A Scaling for Wave Dispersion Relationships in Ice‐Covered Waters

• Published in: Journal of geophysical research. Oceans 2019-11, Vol.124 (11), p.8429-8438
• Main Authors: Yu, Jie, Rogers, W. Erick, Wang, David W.
• Format: Article
• Language: English
• Subjects: Collapse; Dispersion; Dynamic similarity; Elasticity; Geophysics; Ice cover; Ice properties; Inertia; Laboratories; Ocean models; Ocean surface; Ocean waves; Oceans; Parameter identification; Parameters; Propagation; scale collapse of data sets; Scaling; Sea ice; Surface water waves; Theories; Viscosity; Wave dispersion; Wave frequency; Wave propagation; Wavelength; wave‐ice interaction
• ISSN: 2169-9275; 2169-9291
• DOI: 10.1029/2018JC014870

We consider the scaling of dispersion relationships for wave propagation on ice‐covered waters, aiming to identify a set of parameters that are physically meaningful and can be used in various continuum‐based theories. These parameters characterize the relative importance of the effects of ice inertia, effective viscosity, and elasticity, hence can be used to guide the dynamic similarity between different scales. Application to laboratory and field measurements shows scale collapse of data sets toward a general trend. From the dimensionless parameters of the theoretical prediction, the effective ice properties can be estimated more consistently. Plain Language Summary Sea ice covering the ocean surface, in the form of large sheets, floes, or slushy ice‐water mixture, can modify the wavelength and dissipate the energy of ocean waves. Despite the difficulty of modeling the highly heterogeneous ice condition, various mathematical theories exist, describing the dependence of wavelength and dissipation on wave frequency under the effects of ice. These are called the wave dispersion relationships in ice‐covered waters. In this paper, we consider a more efficient way to present various mathematical theories and compare them in a physically meaningful way. We find that the problem can be redefined in terms of nondimensional variables, which, to some extent, reconcile the apparent discrepancies between dissimilar laboratory and field data in the literature. The proposed nondimensionalization (scaling) also allows us to estimate the apparent viscosity and elasticity of the ice cover with better consistence. Nondimensional parameters are identified that characterize the relative importance of the apparent ice viscosity and elasticity, as well as ice inertia, by comparison. Therefore, they can guide the dynamical similarity of wave propagation under ice in different scales. Key Points A simple scaling of dispersion relations is proposed and shown to be effective Dimensionless parameters are identified, which can guide the similarity of wave propagation under ice The method results in scale collapse of data and more consistent estimates of effective ice properties