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Experimental observations are presented of a single surface-piercing column subject to a wide range of surface gravity waves. With the column diameter, D, chosen such that the flow lies within the drag-inertia regime, two types of high-frequency wave scattering are identified. The first is driven by the run-up and wash-down on the surface of the column in the vicinity of the upstream and downstream stagnation points. The second concerns the circulation of fluid around the column, leading to the scattering of a pair of non-concentric wavefronts. The phasing of the wave cycle at which this second mode evolves is dependent upon the time taken for fluid to move around the column. This introduces an additional time-scale, explaining why existing diffraction solutions, based upon a harmonic analysis of the incident waves, cannot describe this scattered component. The interaction between the scattered waves and the next (steep) incident wave can produce a large amplification of the scattered waves, particularly the second type. Evidence is provided to show that these interactions can produce highly localized free-surface effects, including vertical jetting, with important implications for the setting of deck elevations, the occurrence of wave slamming and the development of large run-up velocities.

The observation-based source terms available in the third-generation wave model WAVEWATCH III (i.e., the ST6 package for parameterizations of wind input, wave breaking, and swell dissipation terms) are recalibrated and verified against a series of academic and realistic simulations, including the fetch/duration-limited test, a Lake Michigan hindcast, and a 1-yr global hindcast. The updated ST6 not only performs well in predicting commonly used bulk wave parameters (e.g., significant wave height and wave period) but also yields a clearly improved estimation of high-frequency energy level (in terms of saturation spectrum and mean square slope). In the duration-limited test, we investigate the modeled wave spectrum in a detailed way by introducing spectral metrics for the tail and the peak of the omnidirectional wave spectrum and for the directionality of the two-dimensional frequency–direction spectrum. The omnidirectional frequency spectrum E ( f ) from the recalibrated ST6 shows a clear transition behavior from a power law of approximately f −4 to a power law of about f −5 , comparable to previous field studies. Different solvers for nonlinear wave interactions are applied with ST6, including the Discrete Interaction Approximation (DIA), the more expensive Generalized Multiple DIA (GMD), and the very expensive exact solutions [using the Webb–Resio–Tracy method (WRT)]. The GMD-simulated E ( f ) is in excellent agreement with that from WRT. Nonetheless, we find the peak of E ( f ) modeled by the GMD and WRT appears too narrow. It is also shown that in the 1-yr global hindcast, the DIA-based model overestimates the low-frequency wave energy (wave period T > 16 s) by 90%. Such model errors are reduced significantly by the GMD to ~20%.

An exceptionally strong westward propagating quasi‐6‐day wave (Q6DW) with zonal wavenumber 1 in connection with the rare 2019 Southern Hemispheric Sudden Stratospheric Warming (SSW) is observed by two meteor radars at 30°S and is found to modulate and interact with the diurnal tide and gravity waves (GWs). The diurnal tide is amplified every 6 days and a prominent 21 hr child wave attributed to Q6DW‐diurnal tide nonlinear interaction occurs. Q6DW modulation on GWs is confirmed as the 4–5 day periodicity in GW variances. Simultaneously, the Q6DW appears to shift its period toward the periodicity of the modulated GW variances. Enhancement is also observed in the first results of meteor radar observed Q6DW Eliassen‐Palm flux, which may facilitate the global perturbation and persistence of this Q6DW. We conclude that the observed SSW triggered Q6DW‐tide and Q6DW‐GW interactions play an important role in coupling the lower atmospheric forcings to ionospheric variabilities. Plain Language Summary Our work provides observational evidence for the 6‐day planetary wave‐tide and 6‐day planetary wave‐gravity wave interactions at the Earth's mesosphere and lower thermosphere. The results strongly support the theory that wave‐wave interactions are the primary mechanism coupling planetary waves to ionospheric variability and provide an additional mechanism as the 6‐day wave modulation on the gravity waves. We utilize measurements from two meteor radars to diagnose planetary wave characteristics and identify wave‐wave interactions, and compute the first‐time meteor radar observed Eliassen‐Palm flux. Enhancement is observed in the Eliassen‐Palm flux of 6‐day wave following the SSW maximum phase, which demonstrates that energy of the 6‐day wave is enhanced and therefore, facilitates the global perturbation and persistence of the 6‐day wave for an extended time period. While meteor radar observations are widely used to investigate planetary waves and tides, high meteor detection rate is required for further studying temperature perturbations and small scale waves (e.g., gravity waves). Thus, this work also highlights the capability of a modern multi‐static meteor radar system, Chilean Observation Network De meteOr Radars, in resolving oscillations of small spatial scales over a broad range of periods, and for calculating Eliassen‐Palm flux of planetary waves. Key Points A dominating W1 Q6DW is observed at 30°S and its Eliassen‐Palm flux is enhanced during the 2019 SH SSW Q6DW amplifies the diurnal tide every 6 days and a strong 21 hr child wave is observed Q6DW modulates the gravity wave variances and its frequency appears to shift accordingly

