We present a new numerical procedure to assess the plausibility of a subglacial lake in case of relative small/moderate extension and surging temperate icefield. In addition to the flat signal from Ground Penetrating Radar remote survey of the area, early indication of a likely subglacial lake, required icefield data are: top surface elevation and bathymetry, top surface velocity at some points, in-depth temperature and density profiles of upper layer. The procedure is based on a mathematical model of the evolution of dynamics and thermo-dynamics of the icefield and of a subglacial lake. The Glen's law is adopted for ice rheology and Stokes reduction is applied; Large Eddy Simulation technique is used for the lake. Ice/water phase change is described. Finite volumes for model discretization and a front-tracking technique to follow the moving interface characterize the numerical method. We have applied this procedure to the case of a subglacial lake conjectured in the area of Amundsenisen, Svalbard, and, here, the results of a sensitivity study are discussed. In particular we point out that the effect of firn and snow upper layers on the system, in terms of temperature field, density and water content, has to be included in the modeling, as it contributes to the overcoming of the ice metastable state and the release of subglacial water. Accordingly, ice water content changes have to be carefully described. The depth of the bed depression is confirmed to be critical for the formation of the lake.

In areas of difficult access, such as the arctic ones, the extraction of inter- est zones (e.g. glaciers) from satellite images may be a valuable way to study and monitor their status . This work faces in particular the prob- lem of detecting different zones of glaciers from SAR (Synthetic Aperture Radar) images. In the polar regions the use of the SAR system is funda- mental because it works independently of weather and daylight. Segmentation is a process that allows an image to be divided into disjoint zones in such a way that each extracted area contains homogeneous char- acteristics. The numerical approach, here applied to detect glacier zones, is based on moving boundary modelling and is described by the eikonal equation. The upwind finite difference approximation of the eikonal equa- tion is solved by a fast marching technique, that starts from seed points in the region of interest and generates a front which evolves until the bound- ary of the region is identified. Results from segmentation of glacier images in the Svalbard archipelago acquired by ERS2 SAR (Synthetic Aperture Radar) and Envisat (ESA Environmental Satellite) ASAR (Advanced Synthetic Aperture Radar) are presented and discussed.

In this work we present a mathematical model for the description of the dynamical and thermodynamical evolution of a system consisting of an icefield locally underlaid by a subglacial lake occupying a bed depression. The representation of the phase change ice-water is the clue of the model. The numerical solution is based on a finite volume technique. The computational code is tested to describe a portion of the Amundsenisen Icefield, South-Spitsbergen, Svalbard, where the existence of subglacial lake has been hypothesized. The contribution of firn and snow upper layers to the system in terms of temperature fied, density and water content is shown to be non-negligible in the modelling, as it supports ice to overcome its metastable state and change into liquid phase thus forming the subglacial lake. Lake cavity depth (or, better, the bottom surface area) appears to be critical for the formation of the lake, being directly proportional to the amount of geothermal heat coming in. Numerical simulation results are consistent with the existence of the conjectured subglacial lake within the environmental conditions fixed to measured data. Improvements of ice water content modelling and boundary condition formulation are in progress.

Marine phytoplankton is known to produce surface-active materials as part of its metabolism. The sea surface tension gradient due to the presence of plankton produced surfactants leads to a surface shear stress, commonly known as Marangoni stress, that can be of non-negligible intensity in areas of converging (or diverging) flows, where surface-active material concentrates (or lacks). A natural set-up where this condition can be observed is the Langmuir circulation that establishes in presence of wind and waves and exhibits periodic and permanent areas of alternating convergence and divergence. In the present work we adopt a simplified Large Eddy Simulation model for describing the Langmuir circulation and, by the use of a numerical model previously published, obtain an estimate of the Marangoni stress. The computed Marangoni stress peaks in the converging flow areas to values that are two orders of magnitude higher than in the case of absence of wind burst, previously studied by the authors. Such stress, usually disregarded within the numerical simulations of sea and other basin waters, is in fact capable to modify sensibly the distribution of the ecosystem biological components and should be considered for inclusion in the mathematical modelling.

organizzazione di un minisimposio nell'ambito del convegno Seventh European Conference on Elliptic and Parabolic Problems, Gaeta (Italy), 20 - 25 Maggio 2012.

We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well known and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid phase to the balance of the momentum of the system influences significantly the numerical solution and is necessary in order to get a better match with the experimental observations. Here an up-to-date list of the most meaningful mathematical models and numerical simulations of this test is discussed and the need is shown of an accurate revision of the numerical simulations of melting/solidification processes of pure materials (e.g. artificial crystal growth) produced in the last thirty years and not accounting for the solid phase mechanics.

The mathematical modelling for studying the evolution of a grounded temperate icefield flowing from an ice divide is detailed. The conjecture of the existence of a subglacial lake is considered, in particular regarding the influence of physical and geometrical parameters.

The numerical procedure for the computational solution of the partial differential system for the dynamical and thermo-dynamical evolution of a grounded glacier and a subglacial lake is here detailed.