Floe Size Effect on Gravity Wave Propagation Through Ice Covers

Abstract

When modeling gravity wave propagation through an array of discrete ice floes, considered as a homogenous elastic continuum, the equivalent elasticity is less than the intrinsic material elasticity of ice. The array behaves increasingly like a collection of rigid floating masses when the floe sizes decrease. Extending a former wave flume experiment with polyethylene plates (Sakai & Hanai, 2002, https://web2.clarkson.edu/projects/iahrice/IAHR%202002/Volume%202/189.pdf), we conducted an experiment with saline ice floes at the Hamburg Ship Model Basin (HSVA). Using the measured wave number and the dispersion relation from a continuous elastic plate theory, we determine the equivalent elasticity. Parallel theoretical solutions are obtained using the matched eigenfunction expansion method (Kohout et al., 2007, https://doi.org/10.1016/j.jfluidstructs.2006.10.012), assuming ice floes as an array of thin elastic plates floating over inviscid water. Despite data scatter in laboratory tests, the celerity (phase speed) from the laboratory and theoretical results both show a decreasing trend when the floe size reduces. The corresponding equivalent elastic modulus decreases from the intrinsic modulus to zero. The matched eigenfunction expansion method is then applied to investigate cases under field conditions. Using all the theoretical results, an empirical relation is proposed for the equivalent elasticity in terms of wavelength, floe size, and length scale from the intrinsic elasticity of the floes. In addition to celerity, wave amplitude along the ice cover is compared with the theoretical results. Large discrepancies of wave attenuation from laboratory and theoretical solutions are found, indicating that attenuation mechanisms other than wave scattering need to be considered.Plain Language Summary Ocean wave forecasts in the ice-covered seas require reliable modeling of ice effect on wave propagation. The wave dispersion and damping rate due to the ice cover are different from the propagation in open water. One way is to consider the total effect of a field of fragmented ice floes as one continuous elastic sheet. However, the elasticity of the sheet is not measurable directly, which could be much lower than the intrinsic elasticity of ice. In this study, we examine a single-period wave propagating through an array of ice floes using both physical measurement and a theoretical approach. We analyze data from two laboratory experiments and the parallel theoretical studies. The theoretical studies are also extended into field scales using parameters collected from two field experiments. By assimilating all results, we determine the dependence of the equivalent elasticity of the sheet on the floe size. Furthermore, the surface undulation due to free edges makes the attenuation measurement challenging. Despite this difficulty, extra damping beyond wave scattering is observed.

Wave energy attenuation in fields of colliding ice floes – Part 1: Discrete-element modelling of dissipation due to ice–water drag

“…The second, more important reason was consistency between the dispersion relation used and the assumptions underlying the DEM (individual ice floes and elastic interactions between them). It is also worth pointing out that our observations from the laboratory, described in Part 2, as well as the previous analysis of the LS-WICE data by Cheng et al (2018), provide arguments that viscous damping within the floating ice cover in those experiments was not significant and that Eq. (6) represents the laboratory conditions well (notably, the ice floes floated in clear water, as opposed to many observations of wave damping in the MIZ, where the presence of a frazilpancake mixture gives the surface ocean layer high effective viscosity).…”

“…(25), with α(ω) strongly dependent on the assumed dispersion relation. This result is particularly interesting in view of the results of Cheng et al (2018), who showed that the dispersion relation is strongly affected by floe size, with the wavenumber k increasing with decreasing floe length. The DEM results are presented in Sect.…”

“…In many studies these effects are not taken into account and open-water dispersion relation is assumed (e.g. Meylan et al, 2018), although several observations, including those analysed by Liu and Mollo-Christensen (1988) or Sutherland and Rabault (2016), show the influence of floe size on wave propagation speed (in the LS-WICE experiment discussed in Part 2, for which the present DEM was configured, decreasing wavenumbers with increasing floe size were observed, as analysed by Cheng et al, 2018). The example of attenuation due to icewater drag, discussed in this work, suggests that even small changes of c g may lead to noticeable changes of α.…”

Wave energy attenuation in fields of colliding ice floes – Part 2: A laboratory case study

“…Initial results of the tests relevant to this study (series 2000 and 3000, as described below) are described in Cheng et al (2017). Recently, Cheng et al (2018) used the same data in an analysis of the influence of floe size on wave dispersion. Other LS-WICE results were used to study floe-size distributions in sea ice broken by waves (Herman et al, 2017(Herman et al, , 2018 as well as wave-induced collisions and floe kinematics (Li and Lubbad, 2018).…”

“…., N f , with N f depending on the floe length L x (see later text). Details related to the preparation of the ice sheets and conduction of the tests can be found in Cheng et al (2018) and will not be repeated here. In this section, we only provide information that is relevant to the present study.…”