Self-similarity and self-organization of drifting ice cover in the Arctic basin

Abstract

Ice cover of the Arctic Ocean is a dynamic dissipative system of the geophysical level, in which physicomechanical processes of various scales and intensities occur simultaneously and lead to the formation of a discrete structure of the ice cover. Spatial gradients of the ice drift velocity [1, 2] are formed during interaction between the ocean and the atmosphere. Both deformations of ice and its motion characterize the spatial nonuniformity of ice drift. The local vector of the velocity of ice displacement can differ significantly from the velocity vector of the general ice drift. Ice motions are accompanied by random motion in various directions with different velocities [3]. Chaotic fluctuations of the drift velocity of various scales can cause turbulent ice motion. Significant accelerations in the ice appear only during comparatively short interactions between ice formations in the course of contraction and extension caused by surface and internal waves in the ocean [4]. Diamond-shaped and mosaic fragments of ice formations observed in air photos and satellite images make up self-similar figures, whose size varies from hundreds of meters to hundreds of kilometers. Nonuniformity in the mechanical characteristics of the ice cover facilitates the character of deformations and fractures in the ice. The authors of [5‐7] showed that the relation between the number of ice formations N and their sizes R corresponds to the power law N R – X , where exponent X is linearly related to the fractal dimension of the ensemble of ice cover fragments. A similarity in the dynamic processes upon changing the scale of observation was recorded in seismology [8, 9]. The power law of the distribution of the number of events with respect