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The future behavior of the West Antarctic Ice Sheet (WAIS) may have a major impact on future climate. For instance, ice sheet melt may contribute significantly to global sea level rise. Understanding the current state of WAIS is therefore…
Climate science studies the structure and dynamics of Earth's climate system and seeks to understand how climate changes over time, where the data is usually stored in the format of time series, recording the climate features, geolocation,…
Stuart-Landau limit-cycle oscillators are a paradigm in the study of coherent and incoherent limit cycles. In this work, we generalize the standard Stuart-Landau dimer model to include effects due to an inertia-like term and noise and study…
This chapter is dedicated to the slow dynamics of the climate system, at time scales of one~thousand to one million years. We focus specifically on the phenomenon of ice ages that has characterised the slow evolution of climate over the…
A disordered quasi-liquid layer of water is thought to cover the ice surface, but many issues, such as its onset temperature, its thickness, or its actual relation to bulk liquid water have been a matter of unsettled controversy for more…
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
The full Stokes equations are solved by a finite element method for simulation of large ice sheets and glaciers. The simulation is particularly sensitive to the discretization of the grounding line which separates the ice resting on the…
In this paper, we study how relaxing the classical hydrostatic balance hypothesis affects theoretical aspects of the LU primitive equations well-posedness. We focus on models that sit between incompressible 3D LU Navier-Stokes equations and…
The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In…
Water is one of the most abundant substances on Earth, and ice, i.e., solid water, has more than 18 known phases. Normally ice in nature exists only as Ice Ih, Ice Ic, or a stacking disordered mixture of both. Although many theoretical…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
Numerical ice sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or…
The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the…
Zeitlin's model is a discretisation of the 2-D Euler equations that preserves the underlying geometric structure. This feature makes it suitable for studying the qualitative behaviour of the dynamics. Here, we utilise Arnold's geometric…
The Earth's climate is rapidly changing and some of the most drastic changes can be seen in the Arctic, where sea ice extent has diminished considerably in recent years. As the Arctic climate continues to change, gathering in situ sea ice…
We study analytically the equilibrium and near-equilibrium properties of a model of surfaces relaxing via linear surface diffusion and subject to a lattice potential. We employ the variational mean field formalism introduced by Saito for…
At near-grounded glacier termini, calving can lead to the capsize of kilometer-scale unstable icebergs. The transient contact force applied by the capsizing iceberg on the glacier front generates seismic waves that propagate over…
We analyze the stability of stationary solutions of a singular Vlasov type hydrodynamic equation (HE). This equation was derived (under suitable assumptions) as the hydrodynamical scaling limit of the Hamiltonian evolution of a system…
We study in detail the hydrodynamic theories describing the transition to collective motion in polar active matter, exemplified by the Vicsek and active Ising models. Using a simple phenomenological theory, we show the existence of an…
Sea ice plays a crucial role in the climate system, particularly in the Marginal Ice Zone (MIZ), a transitional area consisting of fragmented ice between the open ocean and consolidated pack ice. As the MIZ expands, understanding its…