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This article is concerned with rigorously justifying the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main distinction of this work compared to previous studies is the absence of…
In this study, we employ and modify the Lorenz energy cycle (LEC) framework as another way to understand the atmospheric circulation on tidally locked terrestrial planets. It well describes the atmospheric general circulation in the…
Systems comprising a turbulent channel flow overlaying a permeable bed can be found in a variety of industrial and natural applications (e.g. urban planning, fracking, submerged vegetation). One important realization of this system is at…
I consider the problem of weakly nonlinear stability of three-dimensional parity-invariant magnetohydrodynamic systems to perturbations, involving large scales. I assume that the MHD state, the stability of which I investigate, does not…
A data-driven framework is presented, that enables the prediction of quantities, either observations or parameters, given sufficient partial data. The framework is illustrated via a computational model of the deposition of Cu in a Chemical…
The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. In this formulation…
We consider a family of stochastic models of evolving two-dimensional Young diagrams, given in terms of certain energies, with Gibbs invariant measures. `Static' scaling limits of the shape functions, under these Gibbs measures, have been…
Constructing high-resolution 3D geological models from sparse 1D borehole and 2D surface data is a highly ill-posed inverse problem. Traditional heuristic and implicit modeling methods fundamentally fail to capture non-linear topological…
Invariant parameterization schemes for the eddy-vorticity flux in the barotropic vorticity equation on the beta-plane are constructed and then applied to turbulence modeling. This construction is realized by the exhaustive description of…
The ocean interior regulates Earth's climate but remains sparsely observed due to limited in situ measurements, while satellite observations are restricted to the surface. We present a depth-aware generative framework for reconstructing…
Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents,…
An innovative computational approach to capturing the essential aspects of an Enhanced Geothermal System (EGS) is formulated. The modified finite element method is utilized to model transient heat and fluid flow within an EGS reservoir.…
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include…
Measurements of atmosphere-surface exchange are largely limited by the availability of fast-response gas analyzers; this limitation hampers our understanding of the role of terrestrial ecosystems in atmospheric chemistry and global change.…
Entropic dynamics (ED) is a general framework for constructing indeterministic dynamical models based on entropic methods. ED has been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved…
Kilometer-scale weather data is crucial for real-world applications but remains computationally intensive to produce using traditional weather simulations. An emerging solution is to use deep learning models, which offer a faster…
A scale invariant, selfsimilar atmospheric eddy continuum exists in the planetary atmospheric boundary layer spanning several orders of magnitude in scales and gives rise to the observed fractal geometry for the global cloud cover pattern.…
The study of flow in fractured porous media is a key ingredient for many geoscience applications, such as reservoir management and geothermal energy production. Modelling and simulation of these highly heterogeneous and geometrically…
We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles --- the Wasserstein geometry --- which allows the deterministic…
The two-layer quasigeostrophic model (2LQG) and the Eady model are two idealized systems illustrating the baroclinic instability of atmospheric jets and ocean currents. The two setups share many ingredients -- background vertically sheared…