Attenuation and directional spreading of ocean wave spectra in the marginal ice zone

Abstract

A theoretical model is used to study wave energy attenuation and directional spreading of ocean wave spectra in the marginal ice zone (MIZ). The MIZ is constructed as an array of tens of thousands of compliant circular ice floes, with randomly selected positions and radii determined by an empirical floe size distribution. Linear potential flow and thin elastic plate theories model the coupled water-ice system. A new method is proposed to solve the time-harmonic multiple scattering problem under a multi-directional incident wave forcing with random phases. It provides a natural framework for tracking the evolution of the directional properties of a wave field through the MIZ. The attenuation and directional spreading are extracted from ensembles of the wave field with respect to realizations of the MIZ and incident forcing randomly generated from prescribed distributions. The averaging procedure is shown to converge rapidly so that only a small number of simulations need to be performed. Far field approximations are investigated, allowing efficiency improvements with negligible loss of accuracy. A case study is conducted for a particular MIZ configuration. Observed exponential attenuation of wave energy through the MIZ is reproduced by the model, while the directional spread is found to grow linearly with distance. Directional spreading is shown to weaken when the wavelength becomes larger than the maximum floe size.

Overview of the Arctic Sea State and Boundary Layer Physics Program

“…New models have been developed as part of this program (e.g., Montiel et al, ), and thus there is an expanding set of schemes to implement and test in WAVEWATCH III. These are noted by “ICn” for dissipation terms and “ISn” for scattering terms.…”

Attenuation and Directional Spreading of Ocean Waves During a Storm Event in the Autumn Beaufort Sea Marginal Ice Zone

“…We also seek to quantify how the directionality of the wavefield changes as waves propagate in the pancake ice cover, as this may inform what the dominant processes governing wave‐ice interactions are in this particular experiment. There is observational (see ; Sutherland & Gascard, ; Wadhams et al, ) and theoretical (see Montiel et al, ; Squire & Montiel, ) evidence suggesting that short waves traveling through the MIZ tend to experience a broadening of the range of wave directions as a result of wave scattering by the constituent ice floes, while long waves have been hypothesized to experience a decrease in their directional range, likely caused by dissipative effects gradually filtering out spectral components. Since dissipative effects dominate over scattering in pancake ice, we expect this latter scenario to govern our wave directionality data.…”

Dispersion Relations, Power Laws, and Energy Loss for Waves in the Marginal Ice Zone

“…Two model paradigms exist to understand wave attenuation. The first is wave scattering (e.g., Bennetts & Squire, ; Kohout & Meylan, ; Montiel et al, ; Peter & Meylan, ), which conserves energy and in which attenuation results from an accumulation of scattering events produced by individual floes, where the floes are conventionally modeled as thin floating elastic plates (e.g., Bennetts & Williams, ; Meylan & Squire, ). Scattering models have been shown to agree reasonably well with experimental measurements (Bennetts & Squire, ; Bennetts & Williams, ; Bennetts et al, ; Kohout & Meylan, ), but only when wavelengths are comparable to floe lengths.…”