Mathematical modeling in studies of Arctic Ocean circulation

A hierarchy of mathematical models adapted to certain physical phenomena of the Arctic Ocean has been developed. The density structure of the Arctic Ocean water is characterized by a well-marked stratification. In this context a two-dimensional model of the upper 200 m of the ocean can be considered as the lowest level of a hierarchy of models. With the help of this model, coupled with the ice drift model, seasonal oscillations of sea level, and variability of barotropic water circulation in the annual cycle, affected by wind, atmospheric pressure and river runoff, were studied. The same model is used to predict level oscillations and ice drift up to 6 days in advance. The multi-layer models are suggested as models of the second level. The diagnostic two-layer model is simple to use on small computers. The prognostic two-layer model allows one to estimate the time when the water circulation becomes stationary in the ocean of real depth. The diagnostic three-dimensional ocean model with a continuous stratification is suggested as the third level model. The elliptical equation relative to denivelation of the free surface is the governing equation of the model. The estimation of the terms of the motion and continuity equations indicates the need to introduce geostrophic corrections for non-linear effects and a horizontal turbulent exchange when calculating vertical current velocity. Tidal motions in the ocean are simulated by means of a joint non-linear model of water and ice motion, taking into account astronomical factors, the earth's tides, effects of loading and self-gravitation, and viscous-elastic interaction of the ice cover. On the basis of these models, the formation features of the diurnal O, K and semi-diurnal M and S harmonics of the tidal potential are studied and the irregularities of the ice cover during the tidal period are calculated