1. Brief review of linear algebra, understanding the basics of modal analysis.
2. Literature review of different techniques (DFT, POD, DMD, Koopman spectral analysis, sPOD, mPOD).
3. Comparison of the different methods, advantages, and disadvantages.
4. Data acquisition. High-fidelity experiments or numerical simulations.
5. Application of the techniques on the data set.
6. Summary and documentation of the results.

Background:

In general, complex fluid flows consist of a range of temporal and spatial „features”. Nowadays, it is a common practice in the analysis of these flows to determine the physically important/dominant modes. This is done by the modal decomposition of an experimental or numerical dataset of a given flow field.

An example of a complex fluid flow can be the von Kármán vortex shedding behind a cylinder as shown in the Figure below.

The flow field above is described by large-scale high-fidelity data that can be obtained by numerical simulation or experiment. The compression of the vast amount of data to a low-dimensional form is useful to understand and model the dynamic behavior of the von Kármán vortex shedding. Applying different modal analysis techniques on the flow field data the dominant modes can be given as the next Figure shows.

The von Kármán vortex shedding is the sum of the dominant modes shown in the Figure above.

[1] – Taira, Kunihiko, et al. „Modal analysis of fluid flows: Applications and outlook.” AIAA journal 58.3 (2020): 998-1022.