# Hydrodynamic stability in the presence of a stochastic forcing:a case study in convection

## TL;DR

This paper studies how stochastic internal heating affects the stability of Rayleigh-Bénard convection, showing that small stochastic forcing has minimal impact while strong forcing destabilizes the system, using a combined analytical and computational approach.

## Contribution

It introduces a novel methodology for analyzing hydrodynamic stability under large-scale stochastic forcing applicable to various systems.

## Key findings

- Small stochastic forcing has negligible effect on stability.
- Strong stochastic forcing destabilizes the conductive state.
- The approach combines rigorous analysis with computational methods.

## Abstract

We investigate the stability of statistically stationary conductive states for Rayleigh-B\'enard convection that arise due to a bulk stochastic internal heating. Our results indicate that stochastic forcing at small magnitude has little to no effect, while strong stochastic forcing has a destabilizing effect. The methodology put forth in this article, which combines rigorous analysis with careful computation, provides an approach to hydrodynamic stability which is applicable to a variety of systems subject to a large scale stochastic forcing.