# Study of Unsteady Flow Phenomena via Cyber-Physical Fluid Dynamics

*Combining cyber-physical fluid dynamics and Koopman analysis in order to study forced fluid-structure systems. *

Fluid-structure interaction is a phenomenon that manifests itself in a vast array of scientific disciplines, ranging from aerodynamics to biology. Although such systems are very complex, recent experimental and theoretical advances have opened a path for the study of previously unexplored flows. Of the recent advances in experimental approaches used by fluid dynamicists, cyber-physical fluid dynamics has seen a notable increase in popularity. By merging an experimental facility with feedback control, cyber-physical setups allow for the investigation of a large parameter space with relative ease (Mackowski & Williamson 2011). Through the establishment of a Captive Trajectory System (CTS), the NOAH Laboratory at Caltech has recently been upgraded to allow for cyber-physical capabilities. Regarding theoretical advances, the Koopman Mode Decomposition (Rowley et al. 2009, Mezić 2013) has recently gained notoriety for providing a linear framework for the analysis of nonlinear problems. Koopman modes and eigenvalues capture dynamically significant structures present in the flow, allowing for a deeper understanding regarding the origins of unsteady fluid-structure phenomena. Furthermore, various algorithms exist for approximating Koopman modes using only experimental data (e.g., Schmid 2010), making it a prime candidate for experimental studies. Our work aims to merge the power of cyber-physical fluid dynamics with the utility of Koopman analysis in order to gain a deeper insight regarding the underlying physics governing fluid-structure systems. In particular, we are interested in fluid-structure systems involving bodies subject to various forcing regimes.

*Maysam Shamai & Beverley J. McKeon*

Funding

This work is funded by ARO MURI grant # W911NF-17-1-0306 and AFOSR DURIP (PI: T. Colonius & B. McKeon)

References

- Mackowski, A.W., and Williamson, C.H.K., “Developing a cyber-physical fluid dynamics facility for fluid-structure interaction studies,”
*Journal of Fluids and Structures*, vol. 27, 2011, pp. 748-757. - Mezić, I., “Analysis of Fluid Flows via Spectral Properties of the Koopman Operator,”
*Annual Review of Fluid Mechanics*, vol. 45, Jan. 2013, pp. 357-378. - Rowley, C.W., Mezić, I., Bagheri, S., Schlatter, P., and Henningson, D.S., “Spectral analysis of nonlinear flows,”
*Journal of Fluid Mechanics*, vol. 641, Nov. 2009, pp. 115-127. - Schmid, P.J., “Dynamic mode decomposition of numerical and experimental data,"
*Journal of Fluid Mechanics*, vol. 656, Jul. 2010, pp.*5-28.*