Two-dimensional unsteady polynya flux model solutions incorporating a parameterisation for the collection depth of consolidated new ice

"Polynya flux models" approximate the evolution of a coastal latent heat polynya by assuming that the position of the polynya edge (P) is determined by a balance between the flux of frazil ice arriving at P and the flux of consolidated new ice removed at P by the offshore ice sheet. If the fluxes are equal, then the polynya is in equilibrium; if they are not, then the polynya is in a state of evolution.

Calculation of the consolidated new ice flux requires knowledge of the collection depth of consolidated new ice (H), and for polynya flux models this is usually taken as constant. However, clearly H should be determined as part of the problem. To this end, the authors have derived a parameterisation for H in terms of (a) the frazil ice depth at P, (b) a term associated with wave radiation stress, and (c) the component, normal to P, of the frazil ice velocity relative to the consolidated new ice velocity. H is now coupled to the polynya edge through its dependence on the normal to P. The inclusion of the parameterisation of H also means that the resulting flux model equations are robust, which is not guaranteed when H is uniform.

In this talk, we apply two-dimensional flux model theory to the case of a polynya opening in the lee of a straight coastal barrier of finite length, which can be thought of as an idealised island. The inclusion of the parameterisation for H means that the methodology appropriate for the case of constant H cannot be followed. Instead, the problem is formulated in terms of a single first-order nonlinear partial differential equation, which is solved by a version of the method of characteristics.