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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

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%.

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 dynamics of wind-generated water waves in the principal stage of the Phillips theory (Phillips, J. Fluid Mech., vol. 2, 1957, pp. 417–445) is investigated by a combined numerical and analytical approach. We perform a number of high-resolution direct numerical simulation (DNS) of turbulent wind over initially calm water to capture the multistage generation of water waves. Detailed analyses are conducted to evaluate the Phillips theory in both physical space and wavenumber space. Numerical evidence is obtained for the existence of a principal stage when the surface elevation variance grows linearly with time. We further propose a random sweeping turbulence pressure–wave interaction model by introducing the random sweeping hypothesis of air pressure fluctuations to the Phillips theory, and obtain an asymptotic solution of the mean square of surface wave elevations over time. This asymptotic analysis captures the temporal oscillations of surface elevation variance in the principal stage, which is also confirmed by our DNS results. The wavenumber spectrum of surface wave elevations is analysed using a time-dependent norm to elucidate the role of the resonance mechanism on wave generation. In physical space, we use the random sweeping turbulence pressure–wave interaction model to obtain a quantitative prediction of the growth rate of surface elevation variance in the principal stage, which is found to agree with the DNS results better than the original Phillips model.

A numerical model that allows one to study numerically the evolution of waves along the test section of a wind-wave tank is offered. The simulations are directly related to wind-wave tank experiments carried out for a range of steady wind velocities. At each wind forcing condition, the evolving wind-wave field is strongly non-homogeneous, with wave energy growth along the test section accompanied by frequency downshifting. The wave parameters measured at a short fetch serve as a basis for generating numerous realizations of the initial conditions in the Monte Carlo numerical simulations. The computations are based on a modified unidirectional spatial version of the Zakharov equation that accounts for wind input and dissipation and is applicable for the whole range of wind velocities employed. The model contains two empirical parameters that are selected by comparison of the experimental and numerical results; the same values of those parameters are applied for all wind forcing conditions. The availability of an experimentally verified numerical model allows one to study the contributions of nonlinear wave–wave interactions, dissipation and wind input separately. Special attention is given to accounting for the three-dimensional and random nature of wind waves as observed in experiments. The suggested model combines approaches adopted in the wind-wave growth theories by Miles and Phillips.

Irregular, unidirectional surface water waves incident on model ice in an ice tank are used as a physical model of ocean surface wave interactions with sea ice. Results are given for an experiment consisting of three tests, starting with a continuous ice cover and in which the incident wave steepness increases between tests. The incident waves range from causing no breakup of the ice cover to breakup of the full length of ice cover. Temporal evolution of the ice edge, breaking front, and mean floe sizes are reported. Floe size distributions in the different tests are analyzed. The evolution of the wave spectrum with distance into the ice-covered water is analyzed in terms of changes of energy content, mean wave period, and spectral bandwidth relative to their incident counterparts, and pronounced differences are found between the tests. Further, an empirical attenuation coefficient is derived from the measurements and shown to have a power-law dependence on frequency comparable to that found in field measurements. Links between wave properties and ice breakup are discussed.

In this work we study features of inertia-gravity wave turbulence in the rotating shallow water equations. On examining the dynamics of waves with varying rotation rates, we find that the turbulent cascade of waves is strongest at low rotation rates, forming a $k^{-2}$ energy spectrum, and a rich distribution of shocks in physical space. At high rotation rates, the forward cascade of waves weakens along with a steeper energy spectra and vanishing of shocks in physical space. The wave cascade is seen to be scale-local, resulting in a noticeable time interval for energy to get transferred from domain scale to dissipative scale. Furthermore, we find that the vortical flow has a non-negligible effect on the wave cascade, especially at high rotation rates. The vortical flow assists in the forward cascade of waves and shock formation at high rotation rates, while the waves by themselves in the absence of the vortical flow lack a forward cascade and shock formation at such high rotation rates. On investigating the physical space structures in the vortical flow and their connections to the wave cascade, we find that strain-dominant regions, that are located around the boundaries of coherent vortices, are the physical space regions that contribute majorly to the forward cascade of waves. Our results in general highlight intriguing features of dispersive inertia-gravity wave turbulence that are qualitatively similar to those seen in three-dimensional homogeneous isotropic turbulence and are beyond the predictions of asymptotic resonant wave interaction theory.

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 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.

The generation of broadband wave energy frequency spectra from narrowband wave forcing in geophysical flows remains a conundrum. In contrast to the long-standing view that nonlinear wave–wave interactions drive the spreading of wave energy in frequency space, recent work suggests that Doppler-shifting by geostrophic flows may be the primary agent. We investigate this possibility by ray tracing a large number of inertia–gravity wave packets through three-dimensional, geostrophically turbulent flows generated either by a quasigeostrophic (QG) simulation or by synthetic random processes. We find that, in all cases investigated, a broadband quasi-stationary inertia–gravity wave frequency spectrum forms, irrespective of the initial frequencies and wave vectors of the packets. The frequency spectrum is well represented by a power law. A possible theoretical explanation relies on the analogy between the kinematic stretching of passive tracer gradients and the refraction of wave vectors. Consistent with this hypothesis, the spectrum of eigenvalues of the background flow velocity gradients predicts a frequency spectrum that is nearly identical to that found by integration of the ray tracing equations.