Sparse nonlinear models of chaotic electroconvection

TL;DR

This paper develops a reduced-order nonlinear model for chaotic electroconvection using sparse identification, capturing complex dynamics driven by charge, electric field, and fluid interactions.

Contribution

It introduces a novel sparse nonlinear modeling approach for high-dimensional electroconvection chaos, extending beyond traditional thermal convection models.

Findings

The model accurately reproduces chaotic dynamics.

It captures key nonlinear interactions.

The approach preserves system symmetries.

Abstract

Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modeling convection has given rise to the development of chaos theory and the reduced-order modeling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh-Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.