A two-dimensional model for the dynamics of sea ice.

*(English)*Zbl 0813.73049This reviewing article develops a systematic analysis of a sea ice pack considered as a thin layer of coherent ice floes and open water regions at the ocean surface. The pack is driven by wind stress and Coriolis force, with responsive water drag on the base of the floes.

The first three sections contain the results of previous modelling and present the theory. The presented analysis provides the systematic reduction of the three-dimensional equations for a mixture of ice and water in a smoothly varying layer at the ocean surface to a two- dimensional theory. The resulting two-dimensional model (in section 4) is a system of partial differential equations and algebraic relations for a horizontal velocity field \(v_ \alpha(x_ \alpha,t)\), layer thickness \(h(x_ \alpha,t)\), auxiliary thicknesses of coherent and ridging ice \(h_ c(x_ \alpha,t)\) and \(h_ r(x_ \alpha,t)\), ice area fraction \(A(x_ \alpha,t)\) and ridging area fraction \(A_ r(x_ \alpha,t)\), ice temperature \(\theta^ I(x_ \alpha,x_ 3,t)\), integrated water pressure \(P^ W(x_ \alpha,t)\) and integrated extra stress \(N^ e_{\alpha \beta}(x_ \alpha,t)\), dynamic water surface \(x_ 3 = z_ w(x_ \alpha,t)\).

Section 5 contains a complete analytic solution constructed for a one- dimensional flow problem, ignoring the lateral Coriolis effect. It describes a pack driven by wind stress against a rigid coast with all regions of convergence, as well as reduction and reversal of the wind stress so that a diverging region expands monotonically from the free rear edge to the coast.

The first three sections contain the results of previous modelling and present the theory. The presented analysis provides the systematic reduction of the three-dimensional equations for a mixture of ice and water in a smoothly varying layer at the ocean surface to a two- dimensional theory. The resulting two-dimensional model (in section 4) is a system of partial differential equations and algebraic relations for a horizontal velocity field \(v_ \alpha(x_ \alpha,t)\), layer thickness \(h(x_ \alpha,t)\), auxiliary thicknesses of coherent and ridging ice \(h_ c(x_ \alpha,t)\) and \(h_ r(x_ \alpha,t)\), ice area fraction \(A(x_ \alpha,t)\) and ridging area fraction \(A_ r(x_ \alpha,t)\), ice temperature \(\theta^ I(x_ \alpha,x_ 3,t)\), integrated water pressure \(P^ W(x_ \alpha,t)\) and integrated extra stress \(N^ e_{\alpha \beta}(x_ \alpha,t)\), dynamic water surface \(x_ 3 = z_ w(x_ \alpha,t)\).

Section 5 contains a complete analytic solution constructed for a one- dimensional flow problem, ignoring the lateral Coriolis effect. It describes a pack driven by wind stress against a rigid coast with all regions of convergence, as well as reduction and reversal of the wind stress so that a diverging region expands monotonically from the free rear edge to the coast.

Reviewer: P.A.Velmisov (Ulyanovsk)

##### MSC:

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

86A40 | Glaciology |

86A05 | Hydrology, hydrography, oceanography |