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

Abstract

Analysis of field measurements of ocean surface wave activity in the marginal ice zone, from campaigns in the Arctic and Antarctic and over a range of different ice conditions, shows the wave attenuation rate with respect to distance has a power law dependence on the frequency with order between two and four. With this backdrop, the attenuation‐frequency power law dependencies given by three dispersion relation models are obtained under the assumptions of weak attenuation, negligible deviation of the wave number from the open water wave number, and thin ice. It is found that two of the models (both implemented in WAVEWATCH III®), predict attenuation rates that are far more sensitive to frequency than indicated by the measurements. An alternative method is proposed to derive dispersion relation models, based on energy loss mechanisms. The method is used to generate example models that predict power law dependencies that are comparable with the field measurements.

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

“…These values of b are also consistent with those found in past studies, noting that the frequency range considered here extends to much higher frequencies than those reported by Meylan et al () and Wadhams (). It should be noted that our b estimates are substantially different from that of Meylan et al (), that is, b ≈3.6, obtained for the same data set extended to a longer time period of measurements than that considered here, based on the analysis conducted by Cheng et al (). We argue that the discrepancy is too large to be explained by the extended period of measurements but reflects the method used to extract attenuation coefficients instead.…”

Overview of the Arctic Sea State and Boundary Layer Physics Program

“…Currently we do not know the mechanism for the energy loss. Meylan et al () also show how we can connect the energy loss mechanism to the power law dependence.…”

“…Meylan et al () analyzed the power law dependence of attenuation on frequency for both measurements and models. The measurements showed universal power law dependence, being approximately four for pancake/frazil ice and two for large floes.…”

A Scaling for Wave Dispersion Relationships in Ice‐Covered Waters

“…The scale collapse manifests the dynamic similarity of wave propagation: A longer wave in a deeper depth propagates similarly as a shorter wave in a shallower depth, if they have the same dimensionless frequency . (During the review of this paper, it was brought to our attention that some readers may regard the power laws of wave attenuation rate k i (which can be treated as the imaginary part of the complex wavenumber in continuum‐based theories of wave dispersion relationship, if the ice cover is dissipative) in Meylan et al () also as a scaling law. Meylan et al () explored empirical curve fittings in terms of dimensional variables, proposing k i ∼ ω 3.27 or more precisely k i = β 1 ω 2 + β 2 ω 4 , based on observations.…”

“…(During the review of this paper, it was brought to our attention that some readers may regard the power laws of wave attenuation rate k i (which can be treated as the imaginary part of the complex wavenumber in continuum‐based theories of wave dispersion relationship, if the ice cover is dissipative) in Meylan et al () also as a scaling law. Meylan et al () explored empirical curve fittings in terms of dimensional variables, proposing k i ∼ ω 3.27 or more precisely k i = β 1 ω 2 + β 2 ω 4 , based on observations. This type of empirical relationships is difficult to be generalized from one scale to another, since the fitting coefficients are dimensional and not physically explainable.…”