Related papers: Some Mathematical and Numerical Issues in Geophysi…
Purely self-gravitating systems of point particles have been extensively studied in astrophysics and cosmology, mainly through numerical simulations, but understanding of their dynamics still remains extremely limited. We describe here…
This study proposes deterministic and stochastic energy-aware hybrid models that should enable simulations of idealized and primitive-equations Geophysical Fluid Dynamics (GFD) models at low resolutions without compromising on quality…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
In this work, we will present a physically consistent theory to derive the governing equations of the Large Eddy Simulation (LES) framework based on first principles rather than the motivation to conduct computationally affordable…
Modeling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems. We show that when the kernel of these emulators is also learned…
We review recent advances in understanding singularity and small scales formation in solutions of fluid dynamics equations. The focus is on the Euler and surface quasi-geostrophic (SQG) equations and associated models.
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an elaborate scheme for building global quasiperiodic solutions…
Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective ("dressed") velocities that depend on…
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. From deterministic viewpoint the 3D Primitive Equations are…
Efficient and effective modeling of complex systems, incorporating cloud physics and precipitation, is essential for accurate climate modeling and forecasting. However, simulating these systems is computationally demanding since…
Extracting information on fluid motion directly from images is challenging. Fluid flow represents a complex dynamic system governed by the Navier-Stokes equations. General optical flow methods are typically designed for rigid body motion,…
We briefly discuss the phenomenological theory of dissipative fluid. We also present some numerical results for hydrodynamic evolution of QGP fluid with dissipation due to shear viscosity only. Its effect on particle production is also…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between…
Compatible finite elements provide a framework for preserving important structures in equations of geophysical fluid dynamics, and are becoming important in their use for building atmosphere and ocean models. We survey the application of…
The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…
This work presents a new vortex dynamic equation for quasi-geostrophic flows over strongly variable sediment bottoms. The equation considers erosion/deposition exchanges near the bottom and the geometrical changes of the bed interface,…
The study of thermal fluctuations in relativistic hydrodynamics has led to numerous important developments in the last decade. We present a bird's eye view of the recent advances on the theory of fluctuations on three fronts; stochastic…
One of the most important topics in geophysics is to study convection in a sea. Based on the algebraic characteristics of the equations of dynamic convection in a sea, we introduce various schemes with multiple parameter functions to solve…
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…