ALBERT

Description: Wave–current interaction can result in significant inhomogeneities of the ocean surface wave field, including modulation of the spectrum, wave breaking rates, and wave statistics. This study presents novel airborne observations from two experiments: 1) the High-Resolution Air–Sea Interaction (HiRes) experiment, with measurements across an upwelling jet off the coast of Northern California, and 2) an experiment in the Gulf of Mexico with measurements of waves interacting with the Loop Current and associated eddies. The significant wave height and slope varies by up to 30% because of these interactions at both sites, whereas whitecap coverage varies by more than an order of magnitude. Whitecap coverage is well correlated with spectral moments, negatively correlated with the directional spreading, and positively correlated with the saturation. Surface wave statistics measured in the Gulf of Mexico, including wave crest heights and lengths of crests per unit surface area, show good agreement with second-order nonlinear approximations, except over a focal area. Similarly, distributions of wave heights are generally bounded by the generalized Boccotti distribution, except at focal regions where the wave height distribution reaches the Rayleigh distribution with a maximum wave height of 2.55 times the significant wave height, which is much larger than the standard classification for extreme waves. However, theoretical distributions of spatial statistics that account for second-order nonlinearities approximately bound the observed statistics of extreme wave elevations. The results are discussed in the context of improved models of breaking and related air–sea fluxes.

Description: 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%.

Description: An analysis of airborne wave observations collected in the Gulf of Tehuantepec is presented. The data include lidar measurements of the surface displacement as a function of two horizontal dimensions in fetch-limited conditions, with fetches between 20 and 500 km and winds between 10 and 20 m s−1. The spatial data have an advantage over the commonly used single-point time series measurements, allowing direct estimates of the wavelength and wave slope, including spatial information such as the lengths of crests exceeding various thresholds. This study presents an analysis of several statistical wind wave parameters, including the joint probability distribution function (pdf) of wave amplitudes and wavelengths; the pdf of wave heights, wavenumber vectors, and wave slopes; as well as the statistics of the lengths of crests exceeding threshold wave heights and slopes. The empirical findings from the lidar data are compared against analytical theories in the literature, including some that had not been tested previously with field data such as the work by M. S. Longuet-Higgins describing the length of contours surrounding large wave heights per unit surface area. The effect of second-order nonlinearities on the distribution of crest lengths per unit surface area is investigated with analytical approximations and stochastic numerical simulations from computed directional wavenumber spectra. The results show that second-order nonlinearities can increase the crest-length distribution of large waves by a factor of 2 or more.

Description: During the Gulf of Tehuantepec Experiment (GOTEX), conducted in February 2004, surface-wave measurements were collected using a scanning lidar [Airborne Topographic Mapper (ATM)] on the National Science Foundation (NSF)/NCAR C-130 aircraft during fetch-limited conditions with winds speeds ranging from 10 to 25 m s−1. The authors present direct comparisons between the observed evolution of the wave field and numerical simulations using a parameterization of the wave energy dissipation. For low and intermediate wavenumbers, the dissipation corresponds to the saturation-based parameterization by Alves and Banner. However, at higher wavenumbers, their formulation cannot maintain saturation of the spectrum. Here, the authors use a dissipation term that forces the spectrum to match the empirical degree of saturation and explicitly balances the wind input and the nonlinear energy fluxes. All model simulations were carried out with “exact” computations of the nonlinear energy transfer because of four-wave resonant interactions and two empirical wind input functions. There is a good agreement for the integral parameters between the observations and the simulations, with root-mean-square (rms) errors between 5% and 12%. The tail of the computed omnidirectional wavenumber spectrum ϕ(k) can be approximated by two ranges: an equilibrium range, where ϕ ∝ k−5/2, and a saturation range, where ϕ = Bk−3, where B is the empirically determined degree of saturation. However, within the equilibrium range, the modeled ϕ overestimates the energy with rms errors between 20% and 50%, and the computed spectra are found to be narrower than the observations by about 10°. Similarly, the modeled bimodal directional distributions, at wavenumbers higher than the spectral peak, exhibit lobe separations and amplitudes that are consistently smaller than the observations. The lobe separation of the bimodal directional distribution for all simulations approximately scales with the square root of the wave age, which is consistent with the observations. The reasons for differences between the measurements and the simulations are discussed.

