# Modal Extraction in Spatially Extended Systems

## TL;DR

This paper presents a practical method for extracting spatial structures and growth rates of slow eigenmodes in extended systems, demonstrated on Rayleigh-Bénard convection, with potential applications to complex dynamical states.

## Contribution

It introduces a novel experimental procedure for characterizing eigenmodes and their spectra in spatially extended systems, enabling analysis of complex dynamical behaviors.

## Key findings

- Successfully constructed the spectrum of linear modes near the secondary instability boundary.
- Demonstrated the technique on Rayleigh-Bénard convection.
- Suggested approach for characterizing complex dynamical states.

## Abstract

We describe a practical procedure for extracting the spatial structure and the growth rates of slow eigenmodes of a spatially extended system, using a unique experimental capability both to impose and to perturb desired initial states. The procedure is used to construct experimentally the spectrum of linear modes near the secondary instability boundary in Rayleigh-B\'{e}nard convection. This technique suggests an approach to experimental characterization of more complex dynamical states such as periodic orbits or spatiotemporal chaos.