Amongst many available data-driven modal decompositions of utility in fluid mechanics, the frequency-domain (spectral) version of the proper orthogonal decomposition (SPOD) plays a special role in the analysis of stationary turbulence. SPOD modes are mutually uncorrelated and optimal in representing structures that evolve coherently in both space and time. Importantly, the SPOD spectrum is also related to the resolvent spectrum of the linearized dynamics and examination of the relationships between the SPOD and resolvent modes yields information about how coherent structures are forced by nonlinear interactions amongst coherent and incoherent turbulence.
We discuss the application of these tools to analyze and model turbulence in high-speed jets. We highlight recent developments utilizing eddy-viscosity models in resolvent analysis to enable RANS-based prediction of coherent structures. We show how SPOD and resolvent analysis can be extended to characterize coherent structures in harmonically-forced turbulent flows whose statistics are phase-locked to the forcing.
Tim Colonius is the Frank and Ora Lee Marble Professor of Mechanical Engineering at the California Institute of Technology, and holds the Cecil and Sally Drinkward Leadership Chair. He received his B.S. from the University of Michigan in 1987 and M.S and Ph.D. in Mechanical Engineering from Stanford University in 1988 and 1994, respectively.
He and his research team use numerical simulations to study a range of problems in fluid dynamics, including aeroacoustics, flow control, instabilities, shock waves, and bubble dynamics. Prof. Colonius also investigates medical applications of ultrasound and is a member of the Medical Engineering faculty at Caltech. He is a Fellow of the American Physical Society and the Acoustical Society of America. He was the recipient of the 2018 AIAA Aeroacoustics Award, the 2021 Stanley Corrsin Award from the American Physical Society, and the 2022 Freeman Scholar Award from the American Society of Mechanical Engineers.