An instability theory of ice--air interaction for the migration of the marginal ice zone

A guided discharge of ice into the belt of subpolar and midlatitude westerlies from the polar region is observed near the east side of both the Antarctic Peninsula and Greenland. Meteorological observations (Schwerdtfeger) show that moderate to strong southerly surface winds often develop along the marginal ice zone (MIZ) near the east side of the Antarctic Peninsula. Such strong winds are generated by surface temperature gradient over ice and water. These surface winds, acting through stress, in turn force the drift of the MIZ. This implies an ice-air feedback mechanism. A coupled air-ice model is established to discuss the instability properties of such a feedback mechanism. the model consists of two parts: thermally forced boundary layer air flow (Kuo) and mechanically forced MIZ drift. the two components are linked through surface temperature gradient and surface wind stress. The coupled ice-air model is solved for different values of the three parameters: (a) mean ice thickness Hi (0.5 m < Hi < 10.5 m), (b) mean surface temperature difference over ice and water DT0 (1°C < DT0 < 21°C), and (c) Brunt-Väisälä frequency (0.32 × 10−2 s−1 < N < 1.45 × 10−2 s−1). The model results show that the ice motion exhibits two bifurcations. First, it bifurcates into decaying or growing mode, which depends in most cases on the mean surface temperature difference DT0 representing the strength of the forcing. When DT0 is small, the decaying mode exists. However, when DT0 exceeds a first critical value which depends on Hi and N (i.e. when N = 1.45 × 10−2 s−1 and Hi = 2.5 m, this critical value is 5°C), the growing mode appears. Second, the growing mode bifurcates into non-oscillatory and oscillatory states depending on DT0 and the properties of ice. If DT0 exceeds the first critical value but does not reach a second critical value which mostly depends on N (i.e. when N = 1.45 × 10−2 s−1, the second critical value is 14°C), and when ice is thin (generally during summer) the ice motion is non-oscillatory; however, when ice is thick (generally during winter) the ice motion is oscillatory. If DT0 exceeds the second critical value, only the non-oscillatory growing mode appears. We also estimate the scale of the ice velocity and compute the growth rate and oscillatory period. These values agree well with the observations and should provide a possible way to predict MIZ migration.