Constitutive Equation and Numerical Method for Sea Ice Dynamics
at meso-micro scale
Dr. Ji Shunying, State Key Laboratory of Structural Analysis for Industrial Equipment,
Dalian University of Technology, Dalian, 116023, China.
Email: jisy@dlut.edu.cn
To study the influence of polar ice on the change of global climate, especially to
provide service to oil/gas exploration in ice covered seas, it is necessary to simulate
and forecast the ice growth and drifting processes with sea ice thermodynamics and
dynamics. In the sea ice dynamics numerical simulation, the constitutive equation and
numerical method are two key works. In the sea ice regions of middle latitude, such
as the Bohai Sea, Baltic Sea and Okhotsk Sea, under the strong actions of wind,
current and tide etc. marine environmental conditions, the ice dynamic process with
ice obvious ridging and rafting are more complex than that of Polar region and
Margin Ice Zone (MIZ). Therefore, to simulate the ice dynamics precisely, the
constitutive equation and numerical method should be constructed considering the ice
dynamic characteristics of the above sea areas.
In the pervious study of sea ice dynamics, a series of constitutive equations were
established, such as elastic-plastic (Coon et al., 1974), viscous-plastic(Hibler,1979),
elastic-viscous-plastic(Hunk, 1997), anisotropic elastic-plastic (Coon et al., 1998;
Pritchard, 1998), in which Hibler’s model was applied widely at large and
meso-scales. In the sea ice dynamic simulation at meso-micro scale, the
spatio-temporal scale decreases obviously, in which the calculating cell from 100 km
to 2 km, the time step from 24 hours to 1 minute. Moreover, with the scale changing,
the ice ridging and rafting become more important, and should be considered
especially in sea ice dynamics. Recent years, some initial mechanics models were
established (Hopkins, 1999; Hibler, 2001), but they can’t be applied expediently in
sea ice dynamics simulation. Based on the theory of viscous - elastic-plastic (VEP)
unified constitutive theory, the mechanical behaviors of elastic, viscous- elastic,
plastic, and viscous-plastic in the sea ice cover deformation should be coupled
together, as well the mechanical parameters should be determined considering the ice
ridging and rafting.
In the simulation of sea ice dynamics, most people used the Eulerian finite difference
(FD) method. To calculate the ice edge perfectly, the particle-in-cell (PIC) method
was adopted (Flato, 1993). While the smoothed-particle hydrodynamics (SPH)(Shen,
1997; Wang, 2000) method was used to avoid the numerical diffusion of FD and PIC
methods. All of above method was established on the postulation of sea ice
continuous distribution. In fact, with the break-up, ridging and rafting of in the ice
cover drifting process, the ice distribution appears continuous and discrete at different
scales. Even a Distributed Mass/Discrete Floe (DMDF) Model was established
(Rheem, 1997), the ice dynamic process can’t be described in details. Therefore,
considering the ice ridging and rafting processes, while the continuous and discrete
distribution of ice cover, a new numerical method of Arbitrary
Lagrangian-Eulerian(ALE) can be adopted coupling the Eulerian and Lagrangian
coordinate systems.
The present work is to construct a new unified VEP constitutive equation and an ALE
numerical method for sea ice dynamics at meso-micro scales, in which the ice ridging
and rafting dynamic processes can be considered perfectly, and the ice edge can also
be simulated precisely.
References
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