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Abstract: In this paper, an ice floe inner stress caused by the wave-induced bending moment is derived to estimate the stress failure of ice floe. The strain and stress failures are combined to establish a wave-induced ice yield scheme. We added ice stress and strain failure module in the Finite-Volume Community Ocean Model (FVCOM), which already includes module of ice-induced wave attenuation. Thus a fully coupled wave-ice dynamical interaction model is established based on the ice and wave modules of FVCOM. This model is applied to reproduce the ice and wave fields of the breakup events observed during the second Sea Ice Physics and Ecosystem Experiment (SIPEX-2) voyage. The simulation results show that by adopting the combined wave-induced ice yield scheme, the model can successfully predict the ice breakup events, which the strain failure model is unable to predict. By comparing the critical significant wave height deduced from strain and stress failure schemes, it is concluded that the ice breakup is caused by the strain failure when wave periods are shorter than a threshold value, while the stress failure is the main reason for the ice breakup when wave periods are longer than the threshold value. Neglecting either of these two ice-break inducement mechanisms could overestimate the ice floe size, and thus underestimate the velocity of the ice lateral melt and increase the error of simulation of polar ice extent.
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Key words:
- wave-ice interaction /
- FVCOM /
- stress failure /
- ice lateral melt
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Figure 1. The force analysis of an ice floe when wave traveling through. Wave crests are lower than the ice floe surface and stay stable (a), and wave crests are over the ice floe surface and ice floe sink to become stable again (b). The red lines are free surfaces. The orange imaginary rectangles are original floe position when it is still unstable. Green vectors are buoyance over free surface while red vectors are ice gravity below free surface.
Figure 2. Changes of the critical significant wave height (SWHc) versus peak period (Tpeak) when ice thickness is 1 m (a), 2 m (b), and 3 m (c). The red, green and blue lines refer to the critical SWH calculated from the critical strain,
${M_{\rm{C}} ^{{\rm{B}} - {\rm{D}}}}_1$ induced critical stress and critical stress calculated from the combination of${M_{{\rm{C}} }^{{\rm{B}} - {\rm{D}}}}_1$ and${M_{{\rm{C}} }^{{\rm{B}} - {\rm{D}}}}_2$ . The solid lines refer to the relatively small critical wave amplitude, comparing the strain and stress yield amplitudes, while the imaginary lines are relatively large ones.Figure 3. The horizontal mesh grid of the ideal model (a) and the ice concentration (b). The green line is the transect which is show in Fig. 4.
Figure 4. Changes of the significant wave height (SWH), peak period (Tpeak) and floe size versus the distance from the ice edge, for Case 1 to Case 4. Different colors, from blue to red, refer to different times, with the time intervals of each adjacent line being 2 h. The numbers are the value at the black dashed line of the final situation.
Table 1. An overview of the two ice floe breakup events, showing the time the events occur, the distances from the ice edge (D), the estimated observed SWH (
$ {\mathrm{S}\mathrm{W}\mathrm{H}}_{\mathrm{o}} $ ), Tpeak ($ {\mathrm{T}\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}_{\mathrm{o}} $ ), the simulated SWH ($ {\mathrm{S}\mathrm{W}\mathrm{H}}_{\rm{s}} $ ), and Tpeak ($ {\mathrm{T}\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}_{\rm{s}} $ )Time D/km $ {\mathrm{S}\mathrm{W}\mathrm{H}}_{\rm{o}} $/m $ {\mathrm{S}\mathrm{W}\mathrm{H}}_{\rm{s}} $/m $ {\mathrm{T}\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}_{\rm{o}} $/s $ {\mathrm{T}\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}_{\rm{s}} $/s Event A 09:00 Sept. 25, 2012 244 0.5 0.37 15 15.4 Event B 13:00 Oct. 1, 2012 455 0.1 0.29 15 15.4 Table 2. Model setting for four cases
Open boundary Wave-induced ice yield scheme SWH/m Tpeak/s Strain model Stress model Case 1 2.2 12 √ Case 2 2.2 12 √ √ Case 3 5 15 √ Case 4 5 15 √ √ -
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