Plasma dynamics in thin domains

TL;DR

This paper develops a geometric framework for the Rotating Shallow Water Magnetohydrodynamics equations, deriving new stochastic models that preserve structure and could enhance uncertainty quantification in space plasma and solar physics.

Contribution

It introduces structure-preserving stochastic RSW-MHD models based on a Lie group invariant variational principle, advancing the modeling of plasma dynamics under uncertainty.

Findings

Derived new stochastic RSW-MHD equations

Preserved geometric structures in stochastic models

Potential applications in space weather and solar physics

Abstract

In the present work, we study the geometric structures of the Rotating Shallow Water Magnetohydrodynamics (RSW-MHD) equations through a Lie group invariant Euler-Poincar\'e variational principle. In this geometric framework, we derive new, structure-preserving stochastic RSW-MHD models by introducing stochastic perturbations to the Lie-Poisson structure of the deterministic RSW-MHD equations. The resulting stochastic RSW-MHD equations provide new capabilities for potential application to uncertainty quantification and data assimilation, for example, in space plasma (space weather) and solar physics, particularly in solar tachocline dynamics.