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Abstract Over the past decade there has been a rapid growth of interest in wave propagation through ice covers. This paper summarizes the author's observation of the modeling efforts on this topic. Models can be theory-based, data-driven, or a combination of the two. A pure data-driven model relies on a large amount of observations and is only becoming available recently. Theory-based models on the other hand have a long history. They are always a simplified version of the reality. As our knowledge grows, theories become more complicated. A theory for waves-in-ice that captures all possible processes does not exist. However, when integrated with observation through calibration, these combined theory + data-based models may be used with some confidence. In this paper, different models, their basic concepts, their calibration and validation are discussed. The present theory-based models do not have the correct spectral attenuation trend as observed from field or laboratory experiments. Hence, through calibration they may fit different parts of the wave spectra but not all. Pure data-driven models can reproduce the correct trend, but its dependability outside the situation where the data are collected is uncertain. In addition to offering tools to forecast waves-in-ice, these model building and validating efforts point to missing mechanisms that should be carefully studied. Despite the many challenges towards building a satisfactory general waves-in-ice model, significant progress has been made for models that work reasonably well in the marginal ice zone. We anticipate much more data will become available in the coming years to help us improve the existing models. [ABSTRACT FROM AUTHOR]

Highlights • Three-layer model developed for gravity wave propagation through ice cover. • Significant boundary layer effect under viscoelastic ice cover. • Model improves comparisons with experimental data relative to previous model. Abstract A three-layer model is presented to simulate gravity wave propagation in an ice-covered sea. Damping from a viscoelastic ice cover and the boundary layer of the water body are considered. This model is shown to converge to three previous models: viscoelastic ice over inviscid water, thin elastic plate over viscous water, and viscous ice over viscous water. The non-monotonic attenuation with respect to the wave period shown previously in the thin elastic plate over viscous water also appears in the proposed model. Sensitivity analysis indicated no significant influence of the thickness of the boundary layer modeled with an eddy viscosity on either the wave dispersion or the attenuation, but a significant effect on wave attenuation from the eddy viscosity. Based on a consistent formulation for a three-layer system, we provide a compact model that combines dissipation from the ice cover and the boundary layer underneath, as well as the associated wave dispersion. [ABSTRACT FROM AUTHOR]

This study presents a continuum approach using a diffusion approximation method to solve the scattering of ocean waves by randomly distributed ice floes. In order to model both strong and weak scattering, the proposed method decomposes the wave action density function into two parts: the transmitted part and the scattered part. For a given wave direction, the transmitted part of the wave action density is defined as the part of wave action density in the same direction before the scattering; and the scattered part is a first order Fourier series approximation for the directional spreading caused by scattering. An additional approximation is also adopted for simplification, in which the net directional redistribution of wave action by a single scatterer is assumed to be the reflected wave action of a normally incident wave into a semi-infinite ice cover. Other required input includes the mean shear modulus, diameter and thickness of ice floes, and the ice concentration. The directional spreading of wave energy from the diffusion approximation is found to be in reasonable agreement with the previous solution using the Boltzmann equation. The diffusion model provides an alternative method to implement wave scattering into an operational wave model. [ABSTRACT FROM AUTHOR]

Modeling ice covers as viscoelastic continua, Zhao and Shen, (2013) applied a two-mode approximate method to determine the transmission and reflection between two different ice covers. This approximate solution considered only two modes of the dispersion relation. In addition, the horizontal boundary conditions were simplified by matching mean values over the interfaces. In this study, we employ a variational method (Fox and Squire, (1990)) to calculate the wave transmission and reflection from two connecting viscoelastic ice covers of different properties. The variational approach minimizes the overall error function at the interface of two ice covers, hence is more rigorous than the previous approximate method that minimized the difference between mean values at the interface. The effect of additional travelling and evanescent modes are also investigated. We compare results from different matching methods, as well as the effects of including additional modes. From this study, we find that additional modes do not always improve the results for our model. For all cases tested, two modes appear to be sufficient. These two modes represent the open-water-like and the elastic-pressure wave-like behavior. The two-mode approximate method and the variational method have similar results except at very short wave periods. [ABSTRACT FROM AUTHOR]

Highlights: [•] Obtained approximate solutions for gravity wave propagating between two viscoelastic plates. [•] Solution procedures are validated with previously studied cases. [•] A mode switching phenomenon with increasing ice rigidity is present. [•] With increasing viscosity, such mode switching may terminate. [•] Transmission/reflection from grease ice to elastic sheet are close to those from open water to elastic sheet. [Copyright &y& Elsevier]

Abstract: In order to model the wave-in-ice climate on a geophysical scale, a continuum viscoelastic model has been developed [Wang, R., Shen, H.H., 2010. Gravity waves propagating into an ice-covered ocean: a viscoelastic model. J. Geophys. Res. 115, C06024. doi:10.1029/2009JC005591]. In this model, two modes were identified to be dominant, each for the low or high elasticity range, respectively. In the intermediate elasticity range, both modes have comparable attenuation rates and wave numbers, and they could be co-dominant. Inspired by the Eigenfunction Expansion Matching Method, this paper presents an approximate approach to solve the wave propagation characteristics in the whole physical range of elasticity. A monochromatic wave propagating from semi-infinite open water into semi-infinite ice-covered water is considered. Only two transmitted wave modes are included in the eigenfunction expansions for the ice-covered water. These two modes correspond to the dominant mode under relatively low or high elasticity, respectively. Evanescent wave modes in open water are ignored. By minimizing the matching errors, the least square solution is obtained. For the pure elastic ice cover, the results are compared with the exact solution from the thin elastic plate model. The comparison is in good agreement when the wave period is larger than 10s. Mild discrepancies exist when the period is smaller than 10s. The present model provides the simplest way to describe wave propagation characteristics in different types of ice covers. [Copyright &y& Elsevier]

