# 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.

**Figure:** Video of transverse velocity field, v, acquired using PIV. U corresponds to the freestream velocity. The cylinder cross-section at the measurement plane is denoted by and the shaded circle corresponds to an obstruction in the field of view by the bottom of the cylinder. Flow is from right to left.

*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.*