One-dimensional thermodynamic model of hummock evolution

Abstract

The one-dimensional thermodynamic model of evolution of hummock formation described. The relative speeds of freezing and melting of a hummock were calculated in the framework of the suggested model. Comparisons of model results with the analogous characteristics of flat sea ice were carried out. It is found that the results obtained agree well with data of field investigations in the Barents Sea.The sea ice cover of the Arctic Basin is not morphologically homogeneous. It represents a set of ice floes of various ages, thicknesses, sizes, and forms. A characteristic feature of a natural sea ice cover is the hummocks formed as a result of pieces of broken ice squeezed out under water or on the ice surface. Interest in research of hummocks is caused by design investigations started in recent years in areas of oil and gas fields on the shelf of the Arctic seas, because hummocks pose a real threat to pipelines on the bottom of the Arctic seas and to oil and gas extraction platforms. A number of original works devoted to thermodynamic modeling of the evolution of hummock formations [5, 7-9] have appeared recently. However, the question about thermodynamic modeling of the hummock evolution is not yet solved. Completely it is connected with a number of objective factors, in particular, with the absence of the generally accepted scheme of hummock formation and a different interpretation of some definitions of hummocks, such as the coefficient of filling and the thickness of the consolidated layer. In the paper, an attempt has been made to create a simple one-dimensional thermodynamic model of hummock formation with the application of the most frequently used principles and parameters of hummock description. Interest in the development of a correct one-dimensional thermodynamic model of hummock evolution is also connected with the fact that it is easy to use such a model in coupled dynamic-thermodynamic models of sea ice cover and, thus, to increase the quality of calculations with these models.For numerical estimation of freeze-up of the newly formed hummock and its subsequent melting, we use a simplified geometric model of crosssection of a hummock, suggested in [3], where data of instrumental observations on fast ice were analyzed. This scheme allows using a one-dimensional approach to calculation of freezing and melting of hummocks, the application of which is justified in a number of works [3,[5][6][7]9]. It is necessary to note that the sail of a hummock in the suggested model is a nonuniform structure consisting of ice pieces and air spaces. It is necessary to note that these air spaces are isolated and are not connected in any way to the atmosphere. Thus, the sail is the porous environment consisting of sea ice and air. The quantity of air inclusions is characterized by the filling coefficient representing the ratio of volume filled with ice to the total volume of hummock sail.The keel filling coefficient is defined in the same way with the only difference that the keel consist of ice pieces and the sea water fillin...

Modeling of freezing and melting hummocks on shelf of Sakhalin Island

“…Analogously to [1], studying the ice melting peculiarities (thermodynamic destruction), one must pay more attention to the hummock sail melting, because, when a sail melted, the melting rate of the consolidated layer should not essentially differ on the plain ice melting rate. Also it is known [6,13], that, in real conditions, melting of hummocks starts earlier than melting of plain ice in the neighboring sections.…”

“…As it can be seen in the figure, due to natural variability of the albedo, time of complete melting can vary by week from the average. Computations of the relative rate of the hummock sail melting (expressed in rate of plain ice melting as in [1]) as a function of the ice surface albedo showed that hummock sails melt faster than plain ice does. Beside that, the melting rate is inversely proportional to the filling coefficient, because, in comparison with plain ice of the same volume, less amount of ice from the hummock sail should melt.…”

“…Hence, the main reason of the greater hummock freezing rate (in comparison with plain ice) is degree of filling of a hummock below the freezing level. As it is shown in [1], the model represents a hummock keel as a compound of ice pieces and sea water that fills the porous space. Thus, decreasing of a hummock's portion, which is filled with water (i.e., increasing the hummock sail filling coefficient), leads to decreasing the upward heat flux that comes to the lower boundary of the hummock's freezing layer.…”

“…An opportunity of applying the model for study of the hummock-like structures formation first was considered in [1], where the partial model validation was performed for ice conditions that are usually observed in the southeastern part of the Barents Sea. Special ice observations carried out during the AARI's expedition in the northeastern shore of Sakhalin Island [10], allowed continuing these researches.…”