The enhancement of wave breaking activity during wave group passage is investigated using coherent field observations of the instantaneous sea surface elevation and whitecap coverage from platform-based stereo video measurements in the central North Sea. Passing wave groups are shown to be associated with a two to three-fold enhancement in the probability distribution of total whitecap coverage W whereas the enhancement of active whitecap coverage W_A is approximately five-fold. Breaking time scales and intermittency characteristics are also investigated with the inclusion of a secondary data set of W and W_A observations collected during a research cruise in the North Pacific. The time scale analysis suggests a universal periodicity in wave breaking activity within a representative sea-surface area encompassing approximately one dominant wave crest. The breaking periodicity is shown to be closely linked to the peak period of the dominant wave components, suggesting that long-wave modulation of wave breaking is a predominant mechanism controlling the intermittency of wave breaking across scales.

We examine how Eulerian statistics of wave breaking and associated turbulence dissipation rates in a field of intermittent events compare with those obtained from sparse Lagrangian sampling by surface following drifters. We use a polydisperse two-fluid model with large-eddy simulation (LES) resolution and volume-of-fluid surface reconstruction (VOF) to simulate the generation and evolution of turbulence and bubbles beneath short-crested wave breaking events in deep water. Bubble contributions to dissipation and momentum transfer between the water and air phases are considered. Eulerian statistics are obtained from the numerical results, which are available on a fixed grid. Next, we sample the LES/VOF model results with a large number of virtual surface-following drifters that are initially distributed in the numerical domain, regularly or irregularly, before each breaking event. Time-averaged Lagrangian statistics are obtained using the time series sampled by the virtual drifters. We show that convergence of statistics occurs for signals that have minimum length of approximately 1000–3000 wave periods with randomly spaced observations in time and space relative to three-dimensional breaking events. We further show important effects of (i) extent of measurements over depth and (ii) obscuration of velocity measurements due to entrained bubbles, which are the two typical challenges in most of the available in situ observations of upper ocean wave breaking turbulence. An empirical correction factor is developed and applied to the previous observations of Thomson et al. Applying the new correction factor to the observations noticeably improves the inferred energy balance of wind input rates and turbulence dissipation rates. Finally, both our simulation results and the corrected observations suggested that the total wave breaking dissipation rates have a nearly linear relation with active whitecap coverage.

Highlights

• The presence of swell in the sea state is shown to modulate the energy in the wind sea spectral tail.

• The f^-4 and f^-5 power laws used to describe the tail of the wind sea spectrum when swell is not present, are extended to the spectra including swell. This requires including swell steepness in the formulation of the power law coefficients and into the equation for the transition frequency between the Equilibrium and Saturation ranges.

• The spectra of large swell with very low winds also display f^-4 and f^-5 power laws. The power law coefficients however are a function of swell steepness, not wind speed.

• Direction of the waves in the high frequency range of the spectrum is that of the wind, no matter the swell size, steepness or direction.

• The reformulation of the equations for the spectral tail to include swell allows development of a simple equation for stress encompassing the swell effect.

We consider the observation and analysis of oceanic rogue waves collected within spatio-temporal (ST) records of 3D wave fields. This class of records, allowing a sea surface region to be retrieved, is appropriate for the observation of rogue waves, which come up as a random phenomenon that can occur at any time and location of the sea surface. To verify this aspect, we used three stereo wave imaging systems to gather ST records of the sea surface elevation, which were collected in different sea conditions. The wave with the ST maximum elevation (happening to be larger than the rogue threshold 1.25H_s) was then isolated within each record, along with its temporal profile. The rogue waves show similar profiles, in agreement with the theory of extreme wave groups. We analyze the rogue wave probability of occurrence, also in the context of ST extreme value distributions, and we conclude that rogue waves are more likely than previously reported; the key point is coming across them, in space as well as in time. The dependence of the rogue wave profile and likelihood on the sea state conditions is also investigated. Results may prove useful in predicting extreme wave occurrence probability and strength during oceanic storms.

A new ship-based stereo video system is used to observe breaking ocean waves (i.e., whitecaps) as three-dimensional surfaces evolving in time. First, the stereo video measurements of all waves (breaking and nonbreaking) are shown to compare well with statistical parameters from traditional buoy measurements. Next, the breaking waves are detected based on the presence of whitecap foam, and the geometry of these waves is investigated. The stereo measurements show that the whitecaps are characterized by local extremes of surface slope, though the larger-scale, crest-to-trough steepness of these waves is unremarkable. Examination of 103 breaking wave profiles further demonstrates the pronounced increase in the local wave steepness near the breaking crest, as estimated using a Hilbert transform. These crests are found to closely resemble the sharp corner of the theoretical Stokes limiting wave. Results suggest that nonlinear wave group dynamics are a key mechanism for breaking, as the phase speed of the breaking waves is slower than predicted by the linear dispersion relation. The highly localized and transient steepness, along with the deviation from linear phase speed, explains the inability of conventional wave buoys to observe the detailed geometry of breaking waves.

