The other area where the sea ice mechanical property has possible role in the formation of sea ice is leads formed over the central part of the Arctic. Although some attention has been given to this process in the past [Smith et al., 1990; Smith and Morrison, 1993] there is lack of quantitative discussion as to where and how much area opens within the central pack. Again this is another dynamically induced feature which may carry some importance to the formation of the cold halocline water.
In this talk, I present some preliminary results from ongoing research on the above areas; first the direct influence of mechanical property of sea ice on coastal polynya, and the second the amount of opening associated with ice deformation. 2 Influence of mechanical property of sea ice on coastal polynya.
Over two decades, highly non-Newtonian, called plastic rheology, has been used to describe large scale stress-strain rate relationship for sea ice. Numerical models based on this rheology capture the basic flow field, Nonetheless, their validity in capturing finer feature such as a deformation field, not to mention actual processes forming leads, is still an open subject. Realizing that the formation and maintenance of coastal polynya and leads in the shear zone strongly depend on this stress-strain rate relationship, our first task is to understand the implication of plastic rheology in observable fields. This allows us to evaluate the validation of this particular rheology directly against observations. Given a wide variety of rheology used in the sea ice literature, i.e. linear viscous, incompressible, cavitating, elastic-viscous, visco-elastic, one would wonder how they differ and what are the implications in the formation of coastal polynya and leads. In other words, how do we categorize them, "rationally?" Looking back in the history, one immediately notices much of distinction among them is rather associated with morphology. Here I would propose the following definition for rheology of a two-dimensional material (note that there is no such a thing. But it is only a start!). Let us denote σ and ε as stress and strain rate andσ1 andσ2 as two principle components of stress andε1, and ε2 for their counterpart in strain rate. Then we define a norm of stress as
with ｜●｜a spectral radius function. With this norm being well defined even for a highly nonlinear rheology, we can categorize a wide variety of rheology by looking at an index n given by
[Ukita, 1998]. What is commonly refer to as plastic rheology and its variation is deflned by n=-1 whereas viscous rheology and granular rheology are defined by n=0 and 1, respectively. It is extremely interesting to note that the Glenn's law as is known in the glacier literature falls just in between the range of n=o and -1.
Moreover, for glacier ice laboratory experiments show that n depends on the ice temperature. The colder the ice, the higher the number, being close to -1. This is intuitively appealing as the colder material becomes more brittle. Which actually poses an interesting question. That is whether or not sea ice in a large scale is more rigid or brittle than a typical glacler ice?
The next step is to relate this index to observable quantities. This can be accomplished by examining a velocity profile in the aforementioned shear zone. It can be shown that when n approaches to -1 the velocity profile tends to have discontinuities, i.e. slips. In contrast, a greater value in the index results in a much smoother profile. Thus in principle one can relate an observed velocity profile in the coastal region to this index, thereby describing the mechanical property of sea ice. Which in turn can be used to describe the formation process of a coastal polynya in a chain of events with shifting wind direction, as well as characteristic width, frequency, and angle of coastal leads.
3 Maximum amount of opening
One of the major conclusions found by the ADIEUX group was that not only divergence but also pure shear motion can cause, or more precisely, associated with an opening of leads and cracks [Thorndike et al., 1975], thereby making a area available for freezing. Here we are facing with two different problems. One is how to estimate the deformation field, and the
