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Leonel Romero and W. Kendall Melville

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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.

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Sarah T. Gille and Leonel Romero

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Autonomous Lagrangian Circulation Explorer (ALACE) floats were designed to measure subsurface velocities throughout the global ocean. In order to transmit their data to satellite, they spend 24 h at the ocean surface during each 10–25-day cycle. During this time the floats behave as undrogued drifters. In the Southern Ocean, floats tend to advect downwind and, in accordance with Ekman theory, slightly to the left of the wind during their time at the surface. Mean displacements are likely to carry floats northward and, correspondingly, with each cycle, the Southern Ocean floats will move into warmer water with higher dynamic height. Because of large variability, the northward trend may not be discernible for any single float: in 2 years' worth of 10-day cycles, a typical float will be displaced 100 ± 270 km northward relative to a float that never surfaces. Float surface velocities and wind speed are statistically correlated at the 95% confidence level. Compared with drogued drifters, floats tend to move more rapidly, are advected more strongly downwind, and are more sensitive to changes in wind speed. Regression coefficients estimated from the differences between float and drogued drifter velocities suggest that floats may be used to estimate the mean upper ocean currents in regions where drogued drifter data are not available.

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Leonel Romero and W. Kendall Melville

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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 k 1 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 k 1 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.

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Leonel Romero and W. Kendall Melville

Abstract

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 ϕk −5/2, and a saturation range, where ϕ = B k −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.

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Leonel Romero, Luc Lenain, and W. Kendall Melville

Abstract

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.

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Leonel Romero, W. Kendall Melville, and Jessica M. Kleiss

Abstract

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(SS 0)n, where S is a measure of the wave slope at breaking, a is a constant, S 0 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.

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Peter P. Sullivan, Leonel Romero, James C. McWilliams, and W. Kendall Melville

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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.

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Leonel Romero, J. Carter Ohlmann, Enric Pallàs-Sanz, Nicholas M. Statom, Paula Pérez-Brunius, and Stéphane Maritorena

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Coincident Lagrangian observations of coastal circulation with surface drifters and dye tracer were collected to better understand small-scale physical processes controlling transport and dispersion over the inner shelf in the Gulf of Mexico. Patches of rhodamine dye and clusters of surface drifters at scales of O(100) m were deployed in a cross-shelf array within 12 km from the coast and tracked for up to 5 h with airborne and in situ observations. The airborne remote sensing system includes a hyperspectral sensor to track the evolution of dye patches and a lidar to measure directional wavenumber spectra of surface waves. Supporting in situ measurements include a CTD with a fluorometer to inform on the stratification and vertical extent of the dye and a real-time towed fluorometer for calibration of the dye concentration from hyperspectral imagery. Experiments were conducted over a wide range of conditions with surface wind speed between 3 and 10 m s−1 and varying sea states. Cross-shelf density gradients due to freshwater runoff resulted in active submesoscale flows. The airborne data allow characterization of the dominant physical processes controlling the dispersion of passive tracers such as freshwater fronts and Langmuir circulation. Langmuir circulation was identified in dye concentration maps on most sampling days except when the near surface stratification was strong. The observed relative dispersion is anisotropic with eddy diffusivities O(1) m2 s−1. Near-surface horizontal dispersion is largest along fronts and in conditions dominated by Langmuir circulation is larger in the crosswind direction. Surface convergence at fronts resulted in strong vertical velocities of up to −66 m day−1.

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Leonel Romero, Yusuke Uchiyama, J. Carter Ohlmann, James C. McWilliams, and David A. Siegel

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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 R 5/4. 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.

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William G. Large, Edward G. Patton, Alice K. DuVivier, Peter P. Sullivan, and Leonel Romero

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Monin–Obukhov similarity theory is applied to the surface layer of large-eddy simulations (LES) of deep Southern Ocean boundary layers. Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes drift) forcing. Two No-Stokes LES are used to determine the extent of the ocean surface layer and to adapt the nondimensional momentum and buoyancy gradients, as functions of the stability parameter. Stokes-forced LES are used to modify this parameter for wave effects, then to formulate dependencies of Stokes similarity functions on a Stokes parameter ξ. To account for wind-wave misalignment, the dimensional analysis is extended with two independent variables, namely, the production of turbulent kinetic energy in the surface layer due to Stokes shear and the total production, so that their ratio gives ξ. Stokes forcing is shown to reduce vertical shear more than stratification, and to enhance viscosity and diffusivity by factors up to 5.8 and 4.0, respectively, such that the Prandtl number can exceed unity. A practical parameterization is developed for ξ in terms of the meteorological forcing plus a Stokes drift profile, so that the Stokes and stability similarity functions can be combined to give turbulent velocity scales. These scales for both viscosity and diffusivity are evaluated against the LES, and the correlations are nearly 0.97. The benefit of calculating Stokes drift profiles from directional wave spectra is demonstrated by similarly evaluating three alternatives.

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