Surface elevation records from two locations in the northeast Pacific are used to examine rogue waves and the relationship to wave groups. Three hundred individual rogue waves with heights greater than 2.2 times the significant wave height are found in analyzing >2 × 106 wave groups. In contrast to recent nonlinear modeling results, we do not find that rogue waves occur at the front of wave groups. There is a tendency for steep waves to occur at the front of a group, but these are not the largest waves of the group and do not meet the rogue wave criterion. Rogue waves are most commonly located in the center of the group, but their height ratio to the neighboring crest is greater than in the average wave group. Assessing group dynamics in terms of spectral width suggests that random superposition of nonlinear waves is sufficient to explain the observations of individual rogue waves.

The spatial variability of open ocean wave fields on scales of O (10 km) is assessed from four different data sources: TerraSAR-X SAR imagery, four drifting SWIFT buoys, a moored waverider buoy, and WAVEWATCH III® model runs. Two examples from the open north-east Pacific, comprising of a pure wind sea and a mixed sea with swell, are given. Wave parameters attained from observations have a natural variability, which decreases with increasing record length or acquisition area. The retrieval of dominant wave scales from point observations and model output are inherently different to dominant scales retrieved from spatial observations. This can lead to significant differences in the dominant steepness associated with a given wave field. These uncertainties have to be taken into account when models are assessed against observations or when new wave retrieval algorithms from spatial or temporal data are tested. However, there is evidence of abrupt changes in wave field characteristics that are larger than the expected methodological uncertainties.

Observations of winds, waves, and turbulence at the ocean surface are compared with several analytic formulations and a numerical model for the input of turbulent kinetic energy by wave breaking and the subsequent dissipation. The observations are generally consistent with all of the formulations, although some differences are notable at winds greater than 15 m/s. The depth dependence of the turbulent dissipation rate beneath the waves is fit to a decay scale, which is sensitive to the choice of vertical reference frame. In the surface following reference frame, the strongest turbulence is isolated within a shallow region of depths much less than one significant wave height. In a fixed reference frame, the strong turbulence penetrates to depths that are at least half of the significant wave height. This occurs because the turbulence of individual breakers persists longer that the dominant period of the waves, and thus the strong surface turbulence is carried from crest to trough with the wave orbital motion.

Shipboard measurements of whitecap coverage are presented from two cruises in the North Pacific, and compared with in situ measurements of wind speed and friction velocity, average wave steepness, and near-surface turbulent dissipation. A threshold power law fit is proposed for all variables, which incorporates the flexibility of a power law with the threshold behavior commonly seen in whitecapping. The fit of whitecap coverage to wind speed, U₁₀, closely matches similar relations from three recent studies, particularly in the range of 6–14 m/s. At higher wind speeds, the whitecap coverage data level off relative to the fits, and an analysis of the residuals shows some evidence of reduced whitecapping in rapidly developing waves. Wave slope variables are examined for potential improvement over wind speed parameterizations. Of these variables, the mean square slope of the equilibrium range waves has the best statistics, which are further improved after normalizing by the directional spread and frequency bandwidth. Finally, the whitecap coverage is compared to measurements of turbulent dissipation. Though still statistically significant, the correlation is worse than the wind or wave relations, and residuals show a strong negative trend with wave age. This may be due to an increased influence of microbreaking in older wind seas.

Nearly all operational ocean models use air-sea fluxes and the ocean shear and stratification to estimate upper ocean boundary layer mixing rates. This approach implicitly parameterizes surface wave effects in terms of these inputs. Here, we test this assumption using parallel experiments in a lake with small waves and in the open ocean with much bigger waves. Under the same wind stress and adjusting for buoyancy flux, we find the mixed layer average turbulent vertical kinetic energy in the open ocean typically twice that in the lake. The increase is consistent with models of Langmuir turbulence, in which the wave Stokes drift, and not wave breaking, is the dominant mechanism by which waves energize turbulence in the mixed layer. Applying these same theories globally, we find enhanced mixing and deeper mixed layers resulting from the inclusion of Langmuir turbulence in the boundary layer parameterization, especially in the Southern Ocean.

Wave and wind measurements at Ocean Weather Station P (OWS-P, 50°N 145°W) are used to evaluate the equilibrium range of surface wave energy spectra. Observations are consistent with a local balance between wind input and breaking dissipation, as described by Philips (1985). The measurements include direct covariance wind stress estimates and wave breaking dissipation rate estimates during a 3 week research cruise to OWS-P. The analysis is extended to a wider range of conditions using observations of wave energy spectra and wind speed during a 2 year mooring deployment at OWS-P. At moderate wind speeds (5–15 m/s), mooring wave spectra are in agreement, within 5% uncertainty, with the forcing implied by standard drag laws and mooring wind measurements. At high wind speeds (>15 m/s), mooring wave spectra are biased low, by 13%, relative to the forcing implied by standard drag laws and mooring wind measurements. Deviations from equilibrium are associated with directionality and variations at the swell frequencies. A spectral wave hindcast accurately reproduces the mooring observations, and is used to examine the wind input.