A simple geometry that exhibits near motion trapping is tested experimentally, along with perturbed versions of the structure. The motion of the freely floating structure and the surrounding wave field is tracked and the near-motion-trapped mode is found, characterised by a slowly decaying heave motion with very small linear radiation of energy. It is found that the latter property is a better discriminator of the perturbed geometries as viscous damping masks fine differences in radiation damping as far as the motion of the structure is concerned. The magnitude of this viscous damping is reasonably well predicted by a simple Stokes oscillatory boundary layer analysis.@en

Two physical phenomena drive the Lagrangian trajectories of neutrally buoyant particles underneath surface gravity wave groups: the Stokes drift results in a net displacement of particles in the direction of propagation of the group, whereas the Eulerian return flow transports such particles in the opposite direction. Generally, the Stokes drift is the larger of the two near the surface, whereas the effects of the return flow dominate at depth. A transition depth can be defined that separates the two regimes. Using a multiple-scales expansion, we provide leading-order estimates of the forward transport, the backward transport, and the transition depth for realistic sea states. We consider the effects of both finite depth and the directionally spread nature of the waves on our estimates. We show that from the perspective of the return flow, almost all seas are of finite depth. In fact, many seas can be shown to be "shallow" from the perspective of the return flow with little variation of this flow with depth. Furthermore, even small degrees of directional spreading can considerably reduce the magnitude of the return flow and its transport.@en

The relative contributions of free waves and bound waves to the formation of an extreme wave event remains a topic of interest in offshore engineering. A variety of methods have been proposed for identifying and removing the bound wave components. The method of “phase separation” or “phase manipulation” repeats simulations/experiments of a wave field with an offset in the initial phase of the wave components and relies upon summation of the resulting wave fields to isolate the bound harmonics, following from a Stokes expansion in steepness; the method has proven effective in isolating bound harmonics but requires that all cases be repeated. Alternatively, the bound harmonics can be removed using a three-dimensional fast Fourier transform (3D-FFT) of the wave field. However, the Fourier transform requires periodicity in the signal and assumes homogeneity in space and stationarity in time, producing spurious modes otherwise. We compare the phase separation and 3D-FFT approaches for a steep, focusing wave group in deep water using the numerical simulation tool, OceanWave3D, and discuss the effectiveness of both methods.@en

Owing to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth below the surface. The motion of particles near the free surface is dominated by the waves and their Stokes drift, whereas particles at large depths follow horseshoe-shaped trajectories dominated by the Eulerian return flow. For unidirectional wave groups, a small net displacement in the direction of travel of the group results near the surface, and is accompanied by a net particle displacement in the opposite direction at depth. For deep-water waves, we study these trajectories experimentally by means of particle tracking velocimetry in a two-dimensional flume. In doing so, we provide visual illustration of Lagrangian trajectories under groups, including the contributions of both the Stokes drift and the Eulerian return flow to both the horizontal and the vertical Lagrangian displacements. We compare our experimental results to leading-order solutions of the irrotational water wave equations, finding good agreement.@en

We have investigated steep three-dimensional surface gravity wave groups formed by dispersive focusing using a fully nonlinear potential flow solver. We find that third-order resonant interactions result in rapid energy transfers to higher wavenumbers and reduced directional spreading during focusing, followed by spectral broadening during defocusing, forming steep wave groups with augmented kinematics and a prolonged lifespan. If the wave group is initially narrow-banded, quasi-degenerate interactions arise, characterised by energy transfers along the resonance angle, of the Phillips 'figure-of-eight' loop. Spectral broadening due to the quasi-degenerate interactions facilitates non-degenerate interactions, characterised by oblique energy transfers at approximately to the spectral peak. We consider the influence of steepness, finite depth, directional spreading and the high-wavenumber tail on spectral evolution. Steepness is found to augment both the quasi-degenerate and non-degenerate interactions similarly. However, a reduction in depth is found to weaken the quasi-degenerate interactions more severely than the non-degenerate interactions. We observe that increased directional spreading reduces spectral evolution, partially because wave groups with more spreading focus for a shorter duration due to linear dispersion. However, we also find that directional spreading reduces the peak rates of energy transfer. Inclusion of the high-wavenumber tail of the Joint North Sea Wave Project spectrum further reduces rates of energy transfer compared with a Gaussian wavenumber spectrum. Thus, directional spreading and the high-wavenumber tail may be integral to a form of spectral equilibrium that reduces rapid energy transfers during a steep wave event.@en

Many ocean engineering problems involve bound harmonics which are slaved to some underlying assumed close to linear time series. When analyzing signals we often want to remove the bound harmonics so as to "linearise" the data or to extract individual bound harmonic components so that they may be studied. For even moderately broadbanded systems filtering in the frequency domain is not sufficient to separate components as they overlap in frequency. One way to overcome this difficulty is to use input signals with the same linear envelope but with different phases and then use simple addition and subtraction of the resulting signals to extract different harmonics. This approach has been established for the analysis of wave groups. In this paper we examine whether this approach can be used on random time series as well. We analyse random wave time series of wave elevation from the towing tank in Shanghai Jiao Tong University and force measurements on a cylinder taken in the Kelvin tank at the University of Strathclyde.@en

High wind speeds generated during hurricanes result in the formation of extreme waves. Extreme waves by nature are steep meaning that linear wave theory alone is insufficient in understanding and predicting their occurrence. The complex, highly transient nature of the direction of wind and hence of waves generated during hurricanes affects this nonlinear behavior. Herein, we examine how this directionality can affect the second-order nonlinearity of extreme waves generated during hurricanes. This is achieved through both deterministic calculations and experiments based on the observations of Young (2006, "Directional Spectra of Hurricane Wind Waves," J. Geophys. Res. Oceans, 111(C8), epub). Our calculations show that interactions between the tail and peak of the spectrum can become significant when they travel in different directions, resulting in second-order difference components that exist in the linear range of frequencies. These calculations are generally supported by experimental observations, but we note the difficulty of generating and focusing the high-frequency tail of the spectrum experimentally. Bound second-order difference components or subharmonics typically exist as low frequency infra-gravity waves. Components that exist in the linear range of frequencies may be missed by conventional methods of processing field data where low-pass filtering is used and hence overlooked. In this note, we show that in idealized directional spreading conditions representative of a hurricane, failing to account for second-order difference components may lead to underestimation of extreme wave height.@en

The net movement of Lagrangian particles under water waves comprises a Stokes drift in the direction of wave propagation and an Eulerian return flow in the opposing direction. Accurate prediction of the Eulerian return flow in the ocean is of importance in modeling the transport of plastic pollution, oil, wreckage, and sediment. Herein, we derive a multiple-scales solution for the Eulerian mean flow under wave packets that is valid for all water depths, relative to both the length of the wave and the length of the wave packet. To validate this solution, we carry out particle tracking velocimetry experiments in a long flume to extract the mean motion from Lagrangian seeding particles under wave packets, finding good agreement. The extraction technique is able to deal with small background motion and subharmonic error waves associated with wave generation by the paddle, the latter being relatively large in finite-depth flume experiments. In finite depth, the return flow is forced by both the divergence of the Stokes transport on the wave-packet scale and the formation of a non-negligible mean set-down underneath the packet, which acts like a bounding streamtube in the form of a convergent-divergent duct. The magnitude of the horizontal return flow is thus enhanced, with particular relevance to transport in the finite-depth coastal environment.@en