PARTICLE-IN-CELL AND FINITE-DIFFERENCE APPROACHES FOR THE STUDY OF MARGINAL ICE-ZONE PROBLEMS

Eulerian Finite Difference (FD) and quasi-Lagrangian Particle-In-Cell (PIC) approaches are applied in the present paper to study Marginal Ic e Zone (MIZ) problems. The elliptical, viscous-plastic, rheological mo del of Hibler (Hibler, W.D. III, 1979. A dynamic thermodynamic sea ice model. J. Phys. Oceanogr., Vol. 9, pp. 815-846) was used. The numeric al implementation of the equations governing the ice motion is describ ed in detail. A Successive Over-Relaxation (SOR) scheme is employed fo r the FD and PIC methods in solving the momentum equation. Following Z hang and Hibler (Zhang, J., Hibler, W.D. III, 1997. On an efficient nu merical method for modeling sea ice dynamics. J. Geophys. Res., Vol. 1 02, pp. 8691-8702), a pseudo time stepping procedure was used to updat e the bulk and shear viscosities, and the other velocity dependent ter ms, while maintaining the ice strength and the old time step velocity appearing in the inertia term partial derivative v/partial derivative t unchanged. By performing these pseudo time step iterations, it was p ossible to (1) ensure that the stresses corresponded to the elliptical yield criterion during plastic deformation, and (2) improve the accur acy of the velocity field and hence, the nonlinear terms involving vel ocities. Two geometrical configurations were examined: a straight MIZ in which the coast was modeled by a straight rigid boundary; and a MIZ in which the coast was considered to be a straight corner-shaped soli d boundary. Special attention was given to the implementation of the b oundary conditions for ice-water interfaces. This is an important elem ent in MIZ problems where one can find complex moving ice-water interf aces, which are not usually observed in the Arctic basin. A simple way to calculate the ice compactness, which is particularly useful for th e PIC method, is described. The present numerical results obtained fro m both the FD and the PIC methods are in general agreement. In particu lar, results obtained from these two approaches for the straight MIZ a re almost identical. However, the PIC method has the advantage of prov iding an exact location of the free edge of the ice. It also appears t o provide a more accurate and trouble-free means to predict deformatio ns within the ice fields. (C) 1998 Elsevier Science B.V. All rights re served.