Tracking the attenuation and nonbreaking dissipation of swells using altimeters

Abstract

A method for systematically tracking swells across oceanic basins is developed by taking advantage of high-quality data from space-borne altimeters and wave model output. The evolution of swells is observed over large distances based on 202 swell events with periods ranging from 12 to 18 s. An empirical attenuation rate of swell energy of about 4 3 10 27 m 21 is estimated using these observations, and the nonbreaking energy dissipation rates of swells far away from their generating areas are also estimated using a point source model. The resulting acceptance range of nonbreaking dissipation rates is 22.5 to 5.0 3 10 27 m 21 , which corresponds to a dissipation e-folding scales of at least 2000 km for steep swells, to almost infinite for small-amplitude swells. These resulting rates are consistent with previous studies using in-situ and synthetic aperture radar (SAR) observations. The frequency dispersion and angular spreading effects during swell propagation are discussed by comparing the results with other studies, demonstrating that they are the two dominant processes for swell height attenuation, especially in the near field. The resulting dissipation rates from these observations can be used as a reference for ocean engineering and wave modeling, and for related studies such as air-sea and wind-wave-turbulence interactions.

Ocean swell within the kinetic equation for water waves

“…The first estimates of the observed rates of swell attenuation were carried out by Snodgrass et al (1966) based on observation at near-shore stations. Their e-folding scale of about 4000 km (the distance at which an exponentially decaying wave height decreases by a factor of e) is consistent with some of today's results of the satellite tracking of swell (Ardhuin et al, 2009Jiang et al, 2016) and with the 238 S. I. Badulin and V. E. Zakharov: Ocean swell within the kinetic equation treatment of these results within the model of swell attenuation due to coupling with the turbulent atmospheric layer (e.g., Tsimring, 1986;Kantha, 2006). The alternative semiempirical model of Babanin (2006) predicts a quite different algebraic law and stronger swell attenuation at shorter distances from the swell source .…”

“…Evidently, this simple balance model gives very tentative estimate of the effect. Nevertheless, visual observations (Badulin and Grigorieva, 2012) and satellite data (Jiang et al, 2016), in our opinion, provide telling arguments for this phenomenon. Thus, "negative dissipation" of swell (in the words of Jiang et al, 2016) could find its explanation within the simple model.…”

“…Tracking of swell events from space gives an alternative scenario of transformation when swell appears to be growing. Satellite tracks can comprise up to 30 % of cases of growing swell; "most of them are not statistically significant" (Jiang et al, 2016). Nevertheless, a possible effect of wind-sea background on long ocean swell opens an important discussion in view of theoretical (Badulin et al, 2008b) and experimental (Benilov et al, 1974;Badulin and Grigorieva, 2012) results that demonstrate swell amplification by a wind-wave background.…”

“…In particular, the locally generated wind-driven waves can switch the swell attenuation to swell amplification. This effect can be considered for interpretation of recent observations of swell from space ("negative" dissipation in the words of Jiang et al, 2016). Many problems of adequate physical description of swell in the ocean are still open.…”

“…These snapshots are adequate for currently known methods of statistical description of waves in research and application models. These can be used for swell tracking in combination with other tools (e.g., wave models as in Jiang et al, 2016). Retracking of swells allows us, first, to relate the swell events to their probable sources -stormy areas -and, secondly, the swell transformation enables us to estimate the effects of other motions of the atmosphere and ocean -seasonal wind activity (e.g., Chen et al, 2002), wave-current interaction (e.g., Beal et al, 1997) and bathymetry effects .…”