We develop and validate a high-order reconstruction (HOR) method for the phase-resolved reconstruction of a nonlinear wave field given a set of wave measurements. HOR optimizes the amplitude and phase of $L$ free wave components of the wave field, accounting for nonlinear wave interactions up to order $M$ in the evolution, to obtain a wave field that minimizes the reconstruction error between the reconstructed wave field and the given measurements. For a given reconstruction tolerance, $L$ and $M$ are provided in the HOR scheme itself. To demonstrate the validity and efficacy of HOR, we perform extensive tests of general two- and three-dimensional wave fields specified by theoretical Stokes waves, nonlinear simulations and physical wave fields in tank experiments which we conduct. The necessary $L$ , for general broad-banded wave fields, is shown to be substantially less than the free and locked modes needed for the nonlinear evolution. We find that, even for relatively small wave steepness, the inclusion of high-order effects in HOR is important for prediction of wave kinematics not in the measurements. For all the cases we consider, HOR converges to the underlying wave field within a nonlinear spatial-temporal predictable zone ${\\mathcal{P}}_{NL}$ which depends on the measurements and wave nonlinearity. For infinitesimal waves, ${\\mathcal{P}}_{NL}$ matches the linear predictable zone ${\\mathcal{P}}_{L}$ , verifying the analytic solution presented in Qi et al. (Wave Motion, vol. 77, 2018, pp. 195–213). With increasing wave nonlinearity, we find that ${\\mathcal{P}}_{NL}$ contains and is generally greater than ${\\mathcal{P}}_{L}$ . Thus ${\\mathcal{P}}_{L}$ provides a (conservative) estimate of ${\\mathcal{P}}_{NL}$ when the underlying wave field is not known.

We present a study on the interaction between wind and water waves with a broad-band spectrum using wave-phase-resolved simulation with long-term wave field evolution. The wind turbulence is computed using large-eddy simulation and the wave field is simulated using a high-order spectral method. Numerical experiments are carried out for turbulent wind blowing over a wave field initialised using the Joint North Sea Wave Project spectrum, with various wind speeds considered. The results show that the waves, together with the mean wind flow and large turbulent eddies, have a significant impact on the wavenumber–frequency spectrum of the wind turbulence. It is found that the shear stress contributed by sweep events in turbulent wind is greatly enhanced as a result of the waves. The dependence of the wave growth rate on the wave age is consistent with the results in the literature. The probability density function and high-order statistics of the wave surface elevation deviate from the Gaussian distribution, manifesting the nonlinearity of the wave field. The shape of the change in the spectrum of wind-waves resembles that of the nonlinear wave–wave interactions, indicating the dominant role played by the nonlinear interactions in the evolution of the wave spectrum. The frequency downshift phenomenon is captured in our simulations wherein the wind-forced wave field evolves for$O(3000)$peak wave periods. Using the numerical result, we compute the universal constant in a wave-growth law proposed in the literature, and substantiate the scaling of wind–wave growth based on intrinsic wave properties.

We study nonlinear resonant wave–wave interactions which occur when ocean waves propagate into a thin floating ice sheet. Using multiple-scale perturbation analysis, we obtain theoretical predictions of the wave amplitude evolution as a function of distance travelled past the ice edge for a semi-infinite ice sheet. The theoretical predictions are supported by a high-order spectral (HOS) method capable of simulating nonlinear interactions in both open water and the ice sheet. Using the HOS method, the amplitude evolution predictions are extended to multiple (coupled) triad interactions and a single ice sheet of finite length. We relate the amplitude evolution to mechanisms with strong frequency dependence – ice bending strain, related to ice breakup, as well as wave reflection and transmission. We show that, due to sum-frequency interactions, the maximum strain in the ice sheet can be more than twice that predicted by linearised theory. For an ice sheet of finite length, we show that nonlinear wave reflection and transmission coefficients depend on a parameter in terms of wave steepness and ice length, and can have values significantly different than those from linear theory. In particular, we show that nonlinear sum-frequency interactions can appreciably decrease the total wave energy transmitted past the ice sheet. This work has implications for understanding the occurrence of ice breakup, wave attenuation due to scattering in the marginal ice zone and the resulting ice floe size distribution.

