SPH Modelling of Sea-ice Pack Dynamics

Abstract

The paper is concerned with the problem of sea-ice pack motion and deformation under the action of wind and water currents. Differential equations describing the dynamics of ice, with its very distinct mateFfigrial responses in converging and diverging flows, express the mass and linear momentum balances on the horizontal plane (the free surface of the ocean). These equations are solved by the fully Lagrangian method of smoothed particle hydrodynamics (SPH). Assuming that the ice behaviour can be approximated by a non-linearly viscous rheology, the proposed SPH model has been used to simulate the evolution of a sea-ice pack driven by wind drag stresses. The results of numerical simulations illustrate the evolution of an ice pack, including variations in ice thickness and ice area fraction in space and time. The effects of different initial ice pack configurations and of different conditions assumed at the coast-ice interface are examined. In particular, the SPH model is applied to a pack flow driven by a vortex wind to demonstrate how well the Lagrangian formulation can capture large deformations and displacements of sea ice.

Simulation of Sea-ice Thermodynamics by a Smoothed Particle Hydrodynamics Method

“…This configuration was chosen for simulations, since it generates both converging and diverging ice flows in the pack domain. Detailed equations describing the wind velocities in the vortex field can be found in papers by Flato (1993), Morland and Staroszczyk (1998) and Staroszczyk (2017). Here we only note that the wind speed is zero at the vortex centre, increases linearly from zero to its maximum value u 0 at some distance R 0 from the vortex centre, and then decreases monotonically to zero with the distance increasing to infinity.…”

“…In the calculations, the kernel function W was adopted in the form of a quintic spline function proposed by Morris (1996). As in an earlier paper by Staroszczyk (2017), the standard smoothing kernels W were modified by following an approach proposed by Belytschko et al (1998). This approach makes it possible to better approximate the field variables at discrete particles located close to the open sea boundaries, so that the current positions of these moving boundaries are traced more accurately.…”

“…In the previous paper (Staroszczyk 2017) the proposed SPH model was applied to simulate the purely mechanical behaviour of an sea-ice pack; that is, the mass conservation equations (9) and (10) were solved without the thermodynamic source terms. In the present paper we first investigate the evolution of the ice thickness and ice concentration in a motionless pack (wind and water drag stresses are zero), in which the ice is subjected only to the action of a temperature field.…”

“…The SPH model presented in this work is an extension of a model developed earlier (Staroszczyk 2017) for simulating the behaviour of sea ice without any thermodynamic effects involved. The model is used to simulate the evolution of an ice pack driven by wind stresses and subject to the mechanism of ice growth/decay due to the phase changes (freezing of water and melting of ice).…”

Smoothed particle hydrodynamics implementation of the standard viscous–plastic sea-ice model and validation in simple idealized experiments

“…Following Wang et al (1998), Ji et al (2005) implemented a new viscoelastic-plastic rheology that was in better agreement with observations from the Bohai Sea. Recently, Staroszczyk (2017) proposed a sea-ice model considering ice behaving as a compressible non-linear viscous material with a (dimensionless) contact-length-dependent parameterization for floe collisions and rafting (Gray and Morland, 1994;Morland and Staroszczyk, 1998). In all of the above, except for Gutfraind and Savage (1997), the same ice particle density definition is used.…”