In a collaboration between the Technische Universität Darmstadt and Technische Universität Berlin the SPyOD package is implemented in python and is freely usable for everyone via git. You can explore the code, contribute, or use it in your own projects via the following link: https://github.com/grigorishat/SPyOD.
This technique was introduced by M. Sieber, C. O. Paschereit and K. Oberleithner, Journal of Fluid Mechanics, 2016.
Spectral Proper Orthogonal Decomposition (SPOD) is a powerful modal analysis technique in fluid mechanics that breaks down complex flow data into distinct modes, capturing dominant flow structures. These modes reveal patterns and dynamics that are often hidden to the naked eye, offering deep insights into the underlying physics. SPOD is especially valuable for identifying coherent structures in turbulent or other unsteady flows, making it an essential tool in fluid mechanics research. Its strength lies in its simplicity—requiring only a single parameter to be adapted. This makes SPOD both powerful and accessible for a wide range of applications.
Below is a movie as an example how SPOD decomposes cloud cavitation about a NACA0015 hydrofoil in dominant modes, taken from my recent publication, G. Hatzissawidis, M. Sieber, K. Oberleithner and P. F. Pelz, Exp. in Fluids, 2025.