Wave run-up phenomena driven by nonlinear wave interactions with a fixed rectangular box are investigated. Experiments are carried out in different types of uni-directional waves with normal incidence. Significant wave run-ups featuring tertiary interaction effects, similar to those reported by Molin et al. (J. Fluid Mech., vol. 528, 2005, pp. 323–354) for a fixed vertical plate, are observed in regular wave tests. Transient wave group tests are conducted for comparison, to facilitate the analysis of the tertiary interactions in irregular waves. The most striking observation is that the wave surface elevations at the centre of the front face of the fixed box can reach $4\\times$ the incident waves even in irregular waves, much larger than the ${\\sim}2\\times$ predicted from linear theory and observed for the transient groups. The extra amplification builds up slowly and is localized on the weather side of the box. It is believed to result from tertiary interactions between the incident and reflected wave fields upstream, which induce a local lensing effect and thus wave focusing on the weather side. These interactions, though a nonlinear process, occur at the first harmonic quantities rather than high harmonics. Supporting evidence is extracted from random wave runs using NewWave analysis, where surface amplifications and phase lag – both key characteristics of tertiary wave interactions – are identified. The identification of these tertiary interactions in irregular waves is new, and may be of practical importance.

This article explores how a submerged elastic plate, clamped at one edge, interacts with water waves. Submerged elastic plates have been considered as potentially effective design elements in the development of wave energy harvesters but their behaviour in a wave field remains largely unexplored, especially experimentally. Positioned at a fixed depth in a wave tank, the flexible plate demonstrates significant wave reflection capabilities, a characteristic absent in rigid plates of identical dimensions. The experiments thus reveal that plate motion is crucial for wave reflection. Sufficiently steep waves are shown to induce a change in the mean position of the plate, with the trailing edge reaching the free surface in some cases. This configuration change is found to be particularly efficient to break water waves. These findings contribute to understanding the potential of elastic plates for wave energy harvesting and wave attenuation scenarios.

We study experimentally the dynamics and statistics of capillary waves forced by random steep gravity waves mechanically generated in the laboratory. Capillary waves are produced here by gravity waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free surface, we characterize statistically the random regimes of capillary waves in the spatial and temporal Fourier spaces. For a significant wave steepness (0.2–0.3), power-law spectra are observed both in space and time, defining a turbulent regime of capillary waves transferring energy from the large scale to the small scale. Analysis of temporal fluctuations of the spatial spectrum demonstrates that the capillary power-law spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to the small scale in a fast time scale, when capillary wave trains are generated in a way similar to the parasitic capillary wave generation mechanism. The frequency and wavenumber power-law exponents of the wave spectra are found to be in agreement with those of the weakly nonlinear wave turbulence theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with wave turbulence theory. These results suggest that theoretical developments beyond the classic wave turbulence theory are necessary to describe the dynamics and statistics of capillary waves in a natural environment. In particular, in the presence of broad-scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions should be reconsidered.

The aim of the present study is to investigate the linear and nonlinear wave dynamics of a falling incompressible viscous fluid when the fluid undergoes an effect of odd viscosity. In fact, such an effect arises in classical fluids when the time-reversal symmetry is broken. The motivation to study this dynamics was raised by recent studies (Ganeshan & Abanov, Phys. Rev. Fluids, vol. 2, 2017, p. 094101; Kirkinis & Andreev, J. Fluid Mech., vol. 878, 2019, pp. 169–189) where the odd viscosity coefficient suppresses thermocapillary instability. Here, we explore the linear surface wave and shear wave dynamics for the isothermal case by solving the Orr–Sommerfeld eigenvalue problem numerically with the aid of the Chebyshev spectral collocation method. It is found that surface and shear instabilities can be weakened by the odd viscosity coefficient. Furthermore, the growth rate of the wavepacket corresponding to the linear spatio-temporal response is reduced as long as the odd viscosity coefficient increases. In addition, a coupled system of a two-equation model is derived in terms of the fluid layer thickness $h(x,t)$ and the flow rate $q(x,t)$. The nonlinear travelling wave solution of the two-equation model reveals the attenuation of maximum amplitude and speed in the presence of an odd viscosity coefficient, which ensures the delay of transition from the primary parallel flow with a flat surface to secondary flow generated through the nonlinear wave interactions. This physical phenomenon is further corroborated by performing a nonlinear spatio-temporal simulation when a harmonic forcing is applied at the inlet.