Sea ice is not horizontally homogeneous on large scales. Its morphology is inherently discrete and made of individual floes. In recent years, sea ice models have incorporated this horizontal heterogeneity. The modelling framework considers an evolution equation for the probability density function of the floe size distribution (FSD) with forcing terms that represent the effects of several physical processes. Despite the modelling effort, a key question remains: What is the FSD emerging from the collection of all forcing processes? Field observations have long suggested that the FSD follows a power law, but this result has not been reproduced by models or laboratory experiments. The theoretical framework for FSD dynamics in response to physical forcings is presented. Wave-induced breakup is further examined with an emphasis on how it affects the FSD. Recent modelling results suggesting the consistent emergence of a log-normal distribution as a result of that process are further discussed. Log-normality is also found in a dataset of floe sizes, which was originally analysed under the power law hypothesis. A simple stochastic process of FSD dynamics, based on random fragmentation theory, is further shown to predict log-normality. We therefore conjecture that, in some situations, the emergent FSD follows a log-normal distribution. This article is part of the theme issue ‘Theory, modelling and observations of marginal ice zone dynamics: multidisciplinary perspectives and outlooks’.

Abstract. Fragmentation of the sea ice cover by ocean waves is an important mechanism impacting ice evolution. Fractured ice is more sensitive to melt, leading to a local reduction in ice concentration, facilitating wave propagation. A positive feedback loop, accelerating sea ice retreat, is then introduced. Despite recent efforts to incorporate this process and the resulting floe size distribution (FSD) into the sea ice components of global climate models (GCM), the physics governing ice breakup under wave action remains poorly understood, and its parametrisation highly simplified. We propose a two-dimensional numerical model of wave-induced sea ice breakup to estimate the FSD resulting from repeated fracture events. This model, based on linear water wave theory and viscoelastic sea ice rheology, solves for the scattering of an incoming time-harmonic wave by the ice cover and derives the corresponding strain field. Fracture occurs when the strain exceeds an empirical threshold. The geometry is then updated for the next iteration of the breakup procedure. The resulting FSD is analysed for both monochromatic and polychromatic forcings. For the latter results, FSDs obtained for discrete frequencies are combined appropriately following a prescribed wave spectrum. We find that under realistic wave forcing, lognormal FSDs emerge consistently in a large variety of model configurations. Care is taken to evaluate the statistical significance of this finding. This result contrasts with the power-law FSD behaviour often assumed by modellers. We discuss the properties of these modelled distributions, with respect to the ice rheological properties and the forcing waves. The projected output will be used to improve empirical parametrisations used to couple sea ice and ocean waves GCM components.

Abstract. Fragmentation of the sea ice cover by ocean waves is an important mechanism impacting ice evolution. Fractured ice is more sensitive to melt, leading to a local reduction in ice concentration, facilitating wave propagation. A positive feedback loop, accelerating sea ice retreat, is then introduced. Despite recent efforts to incorporate this process and the resulting floe size distribution (FSD) into the sea ice components of global climate models (GCMs), the physics governing ice breakup under wave action remains poorly understood and its parametrisation highly simplified. We propose a two-dimensional numerical model of wave-induced sea ice breakup to estimate the FSD resulting from repeated fracture events. This model, based on linear water wave theory and visco-elastic sea ice rheology, solves for the scattering of an incoming time-harmonic wave by the ice cover and derives the corresponding strain field. Fracture occurs when the strain exceeds an empirical threshold. The geometry is then updated for the next iteration of the breakup procedure. The resulting FSD is analysed for both monochromatic and polychromatic forcings. For the latter results, FSDs obtained for discrete frequencies are combined following a prescribed wave spectrum. We find that under realistic wave forcing, lognormal FSDs emerge consistently in a large variety of model configurations. Care is taken to evaluate the statistical significance of this finding. This result contrasts with the power law FSD behaviour often assumed by modellers. We discuss the properties of these modelled distributions with respect to the ice rheological properties and the forcing waves. The projected output can be used to improve empirical parametrisations used to couple sea ice and ocean wave GCM components.

To model the alpha decay, cluster radioactivity, fusion, fission and fragmentation phenomena of microscopic or macroscopic distributions of matter or charge it is useful to simulate these deformed physical objects by geometric shapes allowing the determination of their root mean square radius, volume, surface and Coulomb energies as well as their moments of inertia and quadrupole moments. Most of the shapes used in macroscopic nuclear physics are briefly recalled. In particular, several shape sequences that we have used previously, mainly formed from generalized lemniscatoids, are more extensively detailed. They allow to describe the transitions from one compact configuration to several ones or vice versa.

Different families of geometric shapes, derived mainly from lemniscatoids, are proposed to describe ground and excited states of leptodermous distributions of nuclear matter. The transition from one spherical or ellipsoidal nucleus to several spherical or ellipsoidal nuclei or vice versa (in the decay and entrance channels of nuclear reactions: fission, fusion and fragmentation) is particularly investigated. The geometric characteristics of these configurations are given, allowing the calculations of the system energy, of the dynamics of the reactions and of the angular distribution of the fragments.