[HTML][HTML] An efficient geometric method for incompressible hydrodynamics on the sphere
We present an efficient and highly scalable geometric numerical method for two-
dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite …
dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite …
A Casimir preserving scheme for long-time simulation of spherical ideal hydrodynamics
K Modin, M Viviani - Journal of Fluid Mechanics, 2020 - cambridge.org
The incompressible two-dimensional Euler equations on a sphere constitute a fundamental
model in hydrodynamics. The long-time behaviour of solutions is largely unknown; statistical …
model in hydrodynamics. The long-time behaviour of solutions is largely unknown; statistical …
Zeitlin truncation of a shallow water quasi‐geostrophic model for planetary flow
AD Franken, M Caliaro, P Cifani… - Journal of Advances in …, 2024 - Wiley Online Library
In this work, we consider a Shallow‐Water Quasi Geostrophic equation on the sphere, as a
model for global large‐scale atmospheric dynamics. This equation, previously studied by …
model for global large‐scale atmospheric dynamics. This equation, previously studied by …
Casimir preserving spectrum of two-dimensional turbulence
We present predictions of the energy spectrum of forced two-dimensional turbulence
obtained by employing a structure-preserving integrator. In particular, we construct a finite …
obtained by employing a structure-preserving integrator. In particular, we construct a finite …
Canonical scale separation in two-dimensional incompressible hydrodynamics
K Modin, M Viviani - Journal of Fluid Mechanics, 2022 - cambridge.org
The rules that govern a two-dimensional inviscid incompressible fluid are simple. Yet, to
characterise the long-time behaviour is a knotty problem. The fluid fulfils Euler's equations: a …
characterise the long-time behaviour is a knotty problem. The fluid fulfils Euler's equations: a …
[HTML][HTML] Data-driven stochastic spectral modeling for coarsening of the two-dimensional Euler equations on the sphere
A resolution-independent data-driven subgrid-scale model in coarsened fluid descriptions is
proposed. The method enables the inclusion of high-fidelity data into the coarsened flow …
proposed. The method enables the inclusion of high-fidelity data into the coarsened flow …
Eulerian and Lagrangian stability in Zeitlin's model of hydrodynamics
K Modin, M Perrot - Communications in Mathematical Physics, 2024 - Springer
Abstract The two-dimensional (2-D) Euler equations of a perfect fluid possess a beautiful
geometric description: they are reduced geodesic equations on the infinite-dimensional Lie …
geometric description: they are reduced geodesic equations on the infinite-dimensional Lie …
Energy cycle for the Lorenz attractor
V Pelino, F Maimone, A Pasini - Chaos, Solitons & Fractals, 2014 - Elsevier
In this paper we identify an energetic cycle in the Lorenz-63 system through its Lie–Poisson
structure. A new geometrical view of this Lorenz system is presented and sheds light on its …
structure. A new geometrical view of this Lorenz system is presented and sheds light on its …
Continuous data assimilation closure for modeling statistically steady turbulence in large-eddy simulation
A closure model is presented for large-eddy simulation (LES) based on the three-
dimensional variational data assimilation algorithm. The approach aims at reconstructing …
dimensional variational data assimilation algorithm. The approach aims at reconstructing …
Data-assimilation closure for large-eddy simulation of quasi-geostrophic flow on the sphere
A closure model is presented for large-eddy simulation (LES) based on the three-
dimensional variational data assimilation algorithm. The approach aims at reconstructing …
dimensional variational data assimilation algorithm. The approach aims at reconstructing …