# Optimal perturbations of gravitationally unstable, transient, boundary layers in porous media

## TL;DR

This paper investigates the stability of transient, gravitationally unstable boundary layers in porous media, revealing that traditional analysis can produce unrealistic perturbations and proposing a new physically constrained nonmodal stability method.

## Contribution

The paper introduces a nonmodal stability approach with physical constraints, improving the prediction of instability growth in transient porous media boundary layers.

## Key findings

- Instability onset is highly sensitive to perturbation measures and timing.
- Classical methods may produce physically unrealizable perturbations.
- The new method predicts larger spanwise wavenumbers and smaller amplification for instabilities.

## Abstract

We study gravitationally unstable, transient, diffusive boundary layers in porous media using modal and nonmodal stability methods. Using nonmodal stability theory, we demonstrate that both the onset of linear instabilities and the shape of optimal perturbations are highly sensitive to perturbation amplification measures and also the time at which the boundary layer is perturbed. This behavior is in contrast to traditional studies of steady or non-transient diffusive boundary layers where perturbation dynamics are independent of perturbation measure or time. We demonstrate that any analysis of transient layers produced through classical methods can result in physically unrealizable perturbation structures. To resolve the issue, we propose a nonmodal stability procedure which additionally constrains the perturbation dynamics to physically admissible fields. The proposed procedure predicts that instabilities grow primarily due to unstable perturbations featuring much larger spanwise wavenumbers (modes) and smaller amplifications compared to perturbations predicted using classical methods. We validate our predictions using direct numerical simulations that emulate the onset of convection in physical systems.