Description: A large-eddy simulation (LES) model, which adopts wave-averaged equations with vortex force, is used to investigate Langmuir turbulence and ocean boundary layer (OBL) dynamics in high-wind hurricane conditions. The temporally evolving spatially asymmetric wind and wave Stokes drift velocity imposed in the LES are generated by a spectral wave prediction model adapted to Hurricane Frances traveling at a speed of 5.5 m s−1. The potency of Langmuir turbulence depends on the turbulent Langmuir number, the wind–Stokes drift alignment, and the depth scale of the Stokes profile Ds relative to the OBL depth h. At the time of maximum winds, large-scale vigorous coherent cells develop on the right-hand side of the storm under the inertially rotating winds; the Stokes drift velocity is well tuned to the surface winds. Much weaker cells develop on the left-hand side of the storm, partly because of reduced Stokes production. With misaligned winds and waves the vertical momentum fluxes can be counter to the gradient of Stokes drift, and the cell orientation tracks the direction of the mean Lagrangian shear. The entrainment flux is increased by 20% and the sea surface temperature is 0.25 K cooler on the right-hand side of the storm in the presence of Langmuir turbulence. Wave effects impact entrainment when the ratio Ds/|h| 〉 0.75. Because of wind–wave asymmetry Langmuir cells add quantitatively to the left–right asymmetry already understood for hurricanes due to resonance. And the transient evolution of the OBL cannot be understood simply in terms of equilibrium snapshots.

Description: The authors present airborne observations of fetch-limited waves during strong offshore winds in the Gulf of Tehuantepec. The measurements, collected over a wide range of fetches, include one- and two-dimensional surface wavenumber spectra and turbulent fluxes in winds up to 25 m s−1. The evolution of the wave spectra is in good agreement with the fetch relationships from previous observations. The tails of the observed one-dimensional k1 spectra, in the dominant wave direction, exhibit a power law over a wide range of wavenumbers. The authors present the first quantification of the transition between the equilibrium and saturation ranges for the omnidirectional spectrum in the wavenumber domain. The energy density within the equilibrium range shows a dependence on the wave age. At wavenumbers higher than the spectral peak, the width of the spectrum in the direction orthogonal to the dominant waves is nearly independent of the wave age. However, in the azimuthal direction, the spreading of the spectrum decreases with increasing effective wave age. The bimodal directional distribution, characterized by the lobe amplitude and separation, shows a consistent scaling with both parameters collapsing when scaled by the square root of the wave age. The one-dimensional fetch-limited k1 spectrum is well parameterized with dependence on the effective fetch and friction velocity. At higher wavenumbers within the saturation range, although the one-dimensional saturation in the dominant wave direction is independent of the wind forcing, the saturation in the crosswind direction is weakly dependent on the effective wave age and on average 30% larger than that in the downwind direction. The results are discussed in the context of previous observations and current numerical wind-wave prediction models.

Description: Knowledge of horizontal relative dispersion in nearshore oceans is important for many applications including the transport and fate of pollutants and the dynamics of nearshore ecosystems. Two-particle dispersion statistics are calculated from millions of synthetic particle trajectories from high-resolution numerical simulations of the Southern California Bight. The model horizontal resolution of 250 m allows the investigation of the two-particle dispersion, with an initial pair separation of 500 m. The relative dispersion is characterized with respect to the coastal geometry, bathymetry, eddy kinetic energy, and the relative magnitudes of strain and vorticity. Dispersion is dominated by the submesoscale, not by tides. In general, headlands are more energetic and dispersive than bays. Relative diffusivity estimates are smaller and more anisotropic close to shore. Farther from shore, the relative diffusivity increases and becomes less anisotropic, approaching isotropy ~10 km from the coast. The degree of anisotropy of the relative diffusivity is qualitatively consistent with that for eddy kinetic energy. The total relative diffusivity as a function of pair separation distance R is on average proportional to R5/4. Additional Lagrangian experiments at higher horizontal numerical resolution confirmed the robustness of these results. Structures of large vorticity are preferably elongated and aligned with the coastline nearshore, which may limit cross-shelf dispersion. The results provide useful information for the design of subgrid-scale mixing parameterizations as well as quantifying the transport and dispersal of dissolved pollutants and biological propagules.

Description: A semiempirical determination of the spectral dependence of the energy dissipation due to surface wave breaking is presented and then used to propose a model for the spectral dependence of the breaking strength parameter b, defined in the O. M. Phillips’s statistical formulation of wave breaking dynamics. The determination of the spectral dissipation is based on closing the radiative transport equation for fetch-limited waves, measured in the Gulf of Tehuantepec Experiment, by using the measured evolution of the directional spectra with fetch, computations of the four-wave resonant interactions, and three models of the wind input source function. The spectral dependence of the breaking strength is determined from the Kleiss and Melville measurements of the breaking statistics and the semiempirical spectral energy dissipation, resulting in b = b(k, cp/u*), where k is the wavenumber and the parametric dependence is on the wave age, cp/u*. Guided by these semiempirical results, a model for b(k, cp/u*) is proposed that uses laboratory data from a variety of sources, which can be represented by b = a(S − S0)n, where S is a measure of the wave slope at breaking, a is a constant, S0 is a threshold slope for breaking, and 2.5 〈 n 〈 3 is a power law consistent with inertial wave dissipation scaling and laboratory measurements. The relationship between b(S) in the laboratory and b(k) in the field is based on the relationship between the saturation and mean square slope of the wave field. The results are discussed in the context of wind wave modeling and improved measurements of breaking in the field.