A parameterization of new ice formation in a wave field has been developed. Detailed processes of new sea ice growth with multiple ice types (nilas, grease, and pancake ice) and associated wave attenuation by different sea ice types are presented and implemented into a coupled ROMS and SWAN model. Sea ice formation includes growth and transformation of frazil, grease, pancake, nilas and solid ice. Ice types are determined by thermal condition and the wave fields. Simultaneously, the attenuation of wave energy through the ice cover is dependent on ice types. The two processes are coupled by COAWST. The resulting coupled model is applied to the Bohai Sea. When compared with in-situ data from oil platforms, the model performed well in distinguishing solid ice, pancake and nilas. When compared with previous ice models without the consideration of new ice types, the appearance of solid ice is delayed, the total ice area and ice volume are increased, solid ice thickness is increased while the type-averaged thickness is reduced and heat flux from the ocean to air is increased during the freezing phase. By considering the new ice formation, wave attenuation in the test case is enhanced. • New ice evolution with multiple ice types is formulated. • Multiple type ice and wave interaction is implemented in the model. • The model performs well to distinguish solid ice, pancake ice and nilas. • Considering new ice types increases heat flux from ocean to air. • Considering new ice types enhances wave attenuation. [ABSTRACT FROM AUTHOR]

Abstract: In this study, we report a direct comparison between a physical test and a computer simulation of rapidly sheared granular materials. An annular shear cell experiment was conducted. All parameters were kept the same between the physical and the computational systems to the extent possible. Artificially softened particles were used in the simulation to reduce the computational time to a manageable level. Sensitivity study on the particle stiffness ensured such artificial modification was acceptable. In the experiment, a range of normal stress was applied to a given amount of particles sheared in an annular trough with a range of controlled shear speed. Two types of particles, glass and Delrin, were used in the experiment. Qualitatively, the required torque to shear the materials under different rotational speed compared well with those in the physical experiments for both the glass and the Delrin particles. However, the quantitative discrepancies between the measured and simulated shear stresses were nearly a factor of two. Boundary conditions, particle size distribution, particle damping and friction, including a sliding and rolling, contact force model, were examined to determine their effects on the computational results. It was found that of the above, the rolling friction between particles had the most significant effect on the macro stress level. This study shows that discrete element simulation is a viable method for engineering design for granular material systems. Particle level information is needed to properly conduct these simulations. However, not all particle level information is equally important in the study regime. Rolling friction, which is not commonly considered in many discrete element models, appears to play an important role. [Copyright &y& Elsevier]

• A novel experimental study with discrete floating viscoelastic segments to examine combined dissipative and scattering mechanisms. • Wave dispersion dependent on segment length for more elastic covers, consistent with existing models. • Wave attenuation depending on wave characteristics, segmentation and viscoelastic properties of the floating cover. With climate changes and global warming, the extent of Marginal Ice Zone (MIZ) in the polar region is widening, and there is now more research attention on the wave interactions with broken ice covers within the zone to gain insights into its future sea conditions. Towards this objective, the dispersion and attenuation of surface waves propagating through segmented floating viscoelastic covers was investigated experimentally in this study. The covers were made of oil-doped Polydimethylsiloxane (PDMS) material, with different curing agent percentages to vary their rheological properties. For stiffer covers, the measurements showed that the effect of segmentation on wavelength modification was significant, and the dispersion relation agreed generally with the existing theoretical predictions for discrete floating elastic segments despite the presence of the additional viscosity for the material. At the same time, the earlier empirical formula based on the concept of "equivalent rigidity" to represent the segmented elastic cover, did not work well for the conditions investigated. With more flexible covers, however, the effect of segmentation became insignificant for thin cover thickness. Given the present experimental conditions, we confirmed that the effect of scattering was negligible, and the wave attenuation should be attributed to the various dissipative mechanisms. An empirical relation for the attenuation was established based on the experimental results, to quantitatively relate the attenuation coefficient to the incident wave characteristics and cover properties. The relation identifies a significant inverse relationship with the viscosity of cover material, and thus confirms the essential role of viscoelastic representation for the attenuation predictions. [ABSTRACT FROM AUTHOR]

The sea state of the Beaufort and Chukchi seas is controlled by the wind forcing and the amount of ice-free water available to generate surface waves. Clear trends in the annual duration of the open water season and in the extent of the seasonal sea ice minimum suggest that the sea state should be increasing, independent of changes in the wind forcing. Wave model hindcasts from four selected years spanning recent conditions are consistent with this expectation. In particular, larger waves are more common in years with less summer sea ice and/or a longer open water season, and peak wave periods are generally longer. The increase in wave energy may affect both the coastal zones and the remaining summer ice pack, as well as delay the autumn ice-edge advance. However, trends in the amount of wave energy impinging on the ice-edge are inconclusive, and the associated processes, especially in the autumn period of new ice formation, have yet to be well-described by in situ observations. There is an implicit trend and evidence for increasing wave energy along the coast of northern Alaska, and this coastal signal is corroborated by satellite altimeter estimates of wave energy. [ABSTRACT FROM AUTHOR]