Effects of nonlinear energy transfer on short surface waves

Abstract

[1] The effects of nonlinear energy transfer on the development of the short wave spectrum are evaluated using a diffusion approximation and a modification of this approximation to include nonlocal effects. Both formulations were used to compute the evolution of a JONSWAP-type spectrum, and the results are compared with direct numerical simulations. Terms corresponding to each of these formulations were then incorporated into the wave action equation, and the resulting equation was numerically integrated using a second-order Runge-Kutta method. The results show an increase in the angular width of the spectrum and in the spectral density at high wave numbers as compared with solutions of the action equation without the nonlinear energy transfer term. Example results are presented for the case of a moderately strong internal wave in a light wind, and implications for the remote sensing of these waves using microwave radar are discussed.

Surface Wave Breaking Caused by Internal Solitary Waves: Effects on Radar Backscattering Measured by SAR and Radar Altimeter

“…Fueled by continuous input of energy from an ISW, resonant surface waves grow until they are dissipated by wave breaking or energy transfer to shorter waves via nonlinear hydrodynamic interaction. Lyzenga (2010) found that the energy transfer mechanism, in particular at X-band, also leads to larger modulation depths (or image contrasts) than predicted by previous SAR imaging theories regarding ISWs. However, we conjecture that wave breaking dominates dissipation of resonant waves and that scattering from breaking waves is the dominant contributor to the mechanism that results in large ISW radar signatures.…”

“…It should be noted that other scattering theories, which do not involve wave breaking, have been developed to explain the often observed large radar signatures of ISWs. The SAR imaging theories for ISWs of Thompson (1988), Lyzenga (2010), Craig et al (2012), andChen et al (2017) all yield larger modulation depths than those predicted by the theory of Alpers (1985) and are thus closer to reality; but they all fail to predict the very large ISW radar signatures that are frequently observed. Thus, we conjecture that scattering from breaking waves must be included in a SAR imaging theory for ISWs.…”

“…This theory is successful in explaining SAR observations of ISWs with small modulations of the sea surface roughness (particularly at L-band) but fails to explain the often observed large modulation of the backscattered radar signal (particularly at X-and C-band). Similarly, advanced theories based on weak hydrodynamic interaction theory and the composite surface (or twoscale) Bragg model (Thompson, 1988;Brandt et al, 1999;Lyzenga, 2010) cannot fully explain the large modulations observed in X-band SAR images of ISWs (Thompson and Gasparovic, 1986). In these theories, radar backscattering from breaking surface waves is not included.…”

Effects of Surface Wave Breaking Caused by Internal Solitary Waves in SAR Altimeter: Sentinel-3 Copernicus Products and Advanced New Products

“…Energy in the surface wave field is slowly accumulated under the wind action over thousands of wave periods [11], being redistributed by nonlinear wave-wave interactions [54]. Interestingly, all that energy can be quickly cascaded down to turbulent scales and dissipation-owing to enhanced surface wave breaking from an ISW-within very short time scales (typically of the order of a single internal wave period, about 40 min).…”