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Dispersion Relations, Power Laws, and Energy Loss for Waves in the Marginal Ice Zone
Author(s) -
Meylan M. H.,
Bennetts L. G.,
Mosig J. E. M.,
Rogers W. E.,
Doble M. J.,
Peter M. A.
Publication year - 2018
Publication title -
journal of geophysical research: oceans
Language(s) - English
Resource type - Journals
eISSN - 2169-9291
pISSN - 2169-9275
DOI - 10.1002/2018jc013776
Subject(s) - attenuation , dispersion (optics) , power law , range (aeronautics) , dispersion relation , energy (signal processing) , field (mathematics) , arctic , meteorology , law , geology , mechanics , computational physics , physics , optics , mathematics , materials science , statistics , political science , pure mathematics , composite material , oceanography
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.