to the dispersion properties of surface gravity waves, as first derived by [PERSON] [19] for a point source in deep, open water, and explored by others for more general cases [20; 21; 22; 23]. Wakes travel at the group velocity \(c_{g}\). Boat wakes are typically created when a vessel travels above a minimum value of the length-based Froude number \(F_{L}=U(gL)^{-1/2}\gtrsim 0.1\)[24; 25; 26], where \(L\) and \(U\) are the ship length and speed, respectively, and \(g\) = 9.8 m s\({}^{-2}\) is the gravitational acceleration. Wake amplitude (and associated wave drag) increases with \(U\), reaching a peak near the \"hull speed\" at \(F_{L}\sim\)0.4 [27; 28], limiting the speed of displacement vessels. These wakes typically have two primary components. The first is the dispersive \"divergent\" component whose signal increases in frequency when measured at a fixed point (\"chirp\"). The second is the relatively narrow-banded \"transverse\" wave. Some moderate sized and many small personal water craft can operate in planing or semiplaning mode, and can travel above hull speed by exploiting hydrodynamic lift forces [25; 29]. The transverse component and the total wake height of (semi)planing boats generally decrease as their speed increases above hull speed. The angle from the shipline at which the wake travels is 35\({}^{\circ}\) in the Kelvin solution and increases for \(F_{L}\geq 0.4\)[22; 30; 31; 32]. In shallow water, the depth-based Froude number, \(F_{h}=U(gh)^{-1/2}\), where \(h\) is the water depth, also plays a determining role in the wake angle and propagation. Many earlier studies of boat wakes were restricted to conditions where wakes dominated the wave field, either due to limited wind fetch or relatively high amplitude wakes, in order to better isolate the wake signals. In the more general case, windowed Fourier and wavelet techniques have been widely applied to provide a visualization of the time-frequency behavior of dispersive wake packets that often allows for wakes to be identified and distinguished from wind-generated waves [33; 34; 35; 36]. However, in those studies wakes were generally identified by manual inspection of the wavelet amplitude, a potentially laborious procedure when working with large data sets. One novel aspect of this study was the development of a new wavelet-based objective method for wake identification that yielded the wake start time, duration, and chirp rate.