Observations of Wave Breaking Kinematics in Fetch-Limited Seas
Authors: Kleiss Jessica M. , Melville W. Kendall 
Published: August 2010

Abstract
Breaking waves play an important role in air–sea interaction, enhancing momentum flux from the atmosphere to the ocean, dissipating wave energy that is then available for turbulent mixing, injecting aerosols and sea spray into the atmosphere, and affecting air–sea gas transfer due to air entrainment. In this paper observations are presented of the occurrence of breaking waves under conditions of strong winds (10–25 m s−1) and fetch-limited seas (0–500 km) in the Gulf of Tehuantepec Experiment (GOTEX) in 2004. An airborne nadir-looking video camera, along with a global positioning system (GPS) and inertial motion unit (IMU), provided digital videos of the breaking sea surface and position in an earth frame. In particular, the authors present observations of Λ(c), which is the distribution of breaking wave crest lengths per unit sea surface area, per unit increment in velocity c or scalar speed c, first introduced by O. M. Phillips. In another paper, the authors discuss the effect of processing methodology on the resulting shape of the Λ(c) distribution. In this paper, the elemental method of measuring breaking crests is used to investigate the Λ(c) distributions under a variety of wind and wave conditions. The integral and the first two moments of the Λ(c) distributions are highly correlated with the active breaking rate and the active whitecap coverage. The computation of whitecap coverage yields a larger observational dataset from which the variability of whitecap coverage with wind speed, friction velocity, wave age, and wave slope is presented and compared to previous observations. The dependence of the active breaking rate on the spectral peak steepness is in agreement with previous studies. Dimensional analysis of Λ(c) indicates that scaling with friction velocity and gravity, as in the classical fetch relations, collapses the breaking distributions more effectively than scaling with dominant wave parameters. Significant wave breaking is observed at speeds near the spectral peak in young seas only, consistent with previous studies. The fourth and fifth moments of Λ(c) are related to the flux of momentum transferred by breaking waves to the underlying water and the rate of wave energy dissipation, respectively. The maximum in the fourth moment occurs at breaking speeds of 5–5.5 m s−1, and the maximum in the fifth moment occurs at 5.8–6.8 m s−1, apparently independent of wave age. However, when nondimensionalized by the phase speed at the peak of the local wave spectrum cp, the maxima in the nondimensionalized fourth and fifth moments show a decreasing trend with wave age, obtaining the maxima at dimensionless speeds c/cp near unity at smaller wave ages and moving to lower dimensionless speeds c/cp ≪ 1 at larger wave ages. The angular dependence of Λ(c) is predominantly unimodal and better aligned with the wind direction than the dominant wave direction. However, the directional distribution of Λ(c) is broadest for small c and often exhibits a bimodal structure for slow breaking speeds under developing seas. An asymmetry in the directional distribution is also observed for moderately developed seas. Observations are compared to the Phillips model for Λ(c) in the equilibrium range of the wave spectrum. Although the ensemble of Λ(c) distributions appears consistent with a c−6 function, the distributions are not described by a constant power-law exponent. However, the Λ(c) observations are described well by the Rayleigh distribution for slow and intermediate speeds, yet fall above the Rayleigh distribution for the fastest breaking speeds. From the Rayleigh description, it is found that the dimensionless width of the Λ(c) distribution increases weakly with dimensionless fetch, s/u*e = 1.69χ0.06, where s is the Rayleigh parameter, u*e is the effective friction velocity, and the dimensionless fetch is a function of the fetch X and gravitational acceleration g. The nondimensionalized total length of breaking per unit sea surface area is found to decrease with dimensionless fetch for intermediate to fully developed seas, , where A is the total length of breaking crests per unit sea surface area.