Dynamics of a rotating ellipsoid with a stochastic flattening

TL;DR

This paper introduces a stochastic differential equation model for the Earth's short-term shape fluctuations, linking stochastic shape variations to observed dynamic behaviors through numerical simulations.

Contribution

It develops a novel toy-model incorporating stochastic flattening fluctuations to explain short-term Earth dynamics, bridging experimental data and theoretical modeling.

Findings

Stochastic fluctuations influence short-term Earth's shape dynamics.

Numerical simulations replicate experimental short-term behaviors.

Model suggests stochastic effects are significant in Earth's shape variability.

Abstract

Experimental data suggest that the Earth short time dynamics is related to stochastic fluctuation of its shape. As a first approach to this problem, we derive a toy-model for the motion of a rotating ellipsoid in the framework of stochastic differential equations. Precisely, we assume that the fluctuations of the geometric flattening can be modeled by an admissible class of diffusion processes respecting some invariance properties. This model allows us to determine an explicit drift component in the dynamical flattening and the second zonal harmonic whose origin comes from the stochastic term and is responsible for short term effects. Using appropriate numerical scheme, we perform numerical simulations showing the role of the stochastic perturbation on the short term dynamics. Our toy-model exhibits behaviors which look like the experimental one. This suggests to extend our strategy with a more elaborated model for the deterministic part.