Molecular-dynamics simulation of clustering processes in sea-ice floes

In seasonally ice-covered seas and along the margins of perennial ice pack, i.e., in regions with medium ice concentrations, the ice cover typically consists of separate floes interacting with each other by inelastic collisions. In this paper, hitherto unexplored analogies between this type of ice cover and two-dimensional granular gases are used to formulate a model of ice dynamics at the floe level. The model consists of (i) momentum equations for floe motion between collisions, formulated in the form of a Stokes-flow problem, with floe-size-dependent time constant and equilibrium velocity, and (ii) a hard-disk collision model. The numerical algorithm developed is suitable for simulating particle-laden flow of $N$ disk-shaped floes with arbitrary size distributions. The model is applied to study clustering phenomena in sea ice with power-law floe-size distribution. In particular, the influence of the average ice concentration $\overline{A}$ on the formation and characteristics of clusters is analyzed in detail. The results show the existence of two regimes, at low and high ice concentrations, differing in terms of the exponents of the cluster-size distribution and of the size of the largest cluster.

Figure 1

Fragments of Landsat images showing clustered sea-ice floes off the Antarctic coast (at 121.8${}^{\circ }$W, 73.5${}^{\circ }$S) on 18 February 2008 (a) and 26 January 2008 (b). Source: [12].

Figure 2

A side view of a disk-shaped ice floe under the action of wind and current. The arrows are not to scale. See the text for explanation of the symbols.

Figure 3

Time constant $\tau$ (a), and the coefficient $C$ and the equilibrium floe velocity $|{\mathbf{u}}_{\mathrm{eq}}|$ for wind speed $|{\mathbf{u}}_a|=10$ m/s (b) as functions of the floe diameter $d_i$, for a set of ice thickness values $h$. The lines are drawn every 0.5 m from $h=0.5$ to $3.0$ m. Thick lines correspond to the model setup used in the simulations described in Sec. 4 (see Table ).

Figure 4

Flowchart of the SFC model.

Figure 5

Snapshots (floe positions and velocities, in m/s, shown in gray scale) in a clustered state for $\overline{A}=0.6$ (a), $0.725$ (b), and $0.85$ (c). For better clarity, only equal-size fragments of the model domains are shown.

Figure 6

Scatter plots of instantaneous floe velocity components parallel (a), (c) and perpendicular (b), (d) to the wind direction, as functions of the floe radius $r$, for $\overline{A}=0.6$ (a), (b) and $0.9$ (c), (d). The lines in (a) and (c) mark the equilibrium velocity $|{\mathbf{u}}_{\mathrm{eq}}|$.

Figure 7

Radial distribution function $g_{rdf}$ (a), (c) and floe-floe distance distribution $g_{ffd}$ (b), (d) at the initial (random) and “final” (clustered) phases for $\overline{A}=0.6$ (a), (b) and $0.9$ (c), (d). Symbols along the upper borders of (a) and (c) show radii of the eight largest floes in the sample.

Figure 8

Rank-order distributions of effective cluster radii $r_e={(F_c/\pi )}^{1/2}$ in fully clustered states for $\overline{A}=0.6$, 0.725, and 0.9. Black dots show the corresponding distribution of the radii of single floes. Values are normalized so that $\pi \sum r_{e,i}^2=1$.

Figure 9

Exponent $\alpha$ of the distributions $P\left(r_e\right)$ of effective cluster radii $r_e$ [Eq. (16)] as a function of the mean ice concentration $\overline{A}$. The horizontal dashed line shows the value of ${\alpha }_r=1.5$. The continuous line shows the linear least-squares fit to the data for $\overline{A}>0.7$.

Figure 10

Surface area of the largest cluster $F_{c,1}$ (relative to the total surface area of all floes, $F_{\mathrm{tot}}$) as a function of the mean ice concentration $\overline{A}$. For each value of $\overline{A}$, the minimum and maximum values of $F_{c,1}$ recorded in the quasistationary state are shown.

Figure 11

Fragment of a Landsat image of the Okhotsk Sea (3 March 2003, 157.1${}^{\circ }$E, 58.7${}^{\circ }$N) with clusters of thick ice floes consolidated by thin ice. Source